TESTING FOR GRANGER CAUSALITY BETWEEN RENEWABLE ENERGY CONSUMPTION, GDP, CO2

EMISSION, AND FOSSIL FUEL PRICES IN THE USA.

MustafaYasinYenice Valbona Bejleri Mustafa.yenice@udc.edu vbejleri@udc.edu

University of the District of Columbia 4200 Connecticut Ave, NW, DC, 20008

Abstract: This paper examines the causal relationship between renewable energy consumption, GDP, CO2 emission and fossil fuel prices. Johensen cointegration method, Vector Error Correction Method, and Granger Causality are used for analysis. The data is taken from the US Energy Information Administration, and World Bank, World Development Indicators, 2012, covering the US data from 1949 to 2011. The results suggest that Fossil Fuel Price has a long term relationship with CO2, and Renewable energy consumption. In the short term, we found bidirectional causality between CO2 emission and Fossil Fuel prices. However, the presence of uni-directional causality seems to run from GDP as well as renewable energy to fossil fuel prices.

Keywords: Renewable Energy, Johensen cointegration, Vector Error Correction Model, Granger Causality, USA

1. Introduction

Beginning from the industrial revolution in the 1800s, energy from fossil

fuels, particularly oil, has been very important for economic growth, in manufacturing and industrial sectors. However, energy shortages and crises in the 1970s and recently global warming, climatic changes, and environmental pollution made it necessary to look for alternative energy sources. The sources of fossil fuel are being depleted. Fossil fuels are not renewable and cannot be produced naturally. Renewable energy is seen as an alternative to fossil fuels because of three main reasons [1]. Renewable energy is not depleted as fossil fuels, so it may potentially solve energy shortages and contribute to economic growth. Fossil fuel prices are increasing, while renewable energy can be a cheaper alternative. In addition, carbon dioxide (CO2) is considered to be the main driver of global warming and climate change, while renewable energy is clean.

Renewable energy is an abundant and replenishable source of energy, while other sources are finite and one day will be depleted. It is derived from different resources such as biomass, wind, solar, hydropower, and geothermal. All these renewable energy sources can be produced without damaging the ability to be produced in the future, while fossil fuels are not. The sun is a perfect example of a renewable energy source. It can provide huge amounts of power to use in our regular life. Wind is another example of renewable energy, as well. Wind turbines

can create a constant and abundant supply for individuals. So, there is no inadequacy of renewable energy from the sun, wind, and water.

It is a fact that when people use fossil fuels, carbon dioxides (greenhouse gas) are released to the earth. Greenhouse gases are considered one of the main reasons for global warming and climate change. Therefore, many researchers think that it is time to explore alternative energy sources that do not pollute the environment when they are generated. Renewable energy sources can be harnessed to generate electricity, process heat, fuel and beneficial chemicals with less impact on the environment.

Cost of renewable energy is still high. Therefore, many developed and developing countries are increasingly creating regulations and providing price incentives to support green energy. These countries support the development of energy efficiency; electricity transmission; battery technology; and different renewable energy technologies [2]. In particular they provide investments for weatherizing homes and buildings, grants for manufacturing of advanced batteries and components.

In this paper, we investigate the relationship between CO2 emission, fossil

fuel prices, the GDP, and renewable energy consumption in the USA. Also, some information about previous and future trends in renewable energy consumption presented. It consists of five sections. Section 2 is a review of the literature on renewable energy. Section 3 presents three tests (unit root, cointegration, granger causality) performed to prepare data for in depth analysis and to further investigate the relationships between renewable energy, fossil fuel prices, CO2 emission and GDP. The results are presented in section 4. In conclusion, section 5 summarizes the main findings of the research.

2. Literature Review

Empirical studies show that there is a strong correlation between energy consumption and economic growth. However, this hypothesis has not been proved specifically for renewable energy. Indeed [3] shows that the effect of the Gross Domestic Product (GDP) on renewable energy is mixed. The relationship between renewable energy and the GDP depends on the phase of deployment of renewables. Similarly, Marques and Fuinhas [3] also find the relevance of developing the use of renewables in the energy mix and on their consequences in relation to economic growth in 21 European Union (EU) countries. They find that renewable energy slows economic growth, in the period and for the EU countries analyzed. However, Perry Sadorsky’s [4] research shows that increasing global GDP will increase the consumption of renewable energy. He claims that economic policies that speed economic growth and development will lead to increases in renewable energy consumption.

