




































Economy 
ISSN: 2313-8181 
Vol. 2, No. 1, 32-43, 2015 
www.asianonlinejournals.com/index.php/Economy 

 

 

* Corresponding Author 

 

 

32 

 

An Econometric Investigation of the Determinants of Fossil 

Fuel Consumption: A Multivariate Approach for Ghana 
 

Samuel Yeboah Asuamah
1*

 --- Joseph Ohene-Manu
2
 

 
1
Business School, Accra Institute of Technology (AIT), Accra, Ghana  

2
Department of Economics, Kwame Nkrumah University of Science and Technology (KNUST), Kumasi, Ghana 

 

Abstract 
 

 

 

 

 

 

 

 

 

 

 

 

 

 
This work is licensed under a Creative Commons Attribution 3.0 License 

Asian Online Journal Publishing Group 

 
Contents 

1. Introduction ............................................................................................................................................................................... 33 

2. Methodology .............................................................................................................................................................................. 34 

3. Empirical Results, Discussions, and Analysis ......................................................................................................................... 35 

4. Conclusions ................................................................................................................................................................................ 42 

References ...................................................................................................................................................................................... 42 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The study examines the long run and short run determinants of fossil fuel consumption in Ghana for 

1970-2011 period by using Autoregressive distributed lad model (ARDL). The bound test for 

cointegration produced no evidence of cointegration among the variables. There are no statistical 

significant long run and short run parameters for the fossil fuel consumption function for Ghana. The 

results suggest macro variables such as income, price, trade openness, investment, money supply, and 

government expenditure do not play observable role in fossil fuel consumption. As such, they could not 

be relied on as a policy tool to manage fossil fuel consumption. Future study should consider the issue 

of structural breaks and the direction of causality. 
 
Keywords: Fossil fuel, Consumption determinants, Long run and short run elasticities, Cointegration link, Income, Price, 

ARDL bound approach, Stability test, Non structural break. 

http://creativecommons.org/licenses/by/3.0/


Economy, 2015, 2(1): 32-43 

 

 

 

 

33 

 

1. Introduction 
The examination of the determinants of energy consumption has been discussed widely in energy literature since 

energy is considered as one of the main engines of economic growth (Acaravci and Ozturk, 2012). The analysis took 

prominence in the literature following the empirical works of Kraft and Kraft (1978) for the United States. Fossil fuel 

consumption impact economic performance at both macro-level and the household level. Fossil fuel allows the 

households, firms and the government to run their activities such as transportation and powering of industrial 

machines for production. As the economy grows, fossil fuel usage also increases and this has necessitated the 

examination of factors that influence the consumption of fossil fuel in economies. This is important to avoid energy 

shortages in an economy such as Ghana, which has been experiencing energy shortages resulting in long queues at 

the filling stations. The examination of the determinants helps in assessing the trends and forecast of fossil 

fuel consumption, which is difficult to do (Doherty, 2012). 

The empirical examination of the determinants of fossil fuel consumption has not produced consistent results in 

the literature. The discrepancies in the empirical findings are found in the works Han et al. (2000); Keii (2000); 

Gately and Huntington (2002); Wei (2002); Cooper (2003); Wolde-Rufael (2004); Griffin and Schulman (2005); 

Narayan and Wong (2009); Zou and Chau (2006); Dargay et al. (2007); Narayan and Smyth (2007); Skeer and Wang 

(2007); Hughes et al. (2008); Askari and Krichene (2010); Dargay and Gately (2010); Lee and Lee (2010); Faridul et 

al. (2011); Baumeister and Peersman (2012); Fawcett and Price (2012); and Schryder and Peersman (2012).  

Various variables (Energy price, income, the share of heavy industry output in national income, population, 

financial development, exchange rate, interest rate, population growth, trade, and total traffic volume) have been 

reported in the literature to influence fossil fuel consumption. 

