Excerpt

## Table of Content

Acknowledgment

Acronyms

List of Table

List of Figure

Abstract

CHAPTER ONE: INTRODUCTION

1.1. Background

1.2. Statement of the Problem

1.3. Objective of the Study

1.3.1. General Objectives

1.3.2. Specific Objectives

1.4. Research Questions

1.5. Hypothesis to be tested

1.6. Significance of the Study

1.7. Scope and Limitation of the Study

1.7.1. Scope of the Study

1.7.2. Limitation of the Study

1.8. Organization of the Paper

CHAPTER TWO: METHODOLOGY OF THE STUDY

2.1. Data Types and Sources

2.2. Description of Variables

2.3. Model Specification

2.4. Econometric Estimation Techniques

2.4.1. Testing for Unit Root

2.4.2. Test for Cointegration

2.4.3 Vector Error Correction Model

2.4.4 Causality Test in Vector Error Correction Model

CHAPTER TREE: RESULT AND DISCUSSION

3.1. Descriptive Analysis of Macroeconomic Performance in Ethiopia

3.1.1. Analysis of Aggregate Economic Growth in Ethiopia

3.1.2. Sector Wise Analysis of Economic Growth in Ethiopia

3.1.3. Trends of Domestic Savings and Investment in Ethiopia

3.1.4. Trends of External Sector Economic Growth in Ethiopia

3.1.5. Government Expenditure and Economic Growth

3.1.6. Foreign Aid (ODA) and Economic Growth in Ethiopia

3.1.7. Sectorial Composition of Foreign Aid (ODA) in Ethiopia

3.2. Empirical Results Analysis and Interpretations

3.2.1. Results for Unit-Root Test

3.2.2. Co-integration and Long run Growth Equation Analysis

3.2.3. Short Run VECM Estimation of Economic Growth

3.2.4. Causality Analysis of Aggregate and Sectoral Economic Growth

CHAPTER FOUR: SUMMARY AND CONCLUSION

4.1. Summary

4.2. Conclusion

4.3. Policy Implication

Reference

Appendixes

Appendex1: Sample sectorial ODA flow to Ethiopia from DAC donor

Appendix 2: Acronym of variables used in data analysis

Appendix 3: Results of sample time serious data

## Acknowledgment

First of all I would thank the Almighty God for his an invaluable helps for all things that human beings can perform with help of his supreme power.

Then, I would like to express my sincere gratitude to my major advisor Dr Amsalu Bedemo (PHD) and Mr Wondimu Saketa (MSC) for their genuine and constructive ideas of providing their comments and their patience to go through and forward comments with respect to the work of research work on the title of sectorial analysis of the effect of foreign aid in Ethiopia.

My special thanks would be extended to Mekonnen Bersisa (PhD Candidate), who has given me a genuine and constructive comments starting from the modification of the title by sharing from the meager time he has for his personal study.

Last but not list, I have a great full thanks to my wife S/r Deme Chemeda, our sister Adanech Iteffa and others for their support and taking care of our children Firomsa Fikadu and Bilise Fikadu during my thesis work and reviewing of different sources for the interesting work.

## Acronyms

illustration not visible in this excerpt

## List of Table

Table 1 : Average growth rates of real GDP, per capita GDP and population

Table 2: Annual growth of industrial sectors’ value added (% of GDP)

Table 3: Domestic saving and capital formation annual growth (% of GDP)

Table 4: Annual growth rate of import and export (% of GDP)

Table 5: Current, capital, & external assistance share of GDP and total expenditure

Table 6: Percentage shares of net ODA to economic sectors

Table 7 : Three years average share of sectoral distribution of aid (% of total aid)

