Multivariate Regression Analysis of Oil Price Volatility on GDP Growth in Kenya
Anthony Makau
Macroeconomic Statistics, Kenya National Bureau of Statistics, Nairobi, Kenya
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To cite this article:
Anthony Makau. Multivariate Regression Analysis of Oil Price Volatility on GDP Growth in Kenya. American Journal of Theoretical and Applied Statistics. Vol. 6, No. 1, 2017, pp. 44-51. doi: 10.11648/j.ajtas.20170601.16
Received: January 6, 2017; Accepted: January 16, 2017; Published: February 20, 2017
Abstract: Despite Oil being one of the key drivers of the world economy, the recent fluctuations in oil prices has brought concerns about possible slowdowns in economic growth globally. To cushion their economies from these oil price volatility shocks, a number of developing countries have made structural reforms in their macroeconomic policies as far as domestic petroleum pricing system is concerned. In line with this, Kenya has undertaken to reform the energy sector so as to make it competitive, efficient as well as attracting investment in the sector. The main objective of this study was to investigate if volatility of oil price had an effect on Kenya’s GDP growth rate with Exchange rate and Inflation rate as intervening variables. The study used quarterly data from KNBS, CBK and ERC for the periods 2004 to 2013 to achieve its objective and all analysis were done in R. Analysis showed that fluctuation of Crude oil price in the international market coupled with fluctuations in the exchange rate and inflation rate determined 86.9 per cent of the trend in GDP growth rate. The study found that when crude oil price increases by KSh 1,000 per barrel, the Kenya shilling weakens by a single Kenya shilling for every US dollar and the inflation rate goes up by 1 per cent, then the GDP growth rate decreases by 0.132 percentage points (p=0.000). The study also found that the model used had no serial autocorrelation meaning that the error terms of the regression model at any given two different quarters were linearly uncorrelated. Moreover, Goldfeld-Quandt test statistic was found to be significantly higher than 5% or 1% significance levels. This was despite a plot graph of residuals vs the fitted values of GDP growth rate showing unequal distribution of residuals as the values of fitted GDP growth rate increased. Therefore the model was free from heteroscedasticity. The government should therefore focus on stabilizing exchange rate, increase domestic energy production to reduce reliance on importation of petroleum products and control the level of inflation.
Keywords: Ordinary Least Square, Balance of Payments, Best Linear Unbiased Estimator, Foreign Direct Investment, Heteroscedasticity, Serial Autocorrelation
1. Introduction and Literature Review
1.1. Background of the Study
Oil is one of the key drivers of the economy others being economic output, unemployment, inflation, savings and investments. Since its discovery in the 20^{th}century, demand of oil and oil products mostly used in industries and automobiles has been constantly growing. Fluctuations of international oil price in the recent years have proven to be sources of vulnerability to developing economies. Just like any other developing countries, Kenya has had a lot of setback in its economic performance; from the ever rising inflation, fluctuation in exchange rates among others. Oil prices have acted as a major economic burden since global oil pricing of this crucial commodity is determined entirely by oil exporting countries, such as Saudi Arabia which produces 40% of the global oil and has 73% of the world’s proven oil reserves. This is reflected in the country’s current account of the Balance of Payment (BOP) statistics which has been worsening following the escalating international oil prices due to high demand for oil which has ballooned import bill, coupled with the weakening of the Kenya shilling against major world currencies such as the US dollar.
1.2. Review of Previous Studies on the Subject of Study
Jimenez-Rodriguez & Sanchez (2005) examined the effects of oil price shocks on the real economic activity of the major industrialized countries. They concluded that, oil price increase have an impact on GDP growth of a large magnitude than that of oil price declines, with the latter being statistically insignificant in most cases. Further, among the oil importing countries, oil price increase were found to have a negative impact on the economic activities [1]. A study on the impact of oil price shock and exchange rate volatility on economic growth conducted by Jin (2008) in Japan, the second largest net importer of crude oil after the United States, revealed that oil price increases exert negative impact on economic growth of both countries. Jin (2008) further accredited that the real GDP growth of Japan dropped from 2.5 per cent in 2006 to 1.6 per cent in 2007 owing to oil price shocks [2]. According to Mecheo and Omiti’s study of 2003, petroleum is a major source of energy in Kenya and accounts for over 80 per cent of the country’s commercial energy requirement. However, the study noted that changes in the international oil price are the reason behind the fluctuating import bill on petroleum imports [3]. Li and Zhao (2011) observed that crude oil price fluctuations from 1970s to 2011 have been increasingly erratic. This has led to worsening of terms of trade and BOP’s current account of oil importing countries like Kenya with an adverse impact on businesses, consumers, government budget and the economy at large [4]. Increase in energy prices lead to a considerable rise in production and transportation costs and as a result, wages and inflation goes up, leading to stunted economic growth (O’Neill, Penm and Terrell, 2008) [5]. Oriakhi and Osaze (2013) established that oil price volatility had a direct impact on real government expenditure, real exchange rate and real import, real money supply and inflation [6]. The relationship between crude oil price and economic growth varies depending on a country’s sectoral composition, institutional structures and macroeconomic policies among others (Chuku et al 2010) [7].