The paper is based on microeconomic theory of demand and the concept of elasticity. The theory of demand 

suggests that other thing equal, the demand for a product is a function of the price of the product, the price of 

substitute product, technology and income (Mas-Colell et al., 2007). 

Governments embark on many forms of growth strategies. One of these strategies is the use of energy as an 

engine of growth and development (Kahsai et al., 2010). Policy makers, managers, economists, and energy experts in 

an economy encourage energy conservation and the use of energy efficient sources in the face of limited energy 

supply, coupled with the fact that oil, and gas are imported with the limited foreign currency in economies which are 

not producers of energy.  For example, the energy commission, 2010 report for Ghana indicated Ghana has installed 

capacity (1960MW) that comprises of hydro and thermal that is not sufficient for the current demand level. It is 

expected that fossil fuel demand will increase in future from 1.62 million tonnes (2005) to 2.49 million tonnes (2015) 

(Energy Commission, 2010). This called for the examination of the factors that affect fossil fuel consumption to help 

in energy demand management policy formulation.  

The issue under investigation is to examine empirically the determinants of fossil fuel consumption. The paper 

contributes to the body of knowledge in literature, by empirically assessing the effect of financial development on 

fossil fuel consumption with inconsistent results. This according to researchers such as Shahbaz et al. (2011) may 

results from the type of data used, period covered, the level of economic growth of the countries, the econometric 

estimation models. The current paper adds to the literature in this area. The paper in addition, suggests a conceptual 

fossil fuel demand model for estimating demand for energy in small but open economy. 

This paper contributes to theoretical knowledge as it seeks among other things to provide answers to research 

questions of ‘what’; ‘why’ and ‘how’ as indicated by Sutton and Staw (1995). Explanations are provided for why and 

how variables are linked and the significance of their relation. Reasons are also provided as to why other variables 

are not related or are not explanatory variables. From the review of the literature, there is no consensus on the effect 

of financial development on energy consumption and economic growth as well as the direction of causality among 

the variables. The findings have been mixed. This according to researchers such as Shahbaz et al. (2011) may results 

from the type of data used, period covered, the level of economic growth of the countries, the econometric estimation 

models. The findings provide policy guide for policies makers on energy demand management to ensure sufficient 

energy supply. Shahbaz et al. (2011) indicated that energy demand projections that do not consider variables such as 

financial sector development might produce inaccurate forecast that will work against any conservation policy in an 

economy. The findings serve as reference material for students and researchers in the area of energy economics who 

are interested in investigating energy demand in Small but Open economy, such as Ghana. 

The general objective of the paper is to contribute empirically to the general body of knowledge and research 

work in the area of energy demand in Ghana in order to identify and determine policy options that can achieve 

sufficient energy consumption to spur economic growth. The study contributes to knowledge in energy sufficiency 

by determining factors influencing energy consumption over the 1970-2011 periods. In order to achieve the General 

objective, the researcher specifically: (b) Examine the unit root properties of the series variables (c) Estimate and 

analyse the determinants of fossil fuel energy consumption using Autoregressive distributed lag model (ARDL). 

The paper is based on these research questions: (a) what is the nature of stationarity of the variables? (b) What is 

the nature of cointegration link among the variables? (c) What are the main determinants of fossil fuel consumption?  

The main assumption behind the current paper is the claim that in Ghana fossil fuel consumption is statistically 

influenced by macroeconomic variables (such income, price of energy, trade openness, investment, and government 

expenditure). Empirical data are used to test this claim.  

This study is not without limitations. These limitations do not in any way invalidate the findings of the research. 

The study is based on secondary data. Hence, the study may suffer from error in variable. Any error in the data used 

might not been known by the researcher. Hence, the same data from various sources are compared for uniformity in 

the data set. 

The review of literature is limited to only sources and references dealing with determinant of energy 

consumption, the role of financial development in energy consumption and economic growth, at aggregate and 

disaggregate levels as well as studies base on panel data. 