Table 8: ADF unit root test result for variables in growth equation

Table 9: Johansen co-integration tests result for aggregate Ethiopian economy

Table 10: Johansen co-integration tests result for agricultural sector

Table 11: Johansen co-integration tests result for educational sector

Table 12: Johansen co-integration tests for health sector

Table 13: Normalized long run β Coefficients of aggregate & sectorial level

Table 14: Adjustment (α) coefficients of aggregate and sectorial level

Table 15: Results of weak exogeneity test for aggregate and sectorial levels

Table 16: Result of zero restriction test on β coefficients for aggregate and sectors

Table 17: Stationary of error correction terms in aggregate and sectors

Table 18: Result for dynamic growth equation for real GDP

Table 19: Result for dynamic growth equation for educational and health GDP

Table 20: Johansen cointegration tests for the causality test detection

Table 21: Causality test between GDP and aid at aggregate and sectoral level

## List of Figure

Figure 1: Ethiopian and Sub-Sahara African GDP annual growth

Figure 2: Share of major industrial sectors value added (% of GDP)

Figure 3: Export, import, and trade balance trends (% of GDP)

Figure 4: Export, import, and trade balance trends (% of GDP)

Figure 5: Flow of Bilateral, multilateral and Non DAC aid to Ethiopia

## Abstract

*This study has examined sectoral analysis of the impact of foreign aid on aggregate and sectoral economic growth in Ethiopia over the period 1981 to 2012 using multivariate Vector auto regression analysis. All the necessary time series tests such as stationary test, co-integration test, weak exiguity test, vector error correction, and causality test in vector error correction model and the like are conducted. The empirical result from the growth equation shows that aid has a significant positive impact on educational sector GDP in the long run. On the other hand, foreign aid has positive but insignificant impact on real GDP, agriculture GDP, and health sector GDP of Ethiopia. Foreign aid is effective in enhancing growth at aggregate level of the economy in general and education sector of the economy of Ethiopia in particular. The test result of the study result reveals that there is a bi-directional causal relationship between educational GDP and educational foreign aid in Ethiopia. However, the agricultural and health sector does not show any bi-directional causality with their respective sector aid. This implies that all aid allocated for sectors is ineffective all in all in achieving its objectives of economic development. Therefore, aid recipient country like Ethiopia has to work how to enhance the domestic revenue raising capacity of the country which is at the heart of the mechanism to meet the capital required for the economy in times of short falls and ineffectiveness of external resources.*

*Key words:* *foreign aid, economic growth, sector, aggregate Ethiopia, impact*

## CHAPTER ONE: INTRODUCTION

### 1.1. Background

Developing countries face challenges of massive poverty, slow Gross Domestic Product (GDP) growth, high mortality rates from illnesses, and low levels of education. More than 20 percent of the developing world (1.1 billion) people subsist on less than $1 a day. In some developing countries, such as those of Sub-Saharan Africa (SSA), more than 70 percent of the population lives in extreme poverty (i.e. the proportion of population earning less than $2 a day) (Kumler'07, 2007; Leeson, 2008). The governments in these countries do not have sufficient financial resources to fight these challenges effectively. Foreign aid has played an instrumental role in the implementation of development programs to combat the challenges (Lohani'04, 2004; Pattillo, Polak, & Roy, 2007).

Foreign aid is defined as any flow of capital to a developing countries for the objective that should be non commercial from the point of view of the donor on development, poverty reduction, or income distribution grounds and it should be characterized by concessional terms; that is, the interest rate and repayment period for borrowed capital should be softer (less stringent) than commercial terms (Bakare, 2011; Randhawa, 2012; Todaro & Smith, 2012). Official Development Assistance (ODA), commonly known as foreign aid is a flow of financial resources from developed countries to developing countries on development grounds (Eroglu & Yavaz, 2005; Moreira, 2005; Leeson, 2008; Paul & Pistor, 2009). It is an international transfer of public funds in the form of loans or grants either directly from one government to another (bilateral) or indirectly through multilateral assistance agency such as International Monetary Fund and World Bank (Radelet, 2006; UNCTAD, 2006; Abuzeid, 2009; OECD, 2009).