1.3. Statement of the Problem
Gonzalez and Nabiyev study in 2009 points out that fluctuation of oil price which have become more pronounced than they were in the 1990s have led to unpredictable consequences in an economy [8]. To be able to draw macroeconomic policies in a bid to cushion the economy from these oil price volatility shocks, it is necessary to establish the relationship between the country’s macroeconomic indicators and petroleum oil price fluctuations.
1.4. Significance of the Study
The study would be an eye opener to the current and would be investors in Kenya as they seek to know the vulnerability of investing in the economy. This is a key decision factor especially on Foreign Direct Investment. The government will be able to make informed policies that guide petroleum importation as well as other pertinent substitutes such as hydroelectric and renewable sources of energy to mitigate reliance on a single and unstable source of energy.
1.5. Objectives
General
Investigate the effect of oil price volatility on Kenya’s GDP growth rate using Multivariate Regression technique, exchange rate and inflation rate being the intervening variables.
Specific
i. Derive Multivariate parameter estimates using Ordinary Least Squares (OLS) method.
ii. Validate the OLS parameter estimates by testing and correcting for serial autocorrelation and heteroscedasticity.
iii. Ascertain oil price volatility effect on Kenya’s GDP growth rate, with exchange rate and inflation rate as intervening variables.
1.6. Study Limitations
The findings of this study are limited to the years 2004 to 2013. Thus the finding is a statistic and not a population parameter which is subject to an error margin. The exchange rate regime has undergone through numerous regimes making the study unrepresentative of the previous regimes. In this study, the exchange rate used was for US dollar to Kenya shillings. This is because most of Kenya’s imports especially petroleum products are bought using the US dollar.
2. Methodology
2.1. Introduction
This chapter discusses the methodology used to achieve the objectives under study.
2.2. Data Collection Technique
Data used for this study was sourced from administrative records. This included international crude oil prices from ERC, exchange rate (US Dollars to KSh) from CBK and GDP growth rate; and Inflation rate from KNBS.
2.3. Multivariate Model
The study examined if the trend in GDP growth rate can be explained by fluctuations of oil prices, exchange rate and inflation rate using multivariate linear regression model. Ordinary least square method was used to get the parameter estimates of the model. Multivariate model used to determine the effect of crude oil price on GDP growth rate as intervening variables were introduced one at a time was as follows;
(1)
2.4. Ordinary Least Square Parameter Estimation Method
Considering the above model, is the measure of change in the dependent variable y corresponding to a unit change in the independent variable with the other independent variables remaining constant. From equation (1) it follows that the OLS can be obtained by;
(2)
The above OLS can be minimized by differentiating partially equation (2) with respect to respectively and equating them to zero and replace with. From this procedure, (k+1) normal equations are obtained as follows;
(3)
Multiplying the above equation by and similarly repeating this procedure by multiplying equation by then until . The equations obtained are (k+1) normal equations;
.
.
.
These k+1 normal equations can be re-written in matrix notation as
(4)
Where:
,
and
is a column vector of OLS parameter estimates and is of full rank and the inverse of exists [9], [10].
Thus , which is the OLS parameter estimate of β becomes
(5)
2.5. Diagnostic Tests
2.5.1. Serial Autocorrelation
When the error term in one time period is positively correlated with the error term in the previous time period, we have the 1^{st} order positive autocorrelation.
Consider this model for illustration;
(6)
Where i.e. they are correlated
Let
Where; is some constant
Test for autocorrelation (Durbin Watson test)
The presence of 1^{st} order autocorrelation is detected by testing the significance of in in the following hypothesis;
At level of significance.
Durbin and Watson devised a statistic to