Economy, 2015, 2(1): 32-43 

 

 

 

 

34 

 

These sources are reviewed since they are related to the focus of the current paper and provide enough 

information on all sections of the paper such as the statement of the problem, justification, research questions, 

assumption, theoretical framework, empirical framework, methodology, as well as the significance of the study. 

The paper does not review articles on the problem of the financial sector energy sector and problems of 

economic growth, since this is not the focus of the paper and their inclusion will make them irrelevant.  

The estimated model did not include variables such as education, democracy, and corruption. They are not 

included since the literature reviewed do not identify these variables and hence do not have theoretical and 

conceptual basis for inclusion. 

The ordinary regression analysis (OLS) is not used since the series are not stationary and the use of such analysis 

method produces spurious regression results and produced invalid and unreliable results.  

The issues of structural breaks are not considered in the current paper in the examination of the unit root 

properties of the series variables. The issue of the existence of nonlinearities in the energy demand model is not 

considered. Multivariate demand model is considered not bivariate energy demand model. The multivariate analysis 

is “important because changes in energy use are frequently countered by opposite movements in the employment of 

other factors, due to substitution, resulting in an insignificant overall  impact on output” (Stern, 1998). 

 

2. Methodology 
The determinants of the fossil fuel demand model is performed by first examining the unit root properties of the 

series using the Augmented Dickey and Fuller (1979) (ADF) and the Kwiatkowski et al. (1992) KPSS). Second the 

long run and the short-run links among the variables are examined using the ARDL model (Pesaran and Shin, 1999; 

Pesaran et al., 2001). 

 

2.1. Unit Root Test  
The unit root test is conducted to determine whether the series in model are stationary or non-stationary in order 

to determine the order of integration. If the series are non-stationary they are made stationary through differencing 

before they are used in the estimation. This is done to avoid spurious results. The ADF test is based on the null (Ho) 

assumption that there is a unit root or the series are non-stationary in levels. The alternative hypothesis (H1) states 

that the series are stationary or there is no unit root in the series. The critical values are compared with the calculated 

values at 5%, 1% and 10% levels of significant. The ADF test is as specified in equation (1).  




 
q

i

ttttttt zzz
1

11 )1.......(..............................
 

Where γ = time trend, Z= time series variable in the model, ɛt = error term or stochastic error term.  

The KPSS test serves as a confirmatory test for the ADF test. The null assumption (Ho) of the KPSS is that, the 

series variables under investigation are stationary against the alternative assumption (H1) that the series are non-

stationary (Kwiatkowski et al., 1992). Given that Yt is the series variable under investigation, Kwiatkowski et al. 

(1992) specify an equation as shown in equation (2) to decompose the series into the sum of a deterministic trend (t), 

a random walk (rt) and a stationary error (ɛt). 

)2.......(........................................ttt rtY  
 The random walk is specified as in equation (3) 

)3..(............................................................1 ttt rr  
 Where µt is considered to be IID (0, σ

2
μ). The initial value of rt which is r0 is considered as the fixed and serves 

the role of an intercept in the model. The stationarity assumption is given as σ
2

μ =0. The series variable under 

investigation (Yt) is trend stationary since the error term is stationary. In model (2), Kwiatkowski et al. (1992) set the 

coefficient ξ=0 where the null assumption that the series variable (Yt) is stationary around a level (r0) and not around 

a deterministic trend. This the authors considered as a special case. The test statistics under the KPSS is the Lagrange 

multiplier (LM) statistic under the assumption that σ
2
μ =0, given the assumption that μt is normally distributed and 

that the error term (ɛt) is IID N(0, σ
2
ɛ ). Kwiatkowski et al. (1992) specified a partial sum process of the residuals as 

in equation (4). 

)4.(..............................,.........
1





t

i

it eS

 
Where t= 1, 2, 3, …, T. 

Following equation (4) the LM statistic is specified by Kwiatkowski et al. (1992) as in equation (5). 