When fossil fuels are burned their carbon is returned to the atmosphere in the form of CO2 which is considered to be the main reason of some environmental problems such as global warming, climate change, etc. Menyah and Rufeal[5] point out that renewable energy sources are believed to provide some solutions to the problems of energy security and climate change. However, they found no causality run on renewable energy consumption to CO2 emissions. The [5] shows that renewable energy consumption did not help in decreasing CO2 emissions. There is also evidence to suggest that the US has not reached the threshold point where renewable energy supply starts to mitigate CO2 emissions. According to Chiu and Chang [6], renewable energy supply has to account for 8.39% of the total energy supply before it starts to make any impact on mitigating CO2 emissions. It is important to note that the articles that claim renewable energy does not mitigate CO2 are written in 2009 or before. The recent data [7], [8] show that renewable energy supply accounts for more than 9% percent of total energy supply. Therefore, this may mean that renewable energy has started to mitigate the CO2 emissions.

Rafiq and Alam[9] analyze the determinants of renewable energy consumption in six major emerging economies; Brazil, China, India, Turkey, Indonesia, and Phillipinies that are proactively accelerating the adoption of renewable energy. They find that renewable energy consumption is significantly affected by income and pollutant emission for Brazil, China, India and Indonesia. However, for Philippines and Turkey, the GDP is likely to be the main driver for renewable energy consumption. In the short-run, for Brazil and China bi-directional causalities between renewable energy and income, and between renewable energy and pollutant emission are found.

Coban and Yorgancilar [10] investigate the relationship between economic growth and renewable energy in Turkey using the data from 1970 – 2006. The results of their study show that cointegration is determined between only GDP and wood, one of the renewable energy resources. Also, they find a cointegration relationship between wood and geothermal heating and again between wood and biomass. They show that there is a two way causality relationships between wood and biomass. Coban and Yorgancilar [10] find one-way causality relationship between GDP and biomass; between geothermal heating and GDP; between hydro and geothermal energy and biomass; between hydro and geothermal energy and wood; between geothermal heating and biomass and finally, between geothermal heating and wood.

Ucak [11] investigates the causal relationship between electricity generation from renewable resources and economic growth in The Organization for Economic Co-operation and Development (OECD) countries for 1980-2007. Using panel-data method, this study shows that

there is a long term positive relationship between renewable electricity generation and economic growth, and a one-way causality between these variables. The study finds that an increase in electricity generation from renewable sources contributes sustainable development and long term growth performance.

Shahbaz, et al. [12] examines the relationship between renewable energy consumption, the GDP and CO2 emission in Romania by using annual data for 1980-2008 using a cointegration and causality framework. The results are derived from alternative methodologies for the sake of robustness. They conclude that renewable energy consumption, the GDP and CO2 emission are cointegrated in the long-run. Both in the long and short-run, causality runs from CO2 emission and the GDP to renewable energy consumption. However, in both the real income and CO2 emission equations, there exists no causality between variables in the short-run.

3. Methodology

Model Specification: We assume at the given time (t), renewable energy consumption (REN) is a function of GDP, CO2, and fossil fuel prices (FPRICES).

RENt=F (GDPt, CO2t, FPRICESt), where RENt= Renewable Energy Consumption (Trillion\Btu) GDPt= Gross Domestic Product (US$) CO2t= CO2 Emission (Billion Metric Tons) FPRICES= Fossil Fuel Prices (Dollars per gallon) RENt= a1 + a2GDPt + a3CO2t + a4FPRICESt + Ut, (1) and Ut is the stochastic random term.

The Vector Error Correction Model (VECM) is estimated using annual data on global renewable energy consumption, income (GDP), CO2 emission and fossil fuel prices from 1949 to 2011. The time frame is determined by data availability on renewable energy consumption. In estimating the VECM, all variables are converted to natural logarithms in order to reduce heteroskedasticity. Renewable energy consumption, CO2 emission, fossil fuel prices are from the online database extracted from the US Energy Information Administration [7]. In addition, Real GDP data is taken from the World Bank, World Development Indicators, 2012 [8]. E-Views 6.0 software is used in order to obtain the results [13].

