MACROECONOMIC CONDITIONS AND GROWTH OF MANUFACTURING FIRMS IN GHANA
By
EFFAH – NKYI KING
A THESIS SUBMITTED TO THE FACULTY OF ECONOMICS, UNIVERSITY OF PISA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTERS OF SCIENCE IN ECONOMICS.
ABSTRACT
Macroeconomic variables such as government expenditure , interest rate, exchange rate, trade, inflation rates, unemployment, foreign direct investment and imports of goods and services have proven to be very volatile over time in Ghana and do have potential impacts on the growth of manufacturing firms. This scientific research thus seeks to unravel the causal relationships between some of these crucial macroeconomic indicators and their impact on the growth of manufacturing firms in Ghana. The growth of firms here is basically evaluated in terms of the manufacturing value added as a % of GDP though many research have often focused on real GDP as measure of growth. Manufacturing firms operating in the industrial sector of Ghana is our main focus here as the majority of firms in Ghana fall under this sector though its share of GDP varies with other subrelated sectors like mining and construction. Some of the crucial macroeconomic indicators being explored in this work includes labour force, government expenditure, real effective exchange rate and trade variable as a % of GDP. The major sources of data of this work was secondary data and were obtained from world bank survey data and the Ghana Statistical service website. The data gathered on these variables are a set of time series and spanned the period from 1990 to 2014. The ordinary least square method was employed with the use of Gretl software for obtaining our
estimated co-efficient and the model employed for analysis was a log-log model type. Based on the findings, it is recommended that the government of Ghana should should adopt
some prudent macroeconomic policies in order to ensure that manufacturing firms can expand their operations.
ABBREVIATIONS
GDP - Gross Domestic Product
IMF - International Monetary Fund
TFPG – Total Factor Productivity Growth
ASI – Annual Survey of industries
EPZ - Export Processing Zones
S.E. – Standard error
D.W. – Durbin Watson
UN – United Nations
ERP – Economic Recovery Programme
SAP- Structural Adjustment Programme
GET – Ghana education trust Fund
SOE‟s – State Owned Enterprises
SME’s- Small and Medium Scale Enterprises OLS - Ordinary least square
TABLE OF CONTENTS PAGE TITLE PAGE……….1 ABSTRACT………..………...2 ABBREVIATIONS………3 TABLE OF CONTENTS………....4-7 LIST OF TABLES……….8 LIST OF FIGURES………9 CHAPTER ONE:……….………10 INTRODUCTION………...10 1.1 BACKGROUND OF STUDY………10-12 1.2 STATEMENT OF THE PROBLEM………...13-14 1.3 OBJECTIVE OF THE STUDY………..15-16 1.4 RESEARCH QUESTIONS………..16
1.5 SIGNIFICANCE OF THE STUDY………17- 18 1.6 SCOPE AND LIMITATIONS OF THE STUDY………19
1.7 ORGANISATION OF STUDY………...20
CHAPTER TWO:………21
LITERATURE REVIEW………...21
2.1 INTRODUCTION………..21 2.2 CONCEPT OF MANUFACTURING VALUE ADDITION TO OUTPUT AS AN INDICATOR TO GROWTH OF FIRM………21-24
2.4 THEORITICAL MODELS ON GROWTH OF FIRMS………27
2.4.1 COBB DOUGLASS PRODUCTION FUNCTION………27
2.4.2 STOCHASTIC PRODUCTION FRONTIER………28-29 2.4.2 ENDOGENOUS GROWTH MODELS………...30-33 CHAPTER THREE:………34
RESEARCH METHODOLOGY………34
3.1 INTRODUCTION………34
3.2 SOURCES OF DATA ……….34-38 3.3 COVERAGE OF STUDY……….39
3.4 METHOD OF DATA ANALYSIS………39-40 3.5 MODEL SPECIFICATION & DESCRIPTION OF VARIABLES………...41-42 3.6 TESTING OF HYPOTHESIS ON ESTIMATED PARAMETERS………...43
3.7 R-SQUARED COEFFICIENT OF DETERMINATION AND ADJUSTED R-SQUARED………44-45 3.8 PARAMETERS FOR MODEL CHECKING (T-TEST)……….46-47 3.9 TESTING FOR THE OVERALL SIGNIFICANCE OF THE MODEL ( F-TEST)………48
3.9.1 TESTING OF MULTI –MULTICOLLINEARITY AMONG VARIABLES………...49
3.9.2 TESTING FOR AUTOCORRELATION AMONG ERROR TERMS………50
CHAPTER FOUR:………,52 DATA ANALYSIS, DISCUSSION AND REPRESENTATION OF RESULTS………..52
4.1 INTRODUCTION………52
4.2 MANUFACTURING SECTOR COMPOSITION & SECTORAL VALUE ADDED………52-54
4.3 RELATIVE CONTRIBUTION OF INDUSTRY AND ITS RELATED SUBSECTORS TO GDP (1984-2000) ………...55-56 4.4 RELATIVE CONTRIBUTION OF THE INDUSTRIAL SECTOR AND ITS SUBSECTORS TO GDP,
2001–2005………57-58 4.5 RELATIVE CONTRIBUTION OF SUBSECTORS TO INDUSTRIAL GDP, 2006–12 (%)...59-61 4.6 COMPARISON OF MANUFACTURING VALUE ADDED IN GHANA, KENYA AND CHINA (1989-2013)………62-65 4.7 EMPIRICAL RESULTS AND PERFORMANCE OF THE MODEL………66-68
4.9 RESULTS ON TEST FOR MULTICOLLINEARITY AMONG EXPLANATORY
VARIABLES………69 4.9.1 RESULTS ON TEST OF HYPOTHESIS...70
4.9.2 ECONOMIC & STATISTICAL INTERPRETATION OF CO-EFFICIENTS OF THE
MODEL………..71-74
4.9.3 WHITE'S TEST FOR HETEROSKEDASTICITY……….75-76
CHAPTER FIVE:………...79 FINDINGS, CONCLUSIONS AND RECOMMENDATION………79
5.2 POLICY RECOMMENDATIONS………...79-80
5.3 CONCLUSION………..81
LIST OF TABLES
TABLE 1 DATA OBTAINED ON MACRO-ECONOMIC VARABLES………..35-36 TABLE 2 DATA OBTAINED ON THE INDUSTRIAL SUB-SECTOR………..37-38
TABLE 3 COMPOSITION OF MANUFACTURING SECTOR IN GHANA ………55
TABLE 4 RELATIVE CONTRIBUTION OF INDUSTRY AND ITS RELATED SUBSECTORS TO GDP,1984-2000……….57
TABLE 5 RELATIVE CONTRIBUTION OF THE INDUSTRIAL SECTOR AND ITS SUBSECTORS TO GDP, 2001–2005………59
TABLE 6 RELATIVE CONTRIBUTION OF SUBSECTORS TO INDUSTRIAL GDP, 2006–12 (%)………62
TABLE 7 MANUFACTURING VALUE ADDED IN GHANA, KENYA AND CHINA (1989 – 2013)……….62-63 TABLE 8 OLS, USING OBSERVATIONS 1990-2014 (T = 25)………..67
TABLE 9 TEST OF COLLINEARITY AMONG EXPLANATORY VARIABLES……….69
TABLE 10 WHITE'S TEST FOR HETEROSKEDASTICITY……….75
LIST OF FIGURES
FIGURE 1 STOCHASTIC PRODUCTION FRONTIER………...29 FIGURE 2 SECTORAL VALUE-ADDITION AS % OF GDP………54 FIGURE 3 RELATIVE CONTRIBUTION OF INDUSTRY AND ITS RELATED SUBSECTORS TO GDP, (1984-2000)……….55 FIGURE 4 RELATIVE CONTRIBUTION OF THE INDUSTRIAL SECTOR AND ITS SUBSECTORS TO GDP, (2001–2005)……….58 FIGURE 5 RELATIVE CONTRIBUTION OF SUBSECTORS TO INDUSTRIAL GDP, 2006–10
(%)……….60 FIGURE 6 MANUFACTURING VALUE ADDED IN GHANA, KENYA AND CHINA
CHAPTER ONE INTRODUCTION
1.1 BACKGROUND INFORMATION
Historically, the industrial GDP of the Ghanaian economy has fluctuated over time owing to the fact
that after independence from colonialism several government regimes have pursued some industrial policies which has induced a lot of fluctuations on the GDP across the various subsectors of the industrial sector. Macroeconomic indicators such as interest rate, inflation rate, exchange rate, foreign direct investment, government expenditure, imports and exports have varied over time and these factors have strongly impacted on the growth of manufacturing firms in Ghana. During the pre-independence era Ghana’s manufacturing firms were very few and specifically domestic in nature and contributed little to the GDP of the economy. The low growth of manufacturing firms was also attributed to the fact that much of the natural resources were being sent abroad for value addition.