)5.(..............................,.........2/
1

2







T

t

tSLM

 
In testing for stationarity in the levels of the series, Kwiatkowski et al. (1992) without considering the trend, 

et is considered as the residual from the regression of the series (Y) on an intercept only as shown in equation (6). 

)6.(..............................,.........Ytt Ye



 

 

 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

35 

 

2.2. The ARDL Model
 The ARDL model is used in defining the long run link among the variables. The model is specified as in 

equation (7).  

   

 
















1

1

1

0

,1,1

1,1,331,121110

)7..(........................................

...

m

i

n

i

tyitkikti

tkktttyyt

ezy

zbzbzbybtCCy

  

Equation (7) is an unrestricted error-correction model (ECM). The variable „y’ is regressed on variable „z’. 

Where „z‟ is a vector, that is, Z1, Z2 …, Zk (Belke and Polleit, 2006). The „b‟s measures the long run effects, and γ 

and α‟s are the short run parameters which measures the short run effects. The m and n are the order of lags, t is the 

time trend. According to Belke and Polleit (2006) „k‟ is the number of “forcing variables in the model under 

estimation. The null assumption (Ho) states that there is no cointegration among the variables in the model against 

the alternative assumption (H1) that the variables are cointegrated. That is, H0: b1=b2-b3= … =bk =0   Against the 

alternative hypothesis H1: Not H0. The rejection /Acceptance of the H0 is based on the Wald /F tests. The critical 

value provided by Pesaran et al. (2001) for the bound testing approach is used.  

There are two set of variables for upper limit and lower limit, for series integrated of order one I, (1) and those 

integrated of order zero I (0). It must be noted that the upper limit values are for series integrated of order one, I(1) 

where the lower limit values are for series integrated of order zero, I(0). The computed value (Fob/Wald critical) 

values are compared with the upper and lower limit values for the bound test at various levels of significance such as 

1%, 5% and 10%. In the interpretation of the results, if the computed F-statistics (Fob) lies between the upper limit 

and lower limits the results are considered as inconclusive, and one cannot talk about long run relationship or no long 

run relationship.  

In the case where the Fob is greater than the upper limit values, the Hoare not accepted which indicates significant 

cointegration relationship and statistical significant long run relationship. When the Fob is less than the lower limit 

values of the bound, the Ho is accepted, which means that there is statistical significant cointegration relationship, 

and possible long run relationship. 

In the estimation of the ARDL model, all the values in the model are used as dependent variables and the 

analysis is repeated. In the model in which cointegration relationship is identified, the model is estimated for the long 

run parameters or coefficients. 

The lag selection is based on information such as Akaike (AIC), Schwarz information criteria (SIC). The number 

of regressions estimated in the ARDL model according to Pesaran et al. (2001) is given by (n+1)
k
. where „n‟ is the 

maximum number of lags use in the model and K is the number of series variables in the model under estimation.  

In the ARDL model, aside the estimation of the long run coefficients, per the ARDL model, the error correction 

representation can also be estimated as in equation (8). 

  
  

 
p

i

s

i

q

k

ttktktitit eECMzxyy
1 1 1

111 )8........(....................
 

Equation (8) is used to estimate the short run relationship among the variables. The ARDL model estimated is 

assess for it goodness of fit using various diagnostic tests such as J-B Normality test, Breusch-Godfred LM test,  

ARCH LM test, White Heteroskedasticity test, Ramsey RESET. The stability of the model is tested using the 

cumulative sum of recursive residuals (CUSUM) and the cumulative sum of squares of recursive residuals (CUSUM 

sq). In the use of the two plots, CUSUM and CUSUMSQ, if the statistics stay within the critical bonds of 5% level of 

significance, the null hypothesis of all coefficients in the given regression are stable and cannot be rejected. 