Similarly, Development Assistance Committee (DAC) defines ODA as a grants or loans to developing countries and multilateral agencies active in development that are undertaken by the official sector at concessional terms (if a loan, having a grant element of at least 25%), with the promotion of economic development and welfare as the main objective. Technical cooperation is also included in aid. Grants, loans, and credits to be used in military purposes are excluded (OECD, 2009; Paul & Pistor, 2009).

Despite the volume of ODA from bilateral and multilateral agency flows has grown from an annual rate of under $5 billion in 1960 to $50 billion in 2000 and then to over $128 billion in 2008, the percentage of developed country Gross National Income (GNI) allocated to ODA declined from 0.51 percent in 1960 to 0.23 percent in 2002 before improving to 0.33 percent by 2005 and then to 0.45 percent in 2008 as part of a campaign to increase assistance in the wake of the continued lag in human development in Sub-Saharan Africa (OECD, 2009; Paul & Pistor, 2009; Todaro & Smith, 2012).

Foreign aid is important source of finance in most countries in SSA where it supplements low savings, narrow export earnings and thin tax bases (Bhattarai, 2007; Arellano, Bulíř, Lane, & Lipschitz, 2009). Africa in general and SSA in particular receives a greater share of global aid than any other region in the world with East Africa receiving approximately 25 percent of all ODA to SSA. Within East Africa, Ethiopia receives the largest percentage (7%) of total ODA from all donors, followed by Tanzania (6%). According to OECD DAC statistics, aid to Ethiopia increased from US$1.1 billion in 1995 to US$3.5 billion in 2010 and is concentrated on core social sectors and infrastructure (Nganwa, 2013; Prizzon & Rogerson, 2013).

Most foreign aid is designed to meet one or more of broad economic and development objectives: to stimulate economic growth through building infrastructure, supporting productive sectors such as agriculture, or bringing new ideas and technologies; to strengthen education, health, environmental, or political systems; to support subsistence consumption of food and other commodities, especially during relief operations or humanitarian crises; or to help stabilize an economy following economic shocks (WB, 1998; Radelet, 2006; Bakare, 2011).

### 1.2. Statement of the Problem

Despite these broader objectives of foreign aid as well as the tremendous increases in the follow of foreign aid to developing countries like Ethiopia (under $5 billion in 1960 to $50 billion in 2000 and to over $128 billion in 2008) (OECD, 2009) from time to time, there is controversies about aid effectiveness which go back to decades. There are two general but contending schools of thought with regard to the effectiveness of aid in spurring economic growth in the third world (Gebhard, Kitterman, Mitchell, Nielson, & Wilson, 2008). Research results on the macroeconomic impacts of foreign aid in developing countries are ambiguous. Some studies concluded that this relationship was negative; others concluded it was positive, and others found no relationship at all. Several studies have noted that foreign aid has a positive effect on the economic growth of poor countries (Chenery & Strout, 1966; Burnside & Dollar, 2000; Lohani'04, 2004; Bhattarai, 2007).

Foreign aid is advocated the promotion of economic development and could play a vital role in promoting economic development in the Less Developed Countries (LDCs) which is explained in term of concepts such as the savings gap and the foreign exchange gap (Eroglu & Yavaz, 2005; Shah, Ahmad, & Zahid, 2005). Critics of foreign aid argue that foreign aid discourages domestic saving and domestic tax revenue in developing countries and is simply diverted into consumption instead of investment. They find that grant have a negative effect on domestic revenue. The decline domestic revenue is almost as much as the increase in grant (Benedek, Crivelli, Gupta, & Muthoora, 2012; Bwire, Morrissey, & Lloyda, 2013). Since these countries do not have the technical ability to use the aid effectively, it gets spent on nonproductive activities and poorly conceived projects concluding that there exists no significant correlation between aid and GDP growth because the majority of foreign aid is spent on consumption (Lohani'04, 2004).

