Sectoral Analysis of the Impact of Foreign Aid on Economic Growth in Ethiopia: Time Series Analysis of Agriculture, Education and Health Sectors
©2015
Textbook
79 Pages
Summary
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 growth in the long run. On the other hand, foreign aid has positive but insignificant impact on real GDP growth, agriculture GDP growth, and health sector GDP growth of Ethiopia for the period under consideration. Foreign aid is effective in enhancing economic growth at aggregate level of Ethiopia in general and education sector in particular. The result of the study reveals that there is a bi-directional causal relationship between educational GDP and educational foreign aid in Ethiopia. There is also a unidirectional causality between agricultural aid and agricultural GDP growth. However, the health sector does not show any causality with their respective sector aid. This implies that aid allocated for certain sectors is ineffective in achieving its objectives of economic growth. 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.
Excerpt
Table Of Contents
3.1.6. Foreign Aid (ODA) and Economic Growth in Ethiopia ... 45
3.1.7. Sectoral Composition of Foreign Aid (ODA) in Ethiopia ... 47
3.2. Empirical Results Analysis and Interpretations ... 50
3.2.1. Results for Unit-Root Test ... 50
3.2.2. Co-integration and Long run Growth Equation Analysis ... 51
3.2.3. Short Run VECM Estimation of Economic Growth ... 59
3.2.4. Causality Analysis of Aggregate and Sectoral Economic Growth ... 61
CHAPTER FOUR: SUMMARY AND CONCLUSION ... 66
4.1. Summary ... 66
4.2. Conclusion ... 67
4.3. Policy Implication ... 67
Reference ... 69
Appendixes ... 73
Acronyms
AIC
Akakie
Information
Criteria
ADF
Augmented Dickey-Fuller
DAC
Development
Assistance
Committee
ECT
Error
Correction
Term
GBS
General Budget Support
GCF
Gross
Capital
Formation
GDP
Gross
Domestic
Product
GNI
Gross National Income
EPRDF
Ethiopian Peoples' Revolutionary Democratic Front
IMF
International Monetary Fund
LDCs
Least Developed Countries
MoFED
Ministry of Finance and Economic Development
NGO
Non Governmental Organization
ODA
Official Development Assistance
OECD
Organization for Economic Cooperation and Development
OLS
Ordinary List Square
SSA
Sub-Sahara Africa
UNCTAD
United Nations Conference on Trade and Development
VAR
Vector Auto regression
VECM
Vector Error Correction Model
WB
World Bank
WIDER
World Institute for Development Economics Research
List of Table
Table 1 : Average growth rates of real GDP, per capita GDP and population ... 34
Table 2: Annual growth of industrial sectors' value added (% of GDP) ... 37
Table 3: Domestic saving and capital formation annual growth (% of GDP) ... 39
Table 4: Annual growth rate of import and export (% of GDP) ... 40
Table 5: Current, capital, & external assistance share of GDP and total expenditure ... 45
Table 6: Percentage shares of net ODA to economic sectors ... 46
Table 7: Three years average share of sectoral distribution of aid (% of total aid) ... 48
Table 8: ADF unit root test result for variables in growth equation ... 51
Table 9: Johansen co-integration tests result for aggregate Ethiopian economy ... 52
Table 10: Johansen co-integration tests result for agricultural sector ... 53
Table 11: Johansen co-integration tests result for educational sector ... 53
Table 12: Johansen co-integration tests for health sector ... 53
Table 13: Normalized long run Coefficients of aggregate & sectorial level ... 54
Table 14: Adjustment ( ) coefficients of aggregate and sectorial level ... 54
Table 15: Results of weak exogeneity test for aggregate and sectorial levels ... 55
Table 16: Result of zero restriction test on coefficients for aggregate and sectors ... 56
Table 17: Stationary of error correction terms in aggregate and sectors ... 59
Table 18: Result for dynamic growth equation for real GDP ... 60
Table 19: Result for dynamic growth equation for educational and health GDP ... 61
Table 20: Johansen cointegration tests for the causality test detection ... 63
Table 21: Causality test between GDP and aid at aggregate and sectoral level ... 64
List of Figure
Figure 1: Ethiopian and Sub-Sahara African GDP annual growth ... 35
Figure 2: Share of major industrial sectors value added (% of GDP) ... 36
Figure 3: Export, import, and trade balance trends (% of GDP) ... 42
Figure 4: Current & Capital expenditure, Revenue, & Grant (% of GDP) ... 44
Figure 5: Flow of Bilateral, multilateral and Non DAC aid to Ethiopia ... 47
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 growth
in the long run. On the other hand, foreign aid has positive but insignificant impact on real
GDP growth, agriculture GDP growth, and health sector GDP growth of Ethiopia for the
period under consideration. Foreign aid is effective in enhancing economic growth at
aggregate level of Ethiopia in general and education sector in particular. The result of the