 

2.3. Empirical Model 
The operation model used for estimating the fossil fuel consumption function is as specified in general form in 

equation (9), where FF= fossil fuel consumption; P= price; INV= investment; OPEN= trade openness; M2= money 

supply; Y= income and GE= government expenditure. The data for the estimation of the empirical model span from 

1970-2011 due to the availability of up to date data for the period. Empirical data is taken from World Bank 

Database.  

)9........(..........).........,,2,,,( GEYMOPENINVPfFFt   
 

3. Empirical Results, Discussions, and Analysis 
3.1 Unit Root Properties Tests 

3.1a. Time Series Plot in levels and First Differences of Variables  
The Time Series plot results shown in Figure 1 to Figure 7 indicate the series are not stationary in levels and 

achieved stationarity by differencing (Figure 8 to Figure 13). Since the variables are unit root in levels, shock to the 

variables might have permanent effect and not transitory effects. This calls for scientific investigation of the nature of 

unit root using the KPSS model of unit root. 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

36 

 

 
Figure-1. Time series Plot of Y in levels 

 

 
Figure-2. Time series Plot of GE in levels 

 

 
Figure-3. Time series Plot of M2 in levels 

 

 
Figure-4. Time series Plot of INV in levels 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

37 

 

 
Figure-5. Time series Plot of OPEN in levels 

 

 
Figure-6. Time series Plots of IN in levels 

 

 
Figure-7. Time series Plot of Fossil fuel (FF) use in levels 

 

 
Figure-8. Time series Plot of Y in 1st difference 

 

 
Figure-9. Time series Plot of GE in 1st difference 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

38 

 

 
Figure-10. Time series Plot of M2 in 1st difference 

 

 
Figure-11. Time series Plot of INV in 1st difference 

 

 
Figure-12. Time series Plot of OPEN in 1st difference 

 

 
Figure-13. Time series Plot of IN in 1st difference 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

39 

 

 
Figure-14. Time series Plot of FF Consumption in 1st difference 

 

3.1b. ADF Test (Without Structural Break) 
The results on the ADF test for unit root test are reported in Table 1. The results of the ADF test for unit root in 

levels show that the series are non-stationary in intercept. The null hypothesis of unit root was accepted for all the 

series.  

         
Table-1. ADF stationarity test results with a constant and trend 

Variables  t-statistics ADF/P-Value Results Lag length 

Y 4.85154 1.000 Not stationary 1 

Y-1
st
 dif. -2.08822 0.5519 Not stationary 1 

GE -2.46708 0.3419 Not stationary 1 

GE-1
st
 dif. -5.84979 0.0001062*** Stationary 1 

M2 -1.62565 0.7652 Not stationary 1 

M2-1
st
 dif. -5.98178 7.189e-005*** Stationary 1 

INV -2.92979 0.1642 Not stationary 1 

INV-1
st
 dif. -6.33633 1.653e-007*** Stationary 1 

OPEN -2.03577 0.5649 Not stationary 1 

OPEN-1
st
 dif. -5.43876 0.0003485*** Stationary 1 

IN 6.335 1.000 Not stationary 1 

IN-1
st
 dif. -3.00133 0.1445 Not stationary 1 

FF -2.76126 0.2191 Not stationary 1 

FF-1
st
 dif. -6.94919 3.485e-009*** Stationary 1 

Source: Author‟s computation, 2013/2014: Note: *** and ** denote significance at 1% and 5% levels of significance 

 

Taking the logarithm of the first difference of the series and testing these with intercept and trend makes series 

stationary. That is, the null hypothesis of unit root was rejected. The results are reported in Table 2. These results 

indicate that the series exhibit unit root processes in levels. 