However after independence from 1957, an import substitution approach was adopted by the first government which was focused on setting up more state-owned manufacturing firms that sought to produce manufactured goods which were previously imported in order to promote employment, technology, increment in the per capita income and to reduce poverty. This import substitution approach embedded with tariff protection on manufacturing industries succeeded in minimizing consumer imports
but rather increasing the production of locally manufactured goods .This resulted in an increase in the
growth rate of the manufacturing firms from a 2 per cent share of real GDP in 1957 to 9 percent in 1969 though some other firms experienced a sluggish performance in their shares of real GDP.
By the beginning of the 1970s, the import substitution strategy took a different turn as the economy moved away form a centrally planned economy to a market based economy, a new ideology brought in by the new government. Thus a much liberalized approach was adopted with respect to imports and setting of interest rates. However, this resulted in Balance of payment deficits as imports became too high and so devaluation of the currency had to take place. Owing to the severe imports and its impact on the balance of payment and on manufacturing firms, a new policy had to be taken by the subsequent government. From the late 1970’s to1983 the free market economy approach was abandoned and replaced with import controls, price controls and revaluation of the currency. Though various state owned manufacturing firms were revived, the economy experienced external shocks as a decrease in foreign exchange earnings due to foreign exchange restrictions controls especially during the end of 1982. Moreover large fiscal deficits were being financed by borrowing from domestic sources, this therefore led to increase in money supply, high inflation rate and lending rates and thereby crowding out of private investment .This in a way affected the springing up of private manufacturing firms.
From the period 1980‟s to 2000 a much more liberalized industrialization policy was pursued under the structural adjustment programme (SAP) and the economic recovery programme (ERP). Some of the aims of these programmes were geared towards the manufacturing firms in order to encourage the development of technology of SME‟s in the manufacturing sector, creation of a productive linkage between firms under the various subsectors of the industrial sector and also removal of price controls, and elimination of import licensing and market determination of prices.
Over the course of time the growth rates of the manufacturing subsector continued to dominate though its relative contribution to industrial sector GDP declined. For instance, the manufacturing subsector growth rate increased from 1.8 per cent in 1995 to 3.0 in 1996 and 7.3 per cent in 1997. In 1998, it fell to 4.0 per cent due to the energy crisis but increased the following year to 4.8 per cent before declining to 3.8
per cent in 2000. This liberalized economic recovery programme resulted into competition with firms oversees, and the emergence of the financial markets which resulted in high interest rates, high production costs and many domestic firms became economically inefficient. The high lending rates, unreliable power availability, and high rising fuel prices by the end of 2005 forced many firms, especially those manufacturing firms which are import dependent to cut production. Though the current industrial policy in Ghana aimed at improving the growth of manufacturing firms in Ghana is private sector led and adopts a value- added approach, the value and output of manufacturing firms continues to decline based on current date trends. Macroeconomic problems such as high interest rate, high inflation rate, high imports of goods and services, government policies continues to affect the growth of manufacturing firms in Ghana.
This research, therefore, aims to analyse the macroeconomic economic conditions and the growth of manufacturing firms in Ghana so as to find remedies with regards to industrial polices for restructuring the manufacturing sector.
STATEMENT OF THE PROBLEM
The volatile nature of interest rates, exchange rates, foreign direct investment and inflation rates obviously have affected the growth rates of manufacturing firms in Ghana. There are several reasons which can be attributed to the increasing and decreasing rates of these macroeconomic factors.
Some major causes of high inflation rates in the Ghanaian economy includes deficit financing, persistent increase in the price of fuels, continuous depreciation of the cedi currency, increasing rate of population or labour force, higher wage demands and rural urban migration. High inflation rates coupled with low per capita income have often resulted in low demand of manufactured products resulting in the collapse and significant drop in output of some firms. Some of these issues have undermined the prospects of investment of manufacturing firms in the private sector. The problems of high interest rates have also impacted negatively on the acquisition of loans by potential investors in the economy. For instance in the year 2000 the interest rate was in the range of 40% to 55% and became too high for investors to acquire credit to undertake any meaningful investment. Those already in operation of private manufacturing firms have often founded it difficult to acquire loans under high interest rates to expand their businesses so as to increase output or add-value to their products.
In Ghana exchange rates is also another major crucial factor that influences the growth of
manufacturing firms. Import-dependent firms tend to slow down in production especially when the currency loses its value as most firms have to now purchase these capital goods at a higher cost thereby slowing down their propensity to expand their operations. The exchange rates have also often impacted negatively on export earnings as goods being exported now command lower prices when the currency loses its value, this therefore tends to impact on the profitability of most manufacturing firms.