This study employs a five step procedure in order to determine the relationship between renewable energy, fossil fuel prices, CO2 emission and GDP. These five step procedure consist of unit Root test, taking log and differences, cointegration test with non-stationary data, developing the model, and testing the model with granger causality.

3.1. Unit Root Test

It is suggested that when dealing with time series data, a number of econometric issues can

influence the estimation of parameters using Ordinary Least Squares (OLS). Regressing a time series variable on another time series variable using the OLS estimation can result in a very high

R2, even although there is no meaningful relationship between the variables [14]. This situation reflects the problem of spurious regression between totally unrelated variables generated by a non-stationary process. Therefore, prior to testing Cointegration and implementing the Granger Causality test, the methodology needs to examine the stationary trends; for each individual time series. Most macro-economic data are non-stationary, i.e. they tend to exhibit a deterministic and/or stochastic trend. Therefore, it is recommended that a stationarity (unit root) test be carried out to test for the order of integration. In the case of non-stationary time series, we assume a time dependent mean in order for the standard assumptions for asymptotic analysis in the Granger test to be valid. Therefore, a stochastic process that is said to be stationary allows the correlation between any two values of y taken from different time periods to depend on the difference apart on time between the two values for all t≠s. We first test whether the series used in the regression process is a difference stationary or a trend stationary. The Augmented Dickey-Fuller (ADF) test is used to determine a unit root for the yt in the following equation

𝑛∆𝑦𝑡 = 1

= 𝛽1 + 𝛼𝑦𝑡−1 + γ ΣΔy𝑡−1 + ε𝑡 (2)

where yt represents all variables (in the natural logarithmic form) at time t, Δ is the first difference operator. β1 is a constant, n is the optimum number of lags on the dependent variable. The test for a unit root is conducted on the coefficient of yt-1 in the regression model. The null and alternative hypothesis for the existence of unit root in variable yt is: H0; α = 0 versus H1: α < 0. If the coefficient is significantly different from zero (less than zero) then the hypothesis that y contains a unit root is rejected. Rejection of the null hypothesis indicates stationarity in the series. 3.2 Johansen Cointegration Test

Cointegration, an econometric property of time series variables, is a precondition for the

existence of a long run or equilibrium economic relationship between two or more variables having unit roots, integrated of order one. The Johansen approach shows that two or more random variables are cointegrated if each of the series is themselves non-stationary, and they have a long run equilibrium relationship among the variables [15]. The purpose of the Cointegration tests is to determine whether a group of non - stationary series is cointegrated or not.

We have to examine whether or not there exists a long run relationship between variables (stable and non-spurious co-integrated relationship) that based on ADF test resulted as non-stationary time series. [16] Engle and Granger introduced the concept of cointegration where economic variables might reach a long-run equilibrium that reflects a stable relationship among them. The co-integration equations are of the form:

𝑦𝑡 = µ + Δ𝑦𝑡−1 + ⋯ + Δp 𝑦𝑡−𝑝 + 𝜀𝑡, (3) where yt is an n×1 vector of variables that are integrated of order commonly denoted (1) and εt is an n×1 vector of random errors.

Johansen’s methodology takes its starting point in the vector auto regression (VAR) of order p. VAR can be rewritten as Δ𝑦𝑡 = µ + n𝑦𝑡−1 + ∑ Δ𝑦𝑡−1

𝑝−1𝑖−1 + 𝜀𝑡 (4)

To determine the number of co-integration vectors, [17] this study suggested two test statistics, the first one is the trace (λ trace) and the second test statistic is the maximum eigenvalue (λ max). For more on this method, we suggest reading [17]. 3.3 Granger Causality

Historically, Granger and Sim [18] formalized the application of causality in economics. The standard Granger causality test [19] seeks to determine whether past values of a variable help predict changes in another variable. The null hypothesis (H0) in this case is that the X variable does not Granger cause variable Y and variable Y does not Granger cause variable X.