 
Table-2. ADF stationarity test results with a constant and a time trend 

Variables(1
st
 dif.) t-statistics ADF/P-Value Results Lag length 

∆lnY -5.5524 0.0001*** Stationary 1 

∆lnGE -5.07122 0.0009815*** Stationary 1 

∆lnM2 -6.27268 2.988e-005*** Stationary 1 

∆lnINV -6.50775 1.438e-005*** Stationary 1 

∆lnOPEN -4.67444 0.0007281*** Stationary 1 

∆lnIN -4.7219 0.002565*** Stationary 1 

∆ln EC -5.43042 2.366e-005*** Stationary 1 

∆lnFF -7.24778 4.627e-010*** Stationary 1 

∆lnAEC -6.78405 6.467e-006*** Stationary 1 
                    Source: Author‟s computation, 2013/2014: Note: *** denotes significance at 1% level 

 

3.1c. The KPSS Test (Without Structural Breaks) 
The KPSS test is based on the null assumption (Ho) that the series variables under investigation are stationary 

(series are not unit root) against the alternative hypothesis (H1) that the series are not stationary (series are unit root). 

The KPSS is a reversed test for unit root. It is used in the current paper for confirmation of the stationarity properties 

of the series. The results are reported in Table 3 and Table 4. The series were examined in levels and in first 

difference (Table 3) as were as in their logarithm form (Table 4). The results in Table 3 indicate mixed results. Some 

series are unit root in levels but become stationary in first difference, indicating that they are integrated of order one, 

I(1). Series variables that are stationary at levels are integrated of other zero, I(0). The levels of significance are 1%; 

5% and 10%. Some series are stationary at 10% but not at 1% and 5%. The results based on logarithm form indicate 

the series are stationary in first difference. 

 

 

 

 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

40 

 

Table-3. KPSS stationarity test results with a constant and a time trend 

Variables  t-statistics P-Value Results Lag length 

Y 0.239611 n.a Not stationary 3 

Y-1
st
 dif. 0.230848 n.a Not stationary 3 

GE 0.107255 n.a Stationary 3 

GE-1
st
 dif. 0.0724631 n.a Stationary 3 

M2 0.192296 0.023 Stationary 3 

M2-1
st
 dif. 0.0694082 n.a Stationary 3 

INV 0.139794 0.067 Stationary 3 

INV-1
st
 dif. 0.147786 0.052 Stationary 3 

OPEN 0.134766 0.076 Stationary 3 

OPEN-1
st
 dif. 0.121051 n.a Stationary 3 

IN 0.272644 n.a Not stationary 3 

IN-1
st
 dif. 0.256955 n.a Not stationary 3 

FF 0.230714 n.a Not stationary 3 

FF-1
st
 dif. 0.0993028 n.a Stationary 3 

(Author‟s computation, 2013/2014): Critical values at 10%, 5% and 1% significant levels are 0.122   0.149   0.212 respectively 

 
Table-4. KPSS stationarity test results with a constant and a time trend 

Variable KPSS P-value Results Lag Length 

∆ln Y 0.105237 Stationary 3 

∆lnGE 0.0711901 Stationary 3 

∆lnM2 0.0759265 Stationary 3 

∆lnINV 0.127304 Stationary 3 

∆lnOPEN 0.103818 Stationary 3 

∆lnIN 0.0902278 Stationary 3 

∆FF 0.0871667 Stationary 3 
(Author‟s computation, 2013/2014): Note:  Critical values at 10%, 5% and 1% significant levels are 0.122   0.149   0.212  respectively 

 

3.2. The Cointegration Link, Long Run, and Short Run Estimates 

3.2a. The ARDL Bound Test 
The results reported in Table 5 indicate insignificant cointegration between fossil fuel consumption (FF) and the 

series variables in all the 7 models since the F-statistics values are less than the critical values of the upper bounds at 

the 90%, 95% and 99% levels of significance which is an indication of no cointegration among the series variables. 

The null assumption of no cointegration is not rejected in all the models.  