However, there are also other crucial factors in the Ghanaian economy that have often slowed down the growth of firms. Problems such as shortage of raw materials to feed these manufacturing
industries have compelled most of them to produce at an output level below the optimal level. There is also the problem of poor roads and insufficient infrastructure as most of the finished good are being transported on poor road networks to the final consumer. These occurrences have often paved a way for high prices of manufactured goods. Other issues such as the irregular supply of electricity or irregular power supply have caused some manufacturing firms to produce below capacity.
Though some of these factors have impacted negatively on the growth of firms in Ghana, this research seeks to identify key macroeconomic variables such as government expenditure, real effective exchange rate, labour force and trade variables as the main crucial variables.
1.3 OBJECTIVE OF THE STUDY
The overall objective of this research is to critically assess the impact of macroeconomic variables on the growth of manufacturing firms considering variables such as government expenditure, labour force, trade and real effective exchange rate .The general objective is to enable the researcher have transparent understanding of the major challenges facing manufacturing industries in the economy.
In order to achieve the overall objective of the research this study will attempt to gather time-series data on these macroeconomic indicators for analysis of the manufacturing industry. Firstly data would be collated on these variables from the worldbank site which will focus on the period from 1990 to 2014. In order to make causal inference from our our model the method of ordinary least square would be employed with the help of Gretl Software. The main reasons of causal inference here is to enable the researcher get a clear understanding of the crucial macro-economic indicators that play a major role in impacting on the growth of manufacturing firms in the Ghanaian economy.
However for a clear comprehension of how manufacturing subsector have performed in Ghana over the years especially starting from the post-independence era the study would also seek to make a comparative analysis based on line graphs. To achieve this data would be collated based on compiled data obtained from the Ghana statistical service on the subsectors of the industrial sector which basically include the construction, mining and quarrying and electricity and water.
Another main objective here is to get a coherent understanding of how the industrial subsectors have performed taking into consideration the dominant subsector over the years. This in a way would enable the researcher to get a fair idea of the inter-relationships among the subsectors and also to identify the challenges and constraints facing the manufacturing subsector.
Finally the major objective of these empirical steps and analysis is to enable the researcher to get a holistic understanding of the constraints and challenges facing the manufacturing and its related subsectors in the economy so as to recommend appropriate macroeconomic policies and measures that will ensure a sound macroeconomic stability and higher growth of manufacturing firms in Ghana.
1.4 RESEARCH QUESTIONS
Since our main research study here is to unravel the major macro-economic indicators that influence the growth of manufacturing firms the focus of this study would there aim to answer some research questions. Thus in the course of this research the following hypothetical questions would subsequently be developed to provide objectivity and thoughtfulness.
The first research question would focus on “ How do macro-economic variables influence the output as a measure of growth of manufacturing firms in Ghana?” The main motivation of this hypothetical question is to find out the mechanism in which these macroeconomic variables influence the productivity of firms and their perceived impacts both negative and positive situations. The second research question would touch on “ what are the main significant macroeconomic variables responsible for the growth of manufacturing firms in Ghana?
Lastly based on the findings obtained the research study will intend to answer the following question “what are some of the macroeconomic policies or measures to be adopted by the government of Ghana to ensure that manufacturing firms expand in size and output?”
1.6 SIGNIFICANCE OF THE STUDY
Macroeconomic variables such as interest rate, inflation rate, government expenditure, foreign direct investment, labour force are some indicators that tend to also give a picture of the current trends in the economy. For instance, high interest rate may indicate the economy is expanding as a result of the intense economic activities prompting the demand for money to exceed supply of money. If the interest rate is sensitive to investment it may lead to crowding out of private investment and this may lead to a reduction in investment of private manufacturing firms leading to a fall in GDP as this has always been the case in Ghana. On the issue of volatile nature of inflation rates, empirical evidence in Ghana suggests that high inflation rates on one hand has mainly been attributed to high monetary expansion resulting from government borrowing to finance its budget deficit and the problem of supply constraints from natural resource based sectors like agricultural sector have paved a way for some of the manufacturing firms to operate below their optimum, thereby reducing the GDP of the economy and also resulting in high inflation. Imports of goods and services have also affected most manufacturing firms as local manufacturing firms find it difficult to compete with foreign products that are imported into the country. Wrong macro-economic policies such as overconcentration on government expenditure on a particular subsector of the industrial sector have also led to negative impacts on manufacturing sector. It is very useful to note that the government cannot achieve the aim of raising growth in the manufacturing sector when it even over relies on this sector alone however more needs to be done on other related sub-sectors such as electricity and water which are very vital to the survival of most firms.
In order for the government, to make prudent macroeconomic policies with regards to the growth
of manufacturing firms in Ghana, one must study, analyze and understand the effects of these major
decisions of policy makers, the government and the private sector to proffer some solutions to the problems confronting low growth of manufacturing firms in Ghana.
1.7 SCOPE AND LIMITATIONS OF THE STUDY
In Ghana, there are several macro-economic indicators that tend to influence the growth of manufacturing firms. For instance, exports, imports, foreign direct investment, taxes, inflation, deflation, interest rate and exchange rates. However the context of this research focused on some selected key macroeconomic variables including labour force, real exchange rate, government expenditure and volume of trade as the main parameters used for our causation analysis. The data gathered on the time period of these variables for our econometric analysis spanned between 1990 – 2014.
Looking at the limitations of this study the researcher focused on manufacturing firms as they form the majority of the firms in Ghana under the industrial sector .This research also took into consideration some of the industrial subsectors for a comparative analysis of growth rates among the subsectors. Basically the industrial sector includes the manufacturing, mining and quarrying, electricity and water and construction subsectors.
One of the greatest challenges that the researcher encountered under this study relates to access and collation of hard data due to extreme data gaps situations in the country. This compelled the researcher to limit the study to manufacturing firms with data obtained from secondary sources. Another copious limitation of this study could be attributed to time factor, funding and logistics constraints, which consequently limited the coverage area of the study. The researcher was also faced with unavailability of ample data, difficulty in accessing classified information and lack of information flow.
ORGANISATION OF THE STUDY
The rest of the thesis project is structured as follows.
CHAPTER TWO:
This chapter captures a review of the literature of knowledgeable scholars of the chosen topic by looking at some empirical approaches, definitions, indicators and models to the growth of firms. Some of the models to growth of firms in this chapter basically include the Cobb-Douglas production function , the stochastic production frontier and some endogenous growth models.
CHAPTER THREE:
This chapter outlines the research methodology by looking at the coverage of study, the way in which data was acquired and also specifies the multiple regression model which was being employed for analysis of the data. It also explains the macroeconomic variables being used in the model as well as some scientific procedures employed in our analysis.
CHAPTER FOUR:
The fourth chapter makes an in-depth analysis of overall findings which is premised on acquired data obtained from secondary sources. Much of the data analysis here is being done with the help of software like Gretl and excel. Some of the results obtained here are being supported with literature of scholarly works.