The study of foreign aid on a sectoral basis that is conducted by cross country analysis doesn’t allow us to clearly examine the sectoral impact of aid on sector’s spending. In this respect, different countries have different result for the impact of aid on sectors spending (Paul & Pistor, 2009). Projects financed by foreign aid are often highly visible and important successes such as roads and highways, schools and health clinics, irrigation infrastructure, power plants and so on. But success can be assessed at two levels that are at the micro or project level, which typically shows high rates of success or at the macro level of economy wide growth and poverty reduction, where there is less visible success (WB, 1998; Pettersson, 2007). Generally, there seemed to be a micro–macro paradox, with evidence suggested that aid clearly worked at the micro level but evidence, on balance, relating to the macro level (McGillivray, Feeny, Hermes, & Lensink, 2005; Odusanya, Abidemi, & Akanni, 2011).

Odusanya et al (2011) carried out studies on the impact of foreign aid and public expenditure on economic growth in Nigeria. Their result reveals that foreign aid and public expenditure impact positively on the economic growth with foreign aid indicating a very significant impact on growth. They conclude that foreign aid can have positive effect on economic growth, through public expenditure if properly channeled to the productive sectors of the economy. But Odusanya et al (2011) carried out their studies using static framework. Their conclusions may be incorrect because the economic agents associated with aid administration are dynamic. Also, they did not disaggregate the GDP into different sector levels for the sectorial level study they have conducted. Therefore, this research tends to use dynamic model that will be able to capture the dynamic nature of these agencies. Also, for the sectorial level analysis, this study will use sectorial level GDP instead of aggregate GDP. Hence, such work can usually be conducted in the context of country specific, to capture the different impact of earmarked aid on the sectors. It is therefore pertinent to check whether and to what extent has foreign aid might have caused or contributed to economic growth in Ethiopia.

### 1.3. Objective of the Study

#### 1.3.1. General Objectives

The major objective of the study is to investigate sectoral analysis of the impact of foreign aid on economic growth in Ethiopia

#### 1.3.2. Specific Objectives

The specific objectives of the study are to:

- Analyze the trend of macroeconomic performance Ethiopia under two regime so as to draw implications for economic growth;

- Analysis the causality between foreign aid and economic growth in Ethiopia;

- Analyze the impact of foreign aid on agriculture, education and health sector of economic growth in Ethiopia;

### 1.4. Research Questions

The above specific issues can be met by answering the following research questions.

- What is the causal relationship that exists between foreign aid and economic growth in Ethiopia?

- What is the impact of foreign aid on economic growth of developmental sectors?

- In which sectors of the economy does foreign aid has significant effect?

### 1.5. Hypothesis to be tested

This study is inspired by a new stream of research supports aid works better at sectoral level (micro level) in an individual country based study than at cross country level (macro-level). Specifically the main hypotheses to be empirically tested are:

1. There is no a positive relationship between economic growth and foreign aid in Ethiopia.

2. Foreign aid does not Granger-cause GDP growth in Ethiopia.

3. Sectoral foreign aid does not have impact on sectoral economic growth of agriculture, health and education.

### 1.6. Significance of the Study

The study of sectoral analysis of the impact of foreign aid in Ethiopia is important due to the fact that foreign aid may have differentiated impacts at the sector levels as compared to the result obtained when analyzed at an aggregate level. It is noteworthy that the impact of foreign aid at the sectoral level has not been given consideration in analysis of impact of foreign aid in Ethiopia at large. Therefore, the result of this study is useful for improving policy design, institutional set up, implementation, monitoring and evaluation in the area of foreign aid allocation to public spending in general and sector wise in particular for the sake of economic growth. Finally, the result of the study with respect to sectoral analysis of foreign aid becomes stepping stone for academicians, researchers, students, policy makers and other organization that are in need to use its result as an input in their organization.