The vector autoregression (VAR) model is likely to be used for this purpose. However, Granger (1988) noted that if a set of variables are cointegrated, there must be short- and long-run causality which cannot be captured by the standard first difference VAR model. In this case, one can implement the Granger causality test with the VECM framework as follows:

∆𝑅𝐸𝑁𝑡 = 𝛼1 + �𝑏𝑖

𝑛

𝑖=1

∆𝐿𝑅𝐸𝑁𝑡−𝑖 + �𝑐𝑖

𝑛

𝑖=1

∆𝐿𝐺𝐷𝑃𝑡−𝑖 + �𝑑𝑖

𝑛

𝑖=1

∆𝐿𝐹𝑂𝑆𝑆𝐼𝐿𝑡−𝑖 + �𝑒𝑖

𝑛

𝑖=1

∆𝐿𝐶𝑂𝑁2𝑡−𝑖

+𝜆1𝐸𝐶𝑀𝑡−𝑖 + 𝑒𝑟1𝑡 (5)

∆𝐿𝐺𝐷𝑃𝑡 = 𝛼2 + �𝑐𝑖

𝑛

𝑖=1

∆𝐿𝐺𝐷𝑃𝑡−𝑖 + �𝑏𝑖

𝑛

𝑖=1

∆𝐿𝑅𝐸𝑁𝑡−𝑖 + �𝑑𝑖

𝑛

𝑖=1

∆𝐿𝐹𝑂𝑆𝑆𝐼𝐿𝑡−𝑖

+ ∑ 𝑒𝑖𝑛

𝑖=1 ∆𝐿𝐶𝑂𝑁2𝑡−𝑖 + 𝜆2𝐸𝐶𝑀𝑡−𝑖 + 𝑒𝑟2𝑡 (6)

∆𝐿𝐹𝑂𝑆𝑆𝐼𝐿𝑡 = 𝛼3 + �𝑑𝑖

𝑛

𝑖=1

∆𝐿𝐹𝑂𝑆𝑆𝐼𝐿𝑡−𝑖 + �𝑐𝑖

𝑛

𝑖=1

∆𝐿𝐺𝐷𝑃𝑡−𝑖 + �𝑏𝑖

𝑛

𝑖=1

∆𝐿𝑅𝐸𝑁𝑡−𝑖

+ ∑ 𝑒𝑖𝑛

𝑖=1 ∆𝐿𝐶𝑂𝑁2𝑡−𝑖 + 𝜆3𝐸𝐶𝑀𝑡−𝑖 + 𝑒𝑟3𝑡 (7)

∆𝐿𝐶𝑂2𝑡 = 𝛼4 + �𝑒𝑖

𝑛

𝑖=1

∆𝐿𝐶𝑂2𝑡−𝑖 + �𝑐𝑖

𝑛

𝑖=1

∆𝐿𝐺𝐷𝑃𝑡−𝑖 + �𝑏𝑖

𝑛

𝑖=1

∆𝐿𝑅𝐸𝑁𝑡−𝑖 + �𝑑𝑖

𝑛

𝑖=1

∆𝐿𝐹𝑂𝑆𝑆𝐼𝐿𝑡−𝑖

+ 𝜆4𝐸𝐶𝑀𝑡−𝑖 + 𝑒𝑟4𝑡, (8) where Δ is the first difference operator and L is the natural logarithm (ln).

The residuals erit are assumed to be normally distributed and white noise. ECMt-1 is the lagged

error-correction term derived from the cointegration equation. The ECMt-1 variable will be excluded from that model if the variables are not cointegrated. The optimal lag length n is determined by the

Akaike’s Information Criterion (AIC) because of its superior performance in small sample. We apply the Wald test to ascertain the direction of Granger causality between the variables of interest. In this study, we test the following hypotheses:

H01 : c1 = c2 =… = cn = 0, implying that GDP does not Granger-cause REN, H02 : d1 = d2 =… = dn =0, implying that FOSSIL does not Granger-cause REN, H03 : e1 = e2 =… = en =0, implying that CO2 does not Granger-cause REN,

and so on for the other variables. 4. Results 4.1. Unit Root Test

Table 1 shows that all the variables were not stationary in levels. This can be seen by comparing values of the ADF test statistics with the critical values of the test statistics at the 5% level of significance. Therefore, it is sufficient to conclude that there is a presence of unit. All the variables were differenced once the ADF test was conducted on them. Table 2 reveals that all the variables were stationary at first difference. Implying that the variables are integrated of order one, i.e. I(1). Figure 1 shows the line graph of raw data, log data and, first differences of log data. 4.2. Cointegration Test Result

Table 3 and Table 4 show the results of the cointegration test. Both the trace statistic and maximum eigenvalue statistic indicate that two cointegration equations are significant at the 5 %. These suggest that there is a long run relationship between the variables tested.

The Confident interval rank (R) can be formally used to test the trace and the maximum eigen value statistics [20]. The results presented in Table 3 and 4. Based on the results, H0: r = 2 is not rejected at the 5% level (11.48 < 15.40).

Table 5 shows that there exists a long run relationship between FPRICE as dependent variable, CO2, and REN as independent variables. This conclusion agrees with the a-priori expectation in this study. This implies that an increase in REN, would lead to an increase in FPRICE. However, increasing in CO2, would lead to a decrease in FPRICE.

4.3. The Result of Vector Error Correction Mechanism (VECM) and Granger Causality Test The results of the analysis based on vector error correction mechanism (VECM) and granger causality test is presented in table 6. The equation of error correction model is specified thus. The only significant variables are highlighted. ∆ (LCO2) = 0.0844728452592*ECM1 - 0.00821575607084*ECM2 - 0.0694973404132*∆ (LCO2(-1)) - 0.0937046804516*∆ (LCO2(-2)) - 0.094934164218*∆ (LFPRICE(-1)) - 0.0288408832929*∆ (LFPRICE(-2)) - 0.0378975490957*∆ (LGDP(-1)) - 0.0471124637099*∆ (LGDP(-2)) + 0.0542464236745*∆ (LREN(-1)) + 0.0346883798302*∆ (LREN(-2)) + 0.0204793624879

∆ (LFPRICE) = -0.1810382666627*ECM1 + 0.223187482732*ECM2 - 1.79566725588*∆ (LCO2(-1)) - 2.21639404457*∆ (LCO2(-2)) - 0.0884099378871*∆ (LFPRICE(-1)) - 0.229911458808*∆ (LFPRICE(-2)) + 2.26384739762*∆ (LGDP(-1)) + 1.51687946541*∆ (LGDP(-2)) + 1.04975270176*∆ (LREN(-1)) + 0.40897254073*∆ (LREN(-2)) - 0.190667395416 ∆ (LGDP) = 0.184687906251*ECM1 + 0.0272731455343*ECM2 - 0.129475185584*∆ (LCO2(-1)) - 0.00891604581949*∆ (LCO2(-2)) - 0.047451813484*∆ (LFPRICE(-1)) - 0.0298095003867*∆ (LFPRICE(-2)) + 0.147989955959*∆ (LGDP(-1)) + 0.0475861877833*∆ (LGDP(-2)) + 0.0283505917937*∆ (LREN(-1)) - 0.00658822145533*∆ (LREN(-2)) + 0.0529032477106 ∆ (LREN) = 0.421006586722*ECM1 + 0.0453445604024*ECM2 - 0.818664353117*∆ (LCO2(-1)) + 0.354372882556*∆ (LCO2(-2)) - 0.10360264893*∆ (LFPRICE(-1)) - 0.0821997959542*∆ (LFPRICE(-2)) + 0.12256130105*∆ (LGDP(-1)) - 1.03231915429*∆ (LGDP(-2)) - 0.098740860036*∆ (LREN(-1)) + 0.114527399139*∆ (LREN(-2)) + 0.0862981540687

According to the model, fossil fuel prices have a long-run relationship between CO2 emission and renewable energy consumption. The results show that, the coefficient of ECM1 (-1) is -0.18. It was properly signed and highly significant, indicating that the adjustment is in the right direction to restore the long-run relationship. If there was a change in the level of Fossil Fuel Price, ∆FPRICE ≠ 0, would be disequilibrium in last period (ECM ≠0), in which case some changes in FPRICE would be necessary to restore equilibrium. There was a change in the independent variables in the current period which was caused by changes in equilibrium condition; this implies that FPRICE should also change. The coefficient of ECM is the error correction or disequilibrium correction – coefficient. If the ECM coefficient is greater than zero it means there is a “surplus” in the dependent variable, therefore a reduction is required to restore equilibrium [21].