CHAPTER FIVE:
This is the concluding segment of the comprehensive project work. It is the holistic discussion and summation of the research work including possible suggestions and propositions that could
CHAPTER TWO
LITERATURE REVIEW 2.1 INTRODUCTION
In most literature works several economic indicators to growth of firms are being classified under
several perspectives. This section of the literature review seeks to summarize on these indicators however its main focus here would be on value-addition as a major indicator to growth of firm.
Several empirical theories and models have also been formulated out of some scientific research being undertaken by several scholars to justify the major factors contributing to the growth of manufacturing firms. Some of these empirical research based models and propositions being identified in this work will elaborate on macroeconomic determinants on the productivity of firms, and other contributing micro factors. Some of the theoretical models to growth of firms here include neo-classical growth models such as the Cobb-Douglas production, the stochastic production frontier and some endogenous growth models.
2.2 DEFINITION OF VALUE ADDITION TO OUTPUT AS AN INDICATOR TO GROWTH OF FIRM
Economic indicators to growth of firms often take several dimensions and as a result the concept varies from different perspectives. Firstly the definition to growth of firm may refer to rapid expansion of a firm normally linked to factors such as a rapid increase in output, sales and revenues and value addition to output over some period of years. Based on empirical literature we may have different criteria’s or measures in defining growth of firms. According to Ardishvili et al. (1998) and Delmar (1997) growth indicators of firms could be measured by means of the financial or stock market value, the number of
production. Analytically all these indicators differ in meanings. For instance the firms financial or stock market value as an indicator of growth here refers to the rising trend of the value of stocks of a firm which may be valuated based on stock prices whiles on the other hand indicators such as sales and revenues explains the number of output sold and gross profits earned from selling these outputs.
The value addition to output explains how a firm add values to its output in production. The meaning of value addition to output could be explained in several directions. World bank defines value addition as the “net-output of a sector after adding up all outputs and subtracting intermediate inputs. it is calculated without making deductions for depreciation of fabricated assets or depletion and degradation of national resources”. Angus Maddison et al (1988) in their work “comparisons of real output in
manufacturing” outlines some general definitions of value-added and classifications of value added based on the census concept and the national accounts concept derived from UN guidelines.
In their work the united nations definition of value added is defined as “the increment to the value of commodities and services that is contributed by the producing establishment, that is the value created by the establishment. Aggregated for all the establishments in a given industry, value added is the incremental value of goods and services attributable to that industry.” With regards to the census concept “Value added in the census concept is defined as the value of outputs less the cost of materials and industrial services used”. Whiles the national account concept of value added explains that “ net value created in the economy as a whole but is net only in terms of agriculture and industrial sectors of the economy. To derive the net value added, it is necessary to exclude in addition to the cost of materials and purchased industrial services, the purchase of non-industrial services and to include non-industrial receipts. This additional calculation moves towards value added in the national accounting sense. The national income concept in the national account excludes depreciation charges, that is consumption of fixed capital.”
The UN views it as the most appropriate method of evaluating productivity of firms as the real-value added by an industry would finally constitute the real GDP. Diewert ( 2000) notes that for “ comparing total factor productivity growth at the industrial level ,it is best to use the value added output rather than gross output as the later includes the purchase on intermediate inputs which vary greatly among the industries.”
Value addition to output of firms in an economy is being measured based on some standard procedures known as system of national accounts. The value added approach has being adopted by some countries in estimating the real GDP of the country as it gives the true value of output produced by all related firms in the economy. Sampat Mukherjee (2000) highlights a summarized approach of the value – added process by three stages. The first stage involves “ identifying the various types of producing firms and classifying them into different sectors according to the activities performed by them. The second stage goes with estimation of net value added at factor cost by each producing unit as also by each major sector of the economy and then adding up the net value added figures of all the sectors to obtain the net domestic product. The last stage would involve estimating the net income from abroad”. The Author clearly argues that once the producing sectors of the economy are identified the next step is to find out the net value added figure of each producing unit. The term value added according to Sampat Mukherjee (2000) refers to “the value addition made by each producing unit to the raw material and intermediate goods purchased from other producing unit before selling output to consumers, other businesses, government departments and foreigners. The value added is the difference between the market value of the output produced by the firm or any producing unit and the cost of raw materials and intermediate goods used in the production process”. Ark (1996) confirms that value added remains a useful concept particularly for international comparism of productivity because it is simple, avoids the need of
intra-industry transactions, and bears closer resemblance to primary statistics such as production census and representative firm data.
2.3 EMPIRICAL RESEARCH ON GROWTH OF FIRMS
Several theories and models have been formulated on the growth of firms and most of them tend to solve hypothetical questions such as “what are the main factors that influence the productivity of firms?. Conspicuously, most research on the growth of firms tend to focus on the productivity of firms or at the industrial level often employing total factor productivity as the main yard stick for analysis of growth though other literature works employ value added as a percentage of GDP to define productivity.
Productivity often defines the growth of firms and variables such as real or nominal GDP could be used as a proxy in defining the growth of manufacturing firms. Kumar Mangla et Al ( 2015) defines productivity as the relationship between a flow of output, produced and the inputs which are used to achieve that flow of output. Some scholars have categorized contributing factors to growth of firms. These groups of categorization includes firm level variables, industry level variables and macroeconomic variables. (McPherson, 1996; Mead and Liedholm, 1998) observed that some firm level variables such as the education of the entrepreneur tend to often influence the growth of a firm. Stam and Wennberg (2009) find that growth aspirations are positively and significantly associated with the growth of low-tech firms, but not for high-tech firms. At the industrial level Geroski and Gugler (2004) argues that the degree of competition faced by firms is not always observed to have an impact on growth rates.
Macroeconomic variables have often examined the dynamic relationship between the growth rate of firms and the macroeconomic factors over the course of time normally sometimes examined through real business cycles. Hardwick and Adams (2002) investigated that smaller firms appear to grow relatively faster during booms, whereas larger firms grow faster during recessions and recoveries.
Ahluwalia (1991) investigated the total factor productivity growth (TFPG) in Indian
manufacturing industries based on pooled cross section and time series data obtained from Annual Survey of Industries (ASI) using translog production function. The period of the study was 1964-65 to
1985-86. According to the estimates, TFP had increased at 3.4% per annum during the period of the study. The major reason for growth was due to the economic liberalization policies of 1980’s.
Ray (2012) also determined the determinants of total factor productivity growth in selected manufacturing industries in India. Using OLS technique, the econometric result suggested that trade variables as well as macro-economic variables have relevant significant impact on total factor productivity growth of those industries. The final conclusion for Indian policymakers was the need to open up more to foreign imports, which will help to bring about institutional and technological progress conducive to TFP growth.
Anaman et al. (2009) in their pursuit of evaluating the determinants of the output of the
manufacturing industry in Ghana from 1974 to 2006 employed the co-integration and error correction model analysis to come out with the determinants. They finally proved that the level of output of the manufacturing industry was influenced in the long-run period by the level of per capita real GDP , the export-import ratio and political stability . In the short run period the level of output of the manufacturing industry was influenced by the export- import ratio and political stability. They recommended that the increasing level of manufacturing in Ghana would partly depend on the growth of export-based manufacturing firms.