### 1.7. Scope and Limitation of the Study

#### 1.7.1. Scope of the Study

This study covers a period of thirty two years for a country level analysis in Ethiopia. The study uses aggregate aid, sectoral aid, Government spending, GDP, and other time series data for the period of 1981 to 2012 is used.

#### 1.7.2. Limitation of the Study

The model analysis of the impact of foreign aid in Ethiopia assumes that all aid is allocated through government sector and none of it will be spend though other ways. This is due to the fact that in developing countries like Ethiopia, aid may have come through Non-governmental organizations or other sources that are understate the whole figure of aid that may be used in the study.

The other critical limitation of this study is that in the analysis of aid flows to sectors with recipient’s country wise in the context of the total aid flow during the past three or more decades is greatly hampered by the lack of complete, reliable, and consistent data. The only systematic data available and easily accessible for researcher is foreign aid flows that have been compiled by the OECD/DAC. However, the easily accessible OECD/DAC website does not provide a consistent and comparable breakdown of aid flows from both multilateral and bilateral donors from the early 1970s to the present. This source provides a sectoral classification of aid flows from the 1973 onward only for the bilateral aid and not for the rest of the donors.

Furthermore, the sectoral classification of the total aid flows to individual country like Ethiopia is available only from 1995 to 2012 that the researcher used in the study. Moreover, the data available regarding aid to the sector from the OCED/DAC database has a category of “multi-sectoral” aid which includes aid to more than one sector. Therefore, it is not clear for researcher how much aid from multi-sectoral aid is directly or indirectly goes to which sector of the economy in recipient countries. This also makes us to underestimate the aid allocated to agriculture, education and health sectors which are the main concerns of the study.

### 1.8. Organization of the Paper

The study of research is organized under five chapters. The first chapter deals with the problems and its approaches, which include background of the study, statement of the problem, research objectives, research questions to be answered, significance of the study, hypothesis to be tested, scope and limitation of the study, and organization of the research paper. The second chapter deals with methodology of the study that includes source and type of data, description of variables, model specification, and estimation techniques .Chapter three deals with macroeconomic performance of the country which includes: GDP & its growth trend including per capita GDP, and the share of main economic sectors (agriculture, industry and service) in GDP; trends of gross fixed capital formation and saving; the trends in external market (export-import) and its annual growth; and finally trends and sectoral compositions of ODA flows to Ethiopia. Chapter four presents the estimation results and time series characteristics of the data and tests for long-run relationships and short run model and finally chapter five, the last chapter gives summary, conclusions and policy implication of the study. All the reference materials used in the study are listed under reference.

## CHAPTER TWO: METHODOLOGY OF THE STUDY

### 2.1. Data Types and Sources

Concerns of analyzing the impact of foreign aid are important for Ethiopia due to an increasing per capita of foreign aid and the country’s dependence on it. The study used time series data. For analyzing the impact of foreign aid on economic growth of Ethiopia, the study used country level macro-data covering the period from 1981 to 2012. The choice of the period is based on the availability of relevant data for the study. The relevant data was collected from various sources: National Bank of Ethiopia, Ministry of Finance and Economic Development (MoFED), Ethiopian Economic Association, World Bank, World Development Indicator database, and OECD/CRS websites.

### 2.2. Description of Variables

The major variables that are used in the sectoral analysis foreign aid in Ethiopia include: Real GDP which is the real GDP of an economy over the period 1981-2012 for Ethiopia both at aggregate and at sectoral level for agriculture, health and education which are dependent variables. Furthermore, AGDP is agricultural GDP, EDGDP is educational GDP; and HEGDP is health sector GDP of the country that are used in the analysis. FAID is the ODA as defined by the OECD as percentage of GDP. Also EDUCAID, AGRIAID, and HEALAID are official development assistance allocated for educational, agriculture and health sector as percentage of GDP of the country respectively.