study reveals that there is a bi-directional causal relationship between educational GDP and
educational foreign aid in Ethiopia. There is also a unidirectional causality between
agricultural aid and agricultural GDP growth. However, the health sector does not show any
causality with their respective sector aid. This implies that aid allocated for certain sectors is
ineffective in achieving its objectives of economic growth. 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, sectoral, aggregate, Ethiopia, impact
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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
14
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, Bulí , 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
15
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,
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there seemed to be a micromacro 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 sectoral level study
they have conducted. Therefore, this research tends to use dynamic model that capture the
dynamic nature of these agencies.
Also, for the analysis of sectoral level, this study used sectoral 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:
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Analyze the trend of macroeconomic performance of Ethiopia under two regime so as
to draw implications for economic growth;
Analysis the causality between foreign aid and economic growth both at aggregate and
sectoral level;
Analyze the impact of foreign aid on aggregate agriculture, education and health sector
economic growth in Ethiopia.
1.4. Research Questions
The above specific objectives can be met by answering the following research questions.
What were the trends of macroeconomic performance of Ethiopia in the past and the
then government regime?
What is the causal relationship that exists between foreign aid and economic growth at
aggregate and sectoral 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 researches that 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 any relationship between economic growth and foreign aid in the two regimes
in Ethiopia.
2. Foreign aid does not Granger-cause GDP growth for aggregate and sectoral GDP of
Ethiopia in the past and the present government.
3. Sectoral foreign aid does not have an impact on sectoral economic growth of agriculture,
health and education.
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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
results 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 data analysis in Ethiopia. The
study uses aggregate foreign aid; sectoral level foreign aid of agriculture, education and health;
government spending on aggregate, agriculture, education, and health sectors; aggregate GDP,
health, agriculture, and educational GDP of Ethiopia and other time series data of the period of
1981 to 2012 is used in the analysis.
1.7.2. Limitation of the Study
The model used in the 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 (NGO) or other sources that are understate the whole figure of aid
that is used in the study for the period.
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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. To the best
of my knowledge, 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 foreign aid from 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 in general and to agriculture, health and education sectors
in particular. This also makes us to underestimate the aid allocated to agriculture, education
and health sectors which are the main concerns of this 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 of Ethiopia in
20
the two regimes; the trends in external market (export-import) and its annual growth; and
finally trends and sectoral compositions of ODA flows to Ethiopia. Chapter three also presents
the estimation results and time series characteristics of the data and tests for long-run
relationships and short run model. The last chapter, chapter four, gives summary, conclusions
and policy implication of the study. All the reference materials consulted in the study are listed
under reference. Sample of the test results are listed under the appendix section of the study.
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CHAPTER TWO: METHODOLOGY OF THE STUDY
2.1. Data Types and Sources of Data
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
22
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
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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 are
error terms and, '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
denotes the first difference operator,
are random error terms.
G
G
G
G
24
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 R
2
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,