2.4 THEORITICAL MODELS ON GROWTH OF FIRMS 2.4.1 COBB DOUGLASS PRODUCTION FUNCTION
Apart from these empirical researches on the growth of firms there are however other theoretical models and laws that evaluates growth. For instance the Gilbrat‟s law illustrates the the concept of growth. Gibrat's law also known as the law of proportionate effect (1931) remarked that the proportional rate of growth of a firm is independent of its absolute size. The logical conclusion here is that the large and small firms tend to exhibit the same average proportionate rates in growth..
Neo –classical growth models also often tend to emphasize the concept of growth. For instance through neo- classical production function well known as the cobb-douglas production function we could evaluate the productivity of firms. The Cobb–Douglas production function often expresses the relationship between output of a firm and the combining factors of production often employing labour and capital as the major inputs. The mathematical model is often represented the following way:
Q(L,K) = A L
βK
αwhere Q denotes output, K denotes the amount of hired capital, L denotes the hours of work hired, and where alpha and beta are technological parameters. The parameter A explains the total factor productivity (TFP). It refers to unmeasured variables that affect the productivity of labor and capital which may include climate and geography that determine natural resources, laws and regulations that limits the mode of production. The parameter α measures the relative importance of physical capital in the production process. Whiles beta also measures the contribution of labour in production.
The Cobb-Douglas production firm possess some unique characteristics such as: (i) positive marginal productivity, (ii) diminishing marginal productivity, and (iii) constant returns to scale implying that alpha plus beta equals one. Positive marginal productivity implies that as the firm employs more and more inputs the additions to the overall output of the firm increases. Conversely, diminishing marginal
productivity means the additional output to total output of a firm decreases as more of the inputs are being employed. Whiles constant returns to scale often explains that varying inputs causes output to increase by the same proportion.
2.4.2 STOCHASTIC PRODUCTION FRONTIER
Another very useful theoretical model in defining growth of a firm is the stochastic production frontier model. introduced by introduced by Aigner, Lovell and Schmidt (1977) and Meeusen and Van denk Broeck (1977).Normally to differientiate the sources of productivity change it is very useful to consider the changes in efficiency of a firm. Stochastic frontier models enables us to analyse technical inefficiency with the help of production functions. With this model firms are assumed to produce according to a common technology, and reach the frontier when they attain the maximum possible output for a given set of inputs. Inefficiencies in production may be linked factors such as market imperfections and other factors which cause firms to produce below their maximum attainable output. The model explains that firms can become less inefficient and reach up to the frontier. It is also possible that the frontier shifts, indicating technical progress. In addition, production units can move along the frontier by changing input quantities.
The stochastic frontier method allows us to measure the growth or productivity of a firm by decomposing growth into changes in input use, changes in technology and changes in efficiency.
A mathematical representation of the stochastic production frontier includes the
following. Inq(j)=f(Inx) + Vj - Uj
where qj is the output produced by firm j, x is a vector of factor inputs, Vj is the stochastic (white noise)
error term and Uj is a one-sided error representing the technical inefficiency of firmj. Vj and Uj are assumed to be independently and identically distributed (iid) with their respective variances.
Given that the production of each firm j can be estimated as: In q^(j)=f(Inx) – Uj the efficient level of production defined as: Inq(j)=f(Inx)
where technical efficiency (TE) is defined by InTEj= Inq^j – Inq* = -Uj where TEj = e-Uj , and
is bounded between zero and one in value. If Uj equals zero, then TE equals one, and production is said to be technically efficient. Technical efficiency of the jth firm is therefore a relative measure of its output as a proportion of the corresponding frontier output. A firm in this case is technically efficient if its output level lies on the frontier, which implies that q/q* equals one in value. If TE < 1 implies a shortfall of the current output from maximum feasible attainable outputs. Alternatively the stochastic production frontier can also measure the capacity utilization of firms. In estimating the full utilization production frontier, there is the need to set a distinction between inputs. Below is a diagrammatical representation of the stochastic production frontier.
2.4.2 ENDOGENOUS GROWTH MODELS
Another very useful model in illustrating growth of firms is the endogenous growth model which makes much use of some features of the Cobb-Douglas production function and basically moves in opposite directions with the solow-swan growth model. Whiles the solow-swan growth model seems to focus on how exogenous factors such as technology and population growth rate influence the output per worker in the long run the endogenous growth model touches on endogenous factors such as investment in human capital, innovation, and knowledge are the major drivers to the long run economic growth rate or technological progress. The solow swan growth models are considered as exogenous growth models since the population and technological growth rate are perceived as external forces that are independent from the influence of other macro economic variables such as the savings rate of the economy. However the endogenous growth rate model tends to address some short comings of the neoclassical growth models by looking at the major drivers of technological progress. Though both models seems to throw more light on the economy as a whole they are more or less also interpreted on microeconomic foundations.
The endogenous growth models is based on some general assumptions that enable us to appreciate the growth development of firms in an economy. Firstly the model assumes the existence of multiple firms in an economy and knowledge or technological progress is considered as a public good and non-rival. The assumption of knowledge to be a public and non-rival good here implies that each firm have acess to any new or existing knowledge at no cost across different firms without any conveniences. The model goes on to assume that all factors of production exhibit increasing returns to scale and constant returns to scale to at least a single factor whiles technological progress also comes from learning by doing hypothesis. This hypothesis is based on the fact that when one firm produces a good in the economy there is some sort of knowledge acquisition by other firms that tends to be diffused in the economy thereby
increasing the over all stock of knowledge in the economy and increasing the over all output of firms. Another strong assumption is that many firms exert market influence and make profits from their innovations. However in endogoneus growth models some degree of monopoly takes place simultaneous with some features of perfect competitive market. There are several models embedded in the endogenous theories that tends to explain the major sources of growth of firms. Some famous models such as the romer model and Robert lucas model gives a vivid description of the sources of growth of firms in an economy.