Table 6 indicates that there is a bi-directional Causality running between FPRICE and CO2 emissions. They are negative related, when fossil fuel prices increase one percent, CO2 emission decreases. Same relationship when CO2 emission increases, fossil prices decrease. Besides that, the results indicate a unidirectional causality from GDP to FPRICE. There is also a unidirectional causality from REN to FPRICE.

4.4 Diagnostic Tests

The model specified by equations 8,9,10, and 11 are subjected to three key econometric testing procedures [23]; autocorrelation, heteroscedasticity and structural break. We first carried out diagnostic tests on the ECMs in order to determine the efficiency, unbiasedness and consistency of the specifications.

Auto-correlation test using the LaGrange Multiplier-test is performed to find out if there is mutual statistical independence for the different disturbance terms. If the residuals do not fulfill this condition, then linear dependencies exist between the residuals and hence, they are said to be auto-correlated. The presence of autocorrelation makes ordinary least squares estimators (OLS) less efficient. Because the variance of the estimator is affected, the estimate of the confidence interval also becomes less reliable as shown in Table 7.

Heteroscedasticity test F statistics occurs when the assumption of constant variance of the disturbances is violated. Heteroscedastic might be the case when the variances are in some way dependent on the regressors appearing in the specified equation or when the equation fails to include

all relevant regressors. The presence of heteroscedasticity makes the OLS estimators inefficient in that the property of least variance no longer applies to these estimates. However, they continue to be unbiased and generally consistent. Since heteroscedasticity affects the variance of the parameters, significance tests of the parameters are unreliable as shown in Table 8.

Normality Test for insufficient or finite sample, the t, F, and chi-square statistics require the assumption of normality, it is necessary to check whether time series data follow the normal distribution before conducting other econometric tests. One of the most widely used normality tests is Jarque-Bera test. This test uses two moments: skewness and kurtosis. Skewness measures the degree to which a distribution is not symmetric with respect to its mean value and kurtosis measures the extent of heaviness of the distribution. A normal distribution has the property that skewness is equal to zero and the value of kurtosis is 3. On the other hand, a skewed distribution is not symmetric, and a leptokurtic distribution has heavier tails and higher peak than a normal distribution. If probability at a level of 0.05 of significance, we reject the null hypothesis that the residuals follow a normal distribution, and do not reject otherwise as shown on table 9.

Figure 2 shows the inverse roots of the AR characteristics. This test is used to ensure that the VECM is stable [24]. Each point is less than unity, which satisfies the stability condition.

5. Conclusion The environmental challenge facing many countries including the US is how to balance

sectorial energy supplies in order to produce more secure and cheap energy, and at the same, to reduce CO2 emission [5]. By using Johensen cointegration method, vector error correction method, and Granger causality for the US data from 1949 to 2011, this paper examined the causal relationship between renewable energy consumption, GDP, CO2 emission and fossil fuel prices.

The Granger causality test confirmed the presence of bi-directional causality which runs from

CO2 to fossil fuel prices and vice-versa. This implies that it may not be possible to reduce CO2 emission with using more fossil fuels (potentially leading to lower fossil fuel prices). There is a one-way causality from Renewable Energy consumption to fossil fuel prices. According to the Stern [2], the fossil fuel prices are increasing so renewable energy can be a cheaper alternative. The prices of oil have been rising steadily and the fossil fuel prices can be volatile and unpredictable. Also, from GDP to Fossil fuel prices there is a unidirectional relationship exist. One can say that, GDP growth drives oil growth. IMF [22] supports the idea that world GDP growth and world oil production growth tend to be highly correlated. The empirical results suggest that Fossil Fuel Prices has a long term relationship with CO2, and Renewable energy consumption. Menyah and Rufeal[5] found no causality run on renewable energy consumption to CO2 emissions. Also, the analyses have not found any causality between renewable energy consumption and CO2 emission. As a result, so far renewable energy consumption has not reached a level where it can make a significant contribution to emissions reduction.