   
Table-5. Test for cointegration relationship 

  Critical bounds of the F -statistic: intercept and trend 

 

 

 

 

Models 

90% level   95% level          99% level 

           (0)I      (1)I  

          2.915    3.695 

     (0)I      (1)I  

    3.538   4.428 

 (0)I  (1)I   

5.155     6.265 

Computed F -Stats Decision 

1. FFF(FF/Y, OPEN, GE, IN, INV, M2) na Na 

2. FY(Y/FF, OPEN, GE, IN, INV, M2) 0.064066 Not Cointegrated 

3. FOPEN(OPEN/FF, Y, GE, IN, INV, M2) 0.42434 Not Cointegrated 

4. FGE(GE/FF, Y, OPEN, IN, INV, M2) 0.028877 Not Cointegrated 

5. FIN(IN/FF, Y, OPEN, GE, INV, M2) 0.0024545 Not Cointegrated 

6. FINV(INV/FF, Y, OPEN, GE, IN, M2) 1.0053 Not Cointegrated 

7. FM2(M2/FF, Y, OPEN, GE, IN, INV) 1.6218 Not Cointegrated 
         Source: Author‟s computation, 2013/2014: Note: critical values are obtained from Pesaran et al. (2001) and Narayan (2004). 

 

3.2b. The Long-Run Parametric (Elasticities) Results of the ARDL Test 
The long-run determinant of fossil fuel consumption was estimated with fossil fuel consumption is the dependent 

variable. The results as reported in Table 6 indicate that all the variables are not statistically significant determinants 

of fossil fuel consumption. In addition, the coefficients, which are essentially elasticity estimates, per the log run 

representation, are all inelastic. 

    
Table-6. Estimated long-run coefficients. Dependent variable is lnFF 

Variable Coefficient Std. Error T-ratio P-value 

Constant 1.3322 0.74748 1.7823 0.085* 

Trend 0.033949 0.053678 .63244 0.532 

lnY -0.085712 0.33863 -.25311 0.802 

lnOPEN 0.072535 0.11135 .65141 0.520 

lnGE 0.032240 0.18972 .16993 0.866 

lnIN -0.0086259 0.17411 -.049543 0.961 

lnINV -0.14873 0.14833 -1.0027 0.324 

lnM2 0.34292 0.26928 1.2735 0.212 
Author‟s computation, 2013/2014: ARDL (0) selected based on Akaike Information Criterion.  

Note: * denotes 10% significant level 

 



Economy, 2015, 2(1): 32-43 

 

 

 

 

41 

 

3.2c. The Short-Run Elasticities of the ARDL Model 
The results of short run dynamic equilibrium relationship coefficients estimated with trend, intercept, and error 

correction term (ecm) are reported in Table 7. The values of the short run coefficients are not different from that of 

the long run values since there is lack of cointegration link among the variables in the estimated model (See Table 5). 

The results indicate that all the variables are not statistically significant determinant of fossil fuel consumption in the 

short. The coefficient of -1.0000 indicates that, after 1 percent deviation or shock to the system, the long-run 

equilibrium relationship of fossil fuel consumption is quickly re-established at the rate of about 100% percent per 

annum. The value indicates a very stronger adjustment rate.  

 
Table-7. Short-run representation of ARDL model. ARDL (0) selected based on Akaike Information Criterion. Dependent 

variable:  ∆lnFF 

Variable  Coefficient Standard Error          T-Ratio Prob. Values 

Constant 1.3322 0.74748 1.7823 0.085* 

Trend 0.033949 0.053678 0.63244 0.532 

∆lnFF na na na Na 

∆lnY -0.085712 0.33863 -0.25311 0.802 

∆lnOPEN 0.072535 0.11135 0.65141 0.520 

∆lnGE 0.032240 0.18972 0.16993 0.866 

∆lnIN -0.0086259 0.17411 -0.049543 0.961 

∆lnINV -0.14873 0.14833 -1.0027 0.324 

∆lnM2 0.34292 0.26928 1.2735 0.213 

ecm (-1) -1.0000 0.000 Na Na 

ecm = LNFF-1.3322C-0.033949T + 0.085712LNY-0.072535LNOPEN-0.032240 

LNGE + 0.0086259LNIN + 0.14873LNINV-0.34292LNM2……..(10) 

R-Squared                     0.65746   R-Bar-Squared                   0.58011 

S.E. of Regression            0.13656   F-stat.    F(7,  31)    8.5001[0.000] 

Mean of Dependent Variable    3.0602   S.D. of Dependent Variable      0.21075 

Residual Sum of Squares       0.57813   Equation Log-likelihood        26.7858 

Akaike Info. Criterion       18.7858   Schwarz Bayesian Criterion     12.1316 

DW-statistic                  1.7463 
Source: Author‟s computation, 2013/2014.  