Lucas model focuses much on development of human capital and therefore holds on to the assumption that investment on education enhances the development of human capital which acts as an re-inforcement in determing the growth rate of output of firms . Lucas gives a sharp distinction between two effects of human capital development. The first scenario illustrates a situation where the individual worker acquires training and becomes more productive, whiles the second scenario shows external effects which illustrates spill over effects. Lucas argues that investment in human capital is the main driver to increase in the over all technological progress and this leads to spill over effects on the economy.as human capital develops through training, productivity of capital also increases increase the level of technology. In the Lucas model assumes the following production function of the firm
Yi = A(Ki).(Hi).He
Where A is the technical coefficient, Ki and Hi are the inputs of physical and human capital employed by
firms to produce goods Yi. The variable H refers to the average level of human capital in the economy
whiles the parameter e measures the strength of the external effects from human capital to each
firms productivity. The Lucas model is grounded on the assumption that each firm faces constant returns to scale, while increasing returns to scale is attributed to the whole economy. Each individual firm here
benefits from the average level of human capital in the economy, instead of the aggregate human capital in the entire economy. Thus the main source of growth here is attributed to the level of skills and knowledge in the economy but not the accumulated knowledge or experience of other firms .In the model, technological progress is endogenous as it is driven by investment decisions by firms. Technology here is assumed to be a public good and firms can be treated as price takers as in the perfect competition market. The romer model is also very useful in defining the growth of a firm. Unlike the lucas model which considers development of human capital as the main source of growth of firms the romer model in his first research on endogenous growth in 1986 factored in knowledge in the production function. Romer assumes that human capital is not just the main source of growth but rather accumulation of knowledge acquired through research and development. His main propositions were invariant to arrows assertion of learning by doing hypothesis.
Below is a simplied version of the romer model. Y = A(R) F (Ri,Ki,Li)
Where Y is the total aggregate output; A is the public stock of knowledge which is assumed to be a
public good and acquired from research and development by firms. Ri is the stock of results from
expenditure on research and development by firm i; and Ki and Li are capital stock and labour stock of
firm i respectively. Romer assumes the production function F to be homogeneous of degree one in all its
inputs Ri, Ki, and Li, and treats Ri as a rival good. Romer identified three key elements in his model
namely externalities, increasing returns to scale in the production of output and diminishing returns in the production of new knowledge. According to Romer, research and development by firms are the major drivers of innovation. However this innovation or accumulation of this new knowledge tends to produce some spill over effects in the economy as most firms tend to have access to this new knowledge over time
Thus in his model, accumulation of new knowledge is the main source of long-run growth of a firm which is determined by investment in research technology. In his model research technology exhibits diminishing returns which basically means that investments in research technology will not double the size of existing knowledge. Here in romers model spill over effects as a result of research and development leads to increased production of firms causing them to experience increasing returns to scale and competitive equilibrium is consistent with increasing aggregate returns owing to externalities. Thus analytically romer endogenize macro- variables such as research and development as the main driver to the over all growth of firms in an economy who are assumed to be rational profit maximisers.
Though the endogenous growth models have many logical implications for both developing and developed economies one of its crucial policy implication for firms in a country is that continuous investment in research and development do not produce effects on a single individual firm however spill over effects on the whole firms in the economy.
CHAPTER THREE
RESEARCH METHODOLOGY 3.1 INTRODUCTION
This section of this research work basically deals with the research methodology and basically explains
the way in which data was acquired, the model being employed for econometric analysis of our data and also a detailed description of the variables under study here. It further goes on to analyse the detailed techniques that is being adopted to analyze our model so as to come to a logical conclusion of the acquired data.
3.2 SOURCE OF DATA
The major source of data of this research was secondary and therefore data collection was very flexible and collated from the world bank site, the Ghana Statistical service, and other literature works. The data compiled for econometric analysis are a set of time series specifically on economic variables such as manufacturing value added as a percentage of GDP, government expenditure, trade, real effective exchange rate and labour force which covered the period 1990 to 2014. This period was chosen as this marked the period Ghana started recording positive growth rate in the manufacturing subsector.
Below is the main source of data obtained from the world bank site. Further data compilation was obtained from the Ghana Statistical service website on the various subsectors of the industrial sector which includes the manufacturing , construction, mining and quarrying and the electricity and water subsector. The data below here covers the macro-economic variables which is to be used for econometric analysis followed by data compiled on industrial subsectors.
TABLE 1 DATA OBTAINED ON MACRO-ECONOMIC VARABLES YEAR MVA % OF GDP LABOUR FORCE AT TIME (t) GOVERNMENT EXPENDITURE AS % OF GDP TRADE VARIABLE AS % OF GDP REAL EFFECTIVE EXCHANGE RATE AT TIME (t) 1990 9.8107 585162 9.3115 42.7281 161.27 1991 9.2818 6043306 9.4831 42.4883 164.6 1992 9.3695 6245240 12.1075 45.9936 145.18 1993 10.5094 6481673 14.4493 56.6691 126.87 1994 10.1156 6724212 13.7233 62.0211 102.76 1995 10.2709 6971274 12.0734 57.4230 118.69 1996 9.7253 7203456 12.0437 72.2049 128.97 1997 10.1320 7442583 12.3556 85.4018 136.45 1998 10.0404 7701538 10.3241 80.5995 145.63 1999 10.0715 7962130 10.8433 81.7051 143.84 2000 10.0757 8236250 10.1716 116.0484 94.11 2001 10.0461 8377027 9.7223 110.0459 95.15 2002 10.0707 8508988 9.8727 97.4892 94.75 2003 9.8825 8643793 11.5332 97.2871 94.98 2004 9.5700 8770668 12.1728 99.6703 93.68 2005 9.4601 8901243 15.3081 98.1715 102.33 2006 10.4778 9030102 11.3038 65.9227 107.74 2007 9.3658 9303129 11.5590 65.3543 107.01
2008 8.1384 9601766 11.2424 69.5142 101.87 2009 7.1900 9889878 11.7340 71.5947 93.76 2010 7.0242 10204954 10.3553 75.3778 100 2011 7.0641 10492132 16.6431 86.2954 95.04 2012 6.0363 10789001 20.8879 93.1680 88.98 2013 5.4931 11068845 19.9178 81.6523 89.57 2014 5.1393 11372106 17.9750 88.4514 69.49
TABLE 2 DATA OBTAINED ON THE INDUSTRIAL SUB-SECTOR
RELATIVE CONTRIBUTION OF INDUSTRY AND ITS RELATED SUBSECTORS TO GDP,
YEAR INDUSTRIAL SECTOR MANUFACTURI NG MINING & QUARRYING ELECTRICITY & WATER CONSTRUCTION 1981-90 13.6 64.5 8.7 7.7 18.9 1991-95 16.5 55.0 12.5 10.2 22.4 1996-00 25.2 36.2 22.7 10.5 30.8
Source: Based on data obtained from the Ghana Statistical Service
YEAR INDUSTRIAL SECTOR (% GDP
MANUFACTURING MINING & QUARRYING ELECTRICITY & WATER CONSTRUCTION 2001 24.90 36.69 21.11 10.34 31.86 2002 24.93 36.71 21.06 10.28 31.95 2003 24.90 36.57 20.96 10.19 32.28 2004 24.73 36.37 20.86 10.06 32.72 2005 24.70 36.30 20.40 10.20 33.20 2001- 2005 20.69 36.53 20.88 10.21 32.40
YEAR MANUFACTURING MINING AND QUARRYING
ELECTRICITY WATER AND
SEWERAGE CONSTRUCTION 2006 49.0 13.5 3.8 6.3 27.4 2007 44.0 13.5 2.9 4.8 34.8 2008 38.9 11.8 2.6 3.9 42.7 2009 36.6 10.9 2.5 3.6 46.4 2010 35.5 12.2 3.2 4.4 44.7 2011 25.9 32.8 2.3 3.3 35.7 2012 24.2 32.0 1.8 2.7 39.4
3.3 COVERAGE OF STUDY
This research basically focused on the manufacturing firms since majority of firms in Ghana fall under the manufacturing sector and data was gathered on the manufacturing valued added as a share of GDP. Data obtained was from secondary sources with a major focus on analyzing the impact of macroeconomic
indicators on the output of manufacturing firms in the Ghanaian economy taking into consideration the manufacturing value added as our main dependent variable.