This paper is part of the first author’s MS thesis work. For future work, it would be of

interest to predict the future consumption of renewable energy and compare with the other countries by using panel cointegration test.

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[20] Fadli Fizari Abu Hassan Asari, Nurul Syuhada Baharuddin, Nurmadihah Jusoh, A Vector Error Correction Model (VECM) Approach in Explaining the Relationship Between Interest Rate and Inflation Towards Exchange Rate Volatility in Malaysia,World Applied Sciences Journal, 49-56, 2011. [21] Abel Ariyo Awe ,Olalere Sunday Shina2, The Nexus between Budget Deficit and Inflation in the Nigerian Economy (1980 – 2009), Research Journal of Finance and Accounting, Paper, 2012.

[22] Impact of Oil limits on the economy, http://ourfiniteworld.com/2012/05/07/new-imf-working-paper-models-impact-of-oil-limits-on-the-economy/comment-page-2/

[23] Sifunjo E. Kisaka , Anthony Mwasaru, The Causal Relationship between Exchange Rates and Stock Prices in Kenya, Research Journal of Finance and Accounting, Paper, 2012.

[24] Lutkepohl, H. , New Introduction to Multiple Time Series Analysis, New York, Springer, ISBN 978-3-540-26239-8, 2005.

Tables Table 1 Unit Root test for Stationarity at Levels Levels ADF(t statistics) Probablity Decision LCO2 -2.488 0.1233 Do not reject Ho LGDP -1.0968 0.7117 Do not reject Ho LREN -0.1654 0.9368 Do not reject Ho LFPRICE -0.95 0.7638 Do not reject Ho Note: Significance at 5% level. Table 2 Unit Root test for Stationarity at First Difference (significance at 5% level) Levels ADF(t statistics) Probablity Decision ∆LCO2 -6.599 0.0000 Reject Ho ∆LGDP -8.2611 0.0000 Reject Ho ∆LREN -4.7954 0.0002 Reject Ho ∆LFPRICE -7.6539 0.0000 Reject Ho Table 3 Unrestricted Cointegration Rank Test (Trace) Hypothesized Trace 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * 0.578101 99.05583 47.85613 0.0000

At most 1 * 0.435958 46.41343 29.79707 0.0003 At most 2 0.169366 11.48318 15.49471 0.1835 At most 3 0.002679 0.163622 3.841466 0.6858

Trace test indicates 2 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Table 4 Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized Max-Eigen 0.05

No. of CE(s) Eigenvalue Statistic Critical Value Prob.** None * 0.578101 52.64240 27.58434 0.0000

At most 1 * 0.435958 34.93026 21.13162 0.0003 At most 2 0.169366 11.31955 14.26460 0.1389 At most 3 0.002679 0.163622 3.841466 0.6858

Max-eigenvalue test indicates 2 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Table 5 Normalized cointegrating coefficients 2 Cointegrating Equation(s): Log likelihood 456.7539 Normalized cointegrating coefficients (standard error in parentheses)

LFPRICE LGDP LREN LCO2 1.000000 0.000000 30.52625 -32.47706

(5.20379) (5.86358) 0.000000 1.000000 20.81476 -25.90763

(3.84500) (4.33251) Table 6. Granger Causality TEST

Null Hypothesis X2 Probablity Decision REN does not G. cause CO2 0.62 0.73 Do not Reject CO2 does not G. cause REN 4.27 0.11 Do not Reject REN does not G. cause FPRICE 8.17 0.0167** REJECT FPRICE does not G. cause REN 5.07 0.07 Do not Reject REN does not G. cause GDP 0.28 0.86 Do not Reject GDP does not G. cause REN 5.05 0.08 Do not Reject CO2 does not G. cause FPRICE 10.47 0.0053** REJECT FPRICE does not G. cause CO2 12.51 0.0013** REJECT CO2 does not G. cause GDP 0.56 0.75 Do not Reject GDP does not G. cause CO2 0.08 0.95 Do not Reject FPRICE does not G. cause GDP 5.69 0.058 Do not Reject GDP does not G. cause FPRICE 6.62 0.03** REJECT Notes: **denote significant at 5% Table 7 VEC Residual Serial Correlation LM Tests. Null Hypothesis: no serial correlation at lag order h Sample: 1949 2012; Included observations: 61