PRIV is the total net private capital flows as a percentage of GDP (international remittance can also be classified as part of net private capital flows). Private capital flows consist of net foreign direct investment and portfolio investment. SAV is the domestic savings as a percentage of GDP. TRADE is the openness to trade, which is defined as (X + M) /GDP. That is the addition of export and import divided by GDP. Openness to trade is often hypothesized to raise growth through several channels, such as access to advanced technology from abroad, possibilities of catch-up, greater access to a variety of inputs for production, and access to broader markets that raise the efficiency of domestic production through increased specialization. Various measures of openness have been proposed and tested, with no single ‘best’ measure emerging. For instance, (Durbarry, Gemmell, & Greenaway, 1998) used to measure trade openness by the ratio of total trade to GDP and changes in the terms of trade. X is total value of goods and services exported and M is total value of goods and services imported. Moreover, GOV represents the total amount of government expenditure (developmental plus non developmental) as a percentage of GDP for the period under consideration.

D is dummy variable for major political changes from Derg regime to Ethiopian peoples’ Revolutionary Democratic Front (EPRDF) that takes in to account to see the effect of major shifts in political environment on the performance of economic growth and foreign aid in the short run. The dummies are incorporated in to the model for growth and D took 1 for 1992 to 2012 and 0 otherwise.

### 2.3. Model Specification

Different researcher uses different models. This study employs Vector Autoregressive (VAR) model. One of the main advantages of VAR model over single equation model is that its ability to deal with several endogenous variables(Hayakawa, 2011) and cointegrating vectors, the ability to test for weak exogeneity and parameter restrictions, and to handle both I(1) and I(0) variables in one system. The VAR approach is data based and little economic theory is imposed directly (M’Amanja, Lloyd, & Morrissey, 2005). VAR assumes that all the variables are endogenous.

The model used in this study was rely on the framework of Durbarry, et al (1998) as modified by Odusanya et al (2011) for the case of Nigeria. However, in order to meet the objectives of study in terms of its concentration, as well as on the bases of availability of data on the appropriate variables, foreign aid, total private capital flows, and domestic saving mobilized as a vector of capital sources (domestic and foreign), and openness to trade and total government expenditure as is a vector of control variables from economic growth components over the other variables to capture potential side effects of foreign aid such as ‘Dutch-Disease’ effects and other policy variables that are hypothesized to affect growth are incorporated (Odusanya, Abidemi, & Akanni, 2011). It was hypothesized that economy growth can be related to foreign aid as:

Where: Growth is the real GDP over the period 1981-2012 for Ethiopia;

FAID is the foreign aid (net ODA) flows as percentage of GDP;

PRIV is the total net private capital flows as a percentage of GDP;

SAV is the domestic savings as a percentage of GDP;

TRADE is the openness to trade, which is defined as (X + M) /GDP;

GOV is the total amount of government expenditure as a percentage of GDP.

However, in order to concentrate on the dynamic effect of foreign aid on the economic growth at the sectoral levels, equation 1 is first modified to VAR model as:

Where *FA* and *AG* are foreign aid and annual GDP growth respectively, while and represent their lagged values in *j* years, *p* is the maximum lag length. That is, the Lag Exclusion Wald Tests will be used to select the most appropriate lag length, and l and μ are error terms and, β’s and *a’* s are parameters to be estimated.

Differencing away the fixed effects in equation 2 and 3 by including TRADE, GOV and D (D is dummy variable) it was transformed to equations 4 and 5 respectively which will be used to examine the impact of foreign aid on the Ethiopian economy at the aggregate level. Where Δ denotes the first difference operator, are random error terms.

In the sectoral analysis, the impact of foreign aid on agriculture, health and education will be analyzed. Going by equations 4 and 5, FA will be the foreign aid for agriculture, health and education respectively, while AG will be the agriculture, health, and educational sector GDP growth respectively for the period under consideration in the sectoral analysis.