3.4 METHOD OF DATA ANALYSIS
All the data obtained from the secondary sources were sorted out with the use of tables so as enhance appropriate comparative analysis and also to enable us to get a clear picture of what is to be analyzed taking into account the data being gathered on these varying indicators. Furthermore, the use of tables, line graphs and pie charts have been used to display these data so as to enhance our analysis and make meaningful observations based on some time periods. For inferential statistical purposes we employ Gretl software for such analysis whiles Excel is being used for much of our data representation in the form of pie charts, line graphs and grouped bar charts.
The first step of the researcher in making statistical inference is to employ the ordinary least square method.The model here was by means of multiple regression model in a log-log model . We could obtain this model by employing gretl to transform our variables into natural logs. This is done by first selecting the variables displayed by gretl and going to the menu bar to select the command add by which you can further select log of selected variables. Our major motive of transforming the model into a log-log model is to get a clearer interpretation of our estimated co-efficients since logged variables are normally well
approximated in percentage change wise. Lastly this model would also include some lagged variable assuming the labour force as our lagged variable of one year.
This in a way reduced the sample observations of 25 years to 24 years. In gretl our lagged variable of labour force would be included in our model by selecting the lag button which which brings up the lag screen allowing us to select the number of lags for this variable.
3.5 MODEL SPECIFICATION
The model employed for our research study here is a multiple linear regression transformed into log-log model. The method of ordinary least squares method is being employed to estimate the impact of macroeconomic indicators on the output of manufacturing firms in Ghana.
The model therefore would take the following form :
IN Q
t= β0 + β1 ln(TR
t) + β2 ln(GE
t) + β3 ln(RE
t)
+β4In(LF
t-1)
+ε
tWhere the dependent Variable (IN Qt)
IN Qt = Output measured as manufacturing value added as a % of GDP at time t And explanatory variables include;
TRt
= Trade variable as % of GDP at time t.
GE
t = Government expenditure as % of GDP at time t
RE t
= real effective exchange rate at time t .and
ε
is our random error term which forms the stochastic component of our model andincludes some other macroeconomic determinants which have not being specified in the model.
β0 -
Constant term
β1
,β2
,β3 and β4
are the regression coefficients which estimates the partialelasticities of the independent variables with respect to the dependent variables. IN- Natural logarithm
DESCRIPTION OF VARIABLES
The manufacturing value-added as a percentage of Gross Domestic Product measures the manufacturing output as share of a country’s economy. Manufacturing can be broadly defined as all those economic activities that is aimed at processing raw materials into useful products which may be undertaken either by capital intensive method of production or labor intensive method of production. According to the world bank the value added simply defines “ the net output of the manufacturing sector, calculated after adding up all the outputs and subtracting the intermediate inputs and is calculated without deducting the depreciation of the fabricated assets, or the depletion and degradation of natural resources”.
On the other hand the Government expenditure here as a % of GDP defines how government make use of public money for the general welfare of its citizens. It could be basically measured as a percentage share of Gross Domestic Product in the economy. Government expenditure here often come in different forms such as capital and recurremt expenditure. Capital expenditure here refers to the government expenditure on some specific general goods that takes a long period of time. This may include expenditure on capital goods
such as roads, building of schools , railways, electricity and factories. Whiles on the other hand recuurent expenditure includes expenditure that are incurred by the government at regular intervals. This include expenditure on salaries of workers, agriculture, pensioners , interest on internal and external debt.
Real Effective exchange rate is an index that describes the strength of a currency relative to a basket of other currencies.(wikipidea). According to the world bank this indicator measures the value of a currency against a weighted average of several foreign currencies divided by a price deflator or index of costs.
On the other hand labour force basically describes that section of the entire population that are active or available for work and capable of producing goods and services . This portion of the labour force normally comprises of people who are between the ages of 18 and 60 years who might be working or actively searching for work to do. Trade variable here is the total sum of exports and imports of goods and services which is measured as a share or percentage of gross domestic product.
3.6 TESTING OF HYPOTHESIS ON ESTIMATED PARAMETERS
Since the main focus of this research is to identify the macroeconomic factors influencing
manufacturing output in Ghana the study will therefore seek to test the the following hypotheses employing the two-tailed test with the use of gretl.
(Null Hypothesis) H
0; Trade variable has no significant impact on manufacturing output.
(Alternative Hypothesis) H
1; Trade variable has a significant impact on manufacturing output
(Null Hypothesis)H
0; Government expenditure has no significant impact on manufacturing output.
(Alternative Hypothesis )H
2; Government expenditure has a significant impact on manufacturing output.
(Null Hypothesis)H
0; Real effective exchange rate has no significant impact on manufacturing output.
(Alternative Hypothesis)H
3; Real effective exchange rate has a significant impact on manufacturing output.
(Null Hypothesis) H
0; Labour force has no significant impact on manufacturing output.
(Alternative Hypothesis)H
4; Labour force has a significant impact on manufacturing output.
Based on this literature review and fore knowledge on the Ghanaian economy, we postulate that, after
the estimation of our ols co-efficients of our explanatory variables β1
,
β2, β4to be > 0; This implies thattrade (TR) Government expenditure (GE) and labour force (LF) is expected to have a positive correlation
with manufacturing output. Conversely, we also postulate that the coefficient of β3 to be
<0
; indicating that3.7 R-SQUARED COEFFICIENT OF DETERMINATION AND ADJUSTED R-SQUARED
The multiple regression model in this research work being estimated by the method of ordinary least squares will therefore be also evaluated based on the R-squared which is also known as the co-efficient of determination. The co-co-efficient of determination here will measure the goodness of fit of our regression line. Basically the R-squared also defines the proportion or percentage variation of our
dependent variable that is being explained by the regression model. In a formalized manner the formula of our R-squared is given by the following way;R-squared =1- ESS/TSS ;Where ESS means the explained sum of squares that is the variation of our dependent variable due to the regression model and TSS represents the sum of our residual sum of squares and our explained sum of squares. The residual sum of squares defines the variation of our dependent variable due to our error term. The R-squared takes on some extreme values 0 and 1 such that it is closed and compact such that its limits are such that 0<R^2<1. An R^2 of 1 implies that our regression model estimates 100% of our data and that there is a full variation our dependent variable with respect to our explanatory variables. This therefore implies that we our data points lie on the regression line on the other hand an R-squared of o will mean that our regression model fails to estimate the variation of our dependent variable. This therefore implies that our dependent variable have no relationship with our explanatory variables.