Note: * denotes statistical significance at the 10% level 

 

3.3. The Diagnostic and Stability Tests Results 
The diagnostic tests of the short-run estimation to examine the reliability of the results of the error correction 

model are reported in Table 8. The model passed only the Heteroscadasticity test indicating the variances are 

constant over time. The R
2
 (0.65746) and the adjusted R

2
 (0.58011) in Table 7 are an indication of a very well 

behave model. The coefficient indicate approximately 65.75% of the variations in fossil fuel consumption are 

attributed to the explanatory variable.  

 
Table-8. Short-Run Diagnostic Tests of ARDL Model 

Test Statistics LM Version F Version 

A:Serial Correlation CHSQ(1)=   .47329[.491]    F(1,  30)=   .36854[.548] 

B:Functional Form CHSQ(1)=   1.9411[.164]    F(1,  30)=   1.5713[.220] 

C:Normality CHSQ(2)=   1.0777[.583]        Not applicable 

D:Heteroscedasticity CHSQ(1)=   1.1890[.276]    F(1,  37)=   1.1635[.288] 

A:Lagrange multiplier test of residual serial correlation                   

B:Ramsey's RESET test using the square of the fitted values                 

C:Based on a test of skewness and kurtosis of residuals                     

D:Based on the regression of squared residuals on squared fitted values   

               Source: Author‟s computation, 2013/2014. 

 

Both stability tests (CUSUM and CUSUMSQ) as shown in Figure 15 and 16 revealed that the estimates and the 

variance were stable as the residuals and the squared residuals fall within the various 5% critical boundaries. The null 

assumptions are rejected in both tests. 

  

 
Figure 15. Plot of Cumulative sum of recursive residuals (CUSUM) 



Economy, 2015, 2(1): 32-43 

 

 

 

 

42 

 

 
Figure-16. Plot of Cumulative sum of squares of recursive residuals (CUSUMSQ) 

 

4. Conclusions 
This paper investigated the long run and short run determinants of fossil fuel consumption in Ghana for 1970-

2011 period, by using ARDL model. The results show that there is no long run and short-run determinant evidence 

for fossil fuel. Future changes in fossil fuel consumption could not be predicted using the variables in the model. The 

findings are not in line with the assumption underlying the paper. The findings are expected especially since the 

estimated model did not consider the issue of structural breaks over time.  

The findings do not support orthodox microeconomic contention that price and income influence the demand for 

a product (Mas-Colell et al., 2007). In addition, empirical findings reported by previous researchers (Hughes et al., 

2008; Askari and Krichene, 2010; Dargay and Gately, 2010; Lee and Lee, 2010; Faridul et al., 2011; Baumeister and 

Peersman, 2012; Fawcett and Price, 2012; Narayan and Wong, 2012; Schryder and Peersman, 2012) are not 

supported. These researchers reported that variables such as energy price, income, financial development, trade, 

government expenditure, and investment have significant influence on fossil fuel consumption.  

This is possibly the results of combining both micro and macro variables as regressors. The findings indicate the 

variables in the model could not be relied on as policy variables to manage fossil fuel consumption in the study area. 

Future studies should consider the issue of causality and structural breaks since the current study did not consider 

these issues. Other issues such as population and exchange rate should be considered in future models. Nonlinear 

models should be considered in future modelling of the determinants of fossil fuel consumption. 

 

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