### 2.4. Econometric Estimation Techniques

The method employed in the study is based on recent advancements in the theoretical and empirical aid-growth relationships. As the data used is time series, testing for stationarity (unit root test), co-integration test, Vector Error Correction Model (VECM), and causality test is conducted in the model. The standard estimation and hypothesis testing assumed that all, in particular regression, variables are stationary. A data series is said to be stationary if its error term has zero mean, constant variance and the covariance between any two time periods depends only on the distance or lag between the two periods and not on the actual time which it is computed.

However in reality most macroeconomic variables are non stationary. If variables entering into the estimation are non stationary, then the result obtained using OLS technique would be spurious in the sense that variables would seem to have promising diagnostic test (high R2 and low Durbin Watson test) result just because they have common trend over time rather than actual causation(Harris, 1995). Therefore hypothesis testing and inference using such results will be invalid. To avoid such wrong inferences from the non stationary regressions, the time series property of the data should be checked prior to the estimation of the long run model.

#### 2.4.1. Testing for Unit Root

Unit root test has become a widely popular approach to test for stationary. It has been argued that if a variable has deterministic trend, including trend variable in the regression removes the trend component and makes it stationary. Such process is called trend stationary since the deviation from the trend is stationary. However, most time series data have a characteristic of stochastic trend (that is, the trend is variable cannot be predicted with certainty). In such cases, in order to avoid the problem associated with spurious regression, pre-testing the variables for the existence of unit roots (i.e. non-stationary) becomes compulsory. In general if a variable has stochastic trend, it needs to be differenced in order to obtain stationary. Such process is called difference stationary process (Gujarati D. , 1995). The number of unit roots a given variable posses determines how many times that variable should be differenced in order to attain stationary.

A commonly applied formal test for existence of a unit root in the data is the Dickey-Fuller (DF) tests. It’s simple extension being the Augmented Dickey Fuller (ADF) test. The augmentation is adding lagged values (p) of first differences of the dependent variable as additional regressors which are required to account for possible occurrence of autocorrelation. The Dickey-Fuller test starts with the following first order autoregressive model:

Subtracting Yt-1 from both sides gives

Then the test for stationarity is conducted on the parameter [Abbildung in dieser Leseprobe nicht enthalten] it implies that the variable Y is not stationary. The hypothesis to be tested is formulated as follows:

illustration not visible in this excerpt

Furthermore, the use of equation (7) is appropriate only when the series Yt has a zero mean and no trend term (Harris, 1995). If a variable has a zero mean, it implies that Yt= 0 when t=0 implying no constant term. A constant (drift) is included to the regression since it is difficult to know whether the true value of Y0 is zero or not. Including a constant (α) to equation (7) gives:

However, testing for stationarity using equation (8) is invalid if a series contains a deterministic trend. Because if g=0, the null hypothesis will be accepted that the series contains a stochastic trend when there exists deterministic trend. Thus to avoid such results, it is important to incorporate time trend in the equation above and gives:

Where, T the trend element

For the above equations (equation 8 and 9), the parameter g is used while testing for stationarity and the decision is made using t-statistics that is used for the regression without drift and trend. If the calculated value of t is less than the critical value the null hypothesis is accepted and not if otherwise. Accepting the null hypothesis implies the presence of unit root-i.e. the series is non stationary. However, the DF test has a series limitation in that it suffers from residual autocorrelation. Therefore to overcome this problem, the DF model is augmented with additional lagged first differences of the dependent variable. This is called Augmented Dickey-Fuller model.

The advantage of using ADF over that of DF model is that ADF model avoids the autocorrelation among the residuals. Therefore incorporating lagged first differences of the dependent variable to the above three equations (equations 7, 8 and 9) gives the corresponding ADF model as follows:

Where, Yt is any variable in the model to be tested for stationarity, a is a constant (drift), T is a trend element, k is the lag length, et is an error term, and D is the first difference operator.