In defining our adjusted R-squared we try come out with the of degrees of freedom which enables the regression line to have some error terms around it so that we could actually define the exact correlation between variables.In a formalized manner the adjusted R- squared is expressed the following way Adjusted R-squared = 1 – (1-R^2)*(N-1)/N-K
dependent variable. The adjusted r-squared here is closely related to the R-squared and may increase or decrease depending on the relevancy of the variables included in the model. if there are more inclusion of relevant explanatory variables in our model then the R- squared increases significantly so the adjusted squared will also increase. If there are more inclusion of irrelevant explanatory variables then the adjusted r-squared decreases as the R-r-squared remains constant reflecting that you have lost degrees of freedom.
3.8 PARAMETERS FOR MODEL CHECKING (T-TEST)
In testing for the significance of each explanatory we would normally make a null hypothesis on a single co-efficient of our explanatory variable. This method will therefore involve employing the t-test. We would first start by imposing our null and alternative hypothesis such that
H0 :
βj = 0 and
H1:βj ≠ 0
A true valid t- test here under the null hypothesis can be expressed the following way
t = βj^ - βj (Ho) ~ t(n-k)
S.E βj^
Where βj^ represents our estimated parameter and βj (Ho) represents the parameter under the null hypothesis which is normally given as zero and S.E βj^ defines the standard deviation of our estimated parameter n- k here simply means that the test statistics has the students t-distribution in with n-k degrees of freedom where n – represents the number of observations and k represents the number of variables included in our model. After having obtained our t- value we compare it to the critical value in our t-distribution table. if it exceeds the critical value then we reject the null hypothesis that βj equals zero indicating that our value is significant and has a reasonable effect on our dependent variable if the t-value is less than our critical value then we accept the null hypothesis indicating that there is no level of significance here. since the p – values defines the probability of obtaining our t-statistic we can also employ it to define the significance of our estimated parameter by setting the significance level of alpha (α) =
hypothesis Ho and establish the fact that the parameter is significant and that there is high degree of effect on the dependent variable
.3.9 TESTING FOR THE OVERALL SIGNIFICANCE OF THE MODEL ( F-TEST)
Unlike t-test which normally test the significance of a single parameter here we are testing the over-all significance of our multiple regression model through the F-test for this analysis. However to undertake this test we have to impose the conditions of the null hypothesis that all our estimated parameters beta 1, beta 2 and beta 3 in our multiple regression model equals to zero under the null hypothesis. . If the value exceeds the F-critical value from our chi-squared distribution table then as a rule we would reject the null the
hypothesis and confirm that our variables in the model are statistically significant. If the F-value is less than the critical value then we would accept the null hypothesis and conclude that are our variables are not statistically significant. It is however obvious to note that the F statistic must be employed simultaneously with the p value in concluding that the overall parameters are significant. If our p value is less than the significant level alpha which we set at 0.05% , then we can reject our null hypothesis however this does not mean all our parameters are highly significant. if it is greater than the significant level of alpha then we can accept our null hypothesis with the conclusion that our all parameters are not statistically.
In a formalize way the F-value can be computed by the following way;
F-value
= R^2 / g( 1- R^2)/ (N – K)
Where R^2 defines the r-squared ,g – number of restrictions ,N=number of observations and k implies the number of variables employed in our model.
3.9.1 TESTING OF MULTI –MULTICOLLINEARITY AMONG VARIABLES
Explanatory variables within some models may sometimes exhibit some linear relationships. This often makes the ordinary least square estimators biased and hence makes it to difficult make inference. This research work intends to find out if there are some linear relationships between our explanatory variables by employing the variance inflation factor. The variance inflation factor here would be computed with the help of software to find out if some variables exhibit some collinearity. Mathematically the variance inflation factor could be computed by computing an auxiliary regression for each regressor in the following way. Since in our model we have X1, X2 and X3 variables an auxiliary regression for each variable would imply that
X1 = α 2*X2 + α 3*X3
X2 = α3*X3 + α1* X1 X3 = α 1*X1 + α2*X2
For each auxiliary regression we would compute its R-squared. High values of variance inflation factor would imply collinearity problems.
In a formalized way the variance inflation factor can be written as;
VIF = 1/ ( 1 – Rij – squared) , where Rij simply implies the multiple correlation co-efficient between variable j and the other independent variables.
3.9.2 TESTING FOR AUTOCORRELATION AMONG ERROR TERMS
The term auto-correlation here simply implies the correlation among error terms. That is the correlation that exists between our individual error terms. Error term normally can be correlated with each other or error term in one period may influence the error term in the subsequent period.. The necessity of checking of serial correlation among error terms is due to the fact that if error terms are serially correlated positively across time our model looses its predictive power as the Ols estimators looses its accuracy. A possible check for detecting autocorrelation among our error terms is by employing the
DurbinWatson Statistic which is abbreviated by (DW).
The Durbin Watson Statistic can be expressed by the following formula such that ;
DW =
∑ (
e
it-
e
it)2∑
e
it
2Where T = the number of time periods.
If the DW falls between 1.5 and 2.5, this signifies a no autocorrelation among our error terms. If it falls below 1.5, this signifies positive autocorrelation and if it exceeds 2.5 this shows a negative autocorrelation among our error terms. The motive of detecting autocorrelation among our error terms is thus to make sure our OLS estimates are efficient if there exist no auto-correlation among our error terms.
3.9.3 TESTING FOR HETEROSCEDASTICITY AMONG ERROR TERMS
The term heteroskedacity often explains that the variance of our error terms is not constant but rather changes and this also normally leads to unbiased but inefficient OLS estimates. Inefficient OLS estimates implies that they are not closer to the true parameter and therefore not also highly statistically significant. In detecting the presence of heteroscedasticity among our error terms we would employ the white test with the help of Gretl Software. The basic normal assumption of our multiple regression model is that there should exist homoscedasticity among our error terms so that our OLS estimates become the best unbiased, efficient and with a minimum variance. The white test is therefore a statistical test that indicates whether the variance of our error terms in our regression model is constant. It does so by regressing the square of our error term on our independent variables
.such that e2 = α0 + α1x2 + α2x2 + α3x3 + α2x22 + α3x32 and obtaining the R2 of theauxiliary
regression. Under the assumption of no heteroskedasticity that is α1=α2=α3=0 if that N*R2 belong
to the chi-squared distribution this would imply that we accept the null hypothesis and hold on to the
fact that there is homoscedasticity of errors.. In contrast we reject if there is a high R2 such that