Lags LM-Stat Prob 1 11.20511 0.7967

2 11.60550 0.7707 3 13.82699 0.6116 4 13.85449 0.6096 5 11.65445 0.7674 6 14.31418 0.5753 7 4.454703 0.9979 8 19.39534 0.2487 9 17.50154 0.3539

10 8.761870 0.9229 11 12.94033 0.6771 12 13.52007 0.6344

Probs from chi-square with 16 df. Table 8 reports LM tests for no autocorrelation of the residuals. All p values

are larger than 5% indicating that the residuals do not exhibit any strong evidence of autocorrelation.

Table 9 VEC Residual Heteroskedasticity Tests Results VEC Residual Heteroskedasticity Tests: No Cross Terms (only levels and squares) Date: 10/02/13 Time: 03:08 Sample: 1949 2012 Included observations: 61

Joint test: Chi-sq df Prob. 213.4367 200 0.2449 We do not reject the null hypothesis which is no heteroskedasticity. Table 10 VEC Residual Normality Tests Results Orthogonalization: Cholesky (Lutkepohl) Null Hypothesis: residuals are multivariate normal Date: 10/01/13 Time: 10:36 Sample: 1949 2012 Included observations: 61

Component Skewness Chi-sq df Prob. 1 0.245303 0.611766 1 0.4341

2 0.115829 0.136399 1 0.7119 3 -0.088414 0.079473 1 0.7780 4 0.079269 0.063883 1 0.8005 Joint 0.891521 4 0.9258

Component Kurtosis Chi-sq df Prob. 1 3.047606 0.005760 1 0.9395

2 3.369564 0.347134 1 0.5557 3 2.377010 0.986463 1 0.3206 4 2.198449 1.632982 1 0.2013 Joint 2.972340 4 0.5625

Component Jarque-Bera df Prob. 1 0.617526 2 0.7344

2 0.483533 2 0.7852 3 1.065936 2 0.5869 4 1.696864 2 0.4281

Joint 3.863860 8 0.8692 Normality tests confirm that at the 5% level, the residuals from the VECM are normally distributed.

Figures

Figure 1: Line Graph of raw data, log data and, first differences of log data

2,000

3,000

4,000

5,000

6,000

7,000

1950 1960 1970 1980 1990 2000 2010

CO2

-.08

-.04

.00

.04

.08

.12

1950 1960 1970 1980 1990 2000 2010

DDLCO2

-.6

-.4

-.2

.0

.2

.4

.6

1950 1960 1970 1980 1990 2000 2010

DDLFPRICE

-.04

.00

.04

.08

.12

.16

1950 1960 1970 1980 1990 2000 2010

DDLGDP

-.2

-.1

.0

.1

.2

1950 1960 1970 1980 1990 2000 2010

DDLREN

1

2

3

4

5

6

7

1950 1960 1970 1980 1990 2000 2010

FPRICE

0

4,000

8,000

12,000

16,000

1950 1960 1970 1980 1990 2000 2010

GDP

7.6

7.8

8.0

8.2

8.4

8.6

8.8

1950 1960 1970 1980 1990 2000 2010

LCO2

0.0

0.4

0.8

1.2

1.6

2.0

1950 1960 1970 1980 1990 2000 2010

LFPRICE

5

6

7

8

9

10

1950 1960 1970 1980 1990 2000 2010

LGDP

14.8

15.2

15.6

16.0

16.4

1950 1960 1970 1980 1990 2000 2010

LREN

2,000,000

4,000,000

6,000,000

8,000,000

10,000,000

1950 1960 1970 1980 1990 2000 2010

REN

Figure 2. The inverse roots of the AR characteristics

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

Inverse Roots of AR Characteristic Polynomial