The null hypothesis of ADF is d=0 against alternative hypothesis that d<0. Where [Abbildung in dieser Leseprobe nicht enthalten]. A rejection of this hypothesis means that the time series is stationary or it does not contains a unit root while not rejecting means that the time series is non stationary(Enders, 1995). If the variable that is not stationary in levels appear to be stationary after dth difference, then the variable is said to be integrated of order d I(d).

#### 2.4.2. Test for Cointegration

Before going to examine the causal relationship between aid and economic growth, it is better to check whether the two variables are cointegrating or not. Cointegration means the regressions of one variable over the other is no meaning full (spurious). Economically speaking, two variables will be cointegrated if they have a long-term, or equilibrium, relationship between them (Gujarati D. , 2004). Despite variables are being individually non stationary, a linear combination of two or more time series can be stationary. Cointegration among the variables reflects the presence of long run relationship among non stationary variables in the system.

Testing for cointegration is important because differencing the variables to attain stationarity generates a model that does not show long run behavior of the variables. Thus testing for cointegration is the same as testing for long run relationship. In general, if variables that are integrated of order‘d’ produce a linear combination which is integrated of order less than ‘d’ say ‘b’, then the variables are cointegrated and hence have long run relationship(Gujarati D. , 2004). In order to determine whether or not a long-run equilibrium relationship exists among the unit root variables in a given model, we need to test empirically that the series in the model are cointegrated. To conduct test for co-integration, the study used Johanson (1988) maximum likelihood estimation procedure.

To conduct a test for co-integration in a multivariate framework using Johansen’s maximum likelihood procedure, first the general VAR model of relationship between the variables should have to be formulated. Thus a general VAR (p) of the following form is formulated:

Where Xt is a (mx1) vector of stochastic I(1) variables, Wt is a (qx1) vector of deterministic variables (for instance trend and dummy variables), and each i (i=1….p) and Ψ are (mxm) and (mxq) matrices of parameters. et is a (mx1) vector of normally and independently distributed disturbances with zero mean and non-diagonal covariance matrix (vector of white noise disturbance terms), and t=1….T (T is the number of observation).

Providing the variables are (at most) integrated of order one i.e. I(1) and co-integrated also has an equilibrium error correction representation that is observationally equivalent but which facilitates estimation and hypothesis testing, as all terms are stationary. The vector error correction model (VECM) is:

illustration not visible in this excerpt

Simplifying equation (14) gives:

illustration not visible in this excerpt

Where, [Abbildung in dieser Leseprobe nicht enthalten] and

From the above equation, the long run relationship among the variables is captured by the term pXt-p *.* The i coefficients estimate the short run effects of shocks on DXt and thereby allow the short and long run responses to differ. In the Johansen (1988) procedure, determining the rank of p (i.e. the maximum number of linearly independent stationary columns in p) provides the number of cointegrating vector between the elements in x. In this connection, there are three cases worth mentioning. (i), If the rank of p is zero it points that the matrix is null which means that the variables are not co-integrated. In such case the above model is used in first difference, with no long run information,( ii), If the rank of p equals the number of variables in the system (say n) then p has full rank which implies that the vector process is stationary. Therefore the VAR can be tested in levels, (iii), If p has a reduced rank i. e. 1<r(p)<n it suggests that there exists r<(n-1) cointegrating vector where r is the number of co-integration in the system.

The matrix p is given by (p=αβ'), where β coefficients show the long run relationship between the variables in the system(Cointegration parameters) and α coefficients show the amount of changes in the variables to bring the system back to equilibrium i.e. it shows the speed with which disequilibrium from the long run path is adjusted. To identify the number of cointegrating vectors, the Johansen procedure provides n eigenvalues (λ) characteristic roots whose magnitude measures the degree of correlation of the cointegration relations with the stationary elements in the model.

**[...]**

- Quote paper
- Fikadu Goshu (Author), 2014, Sectoral Analysis of the Impact of Foreign Aid on Economic Growth in Ethiopia. The Case of Agriculture, Education and Health Sectors, Munich, GRIN Verlag, https://www.grin.com/document/281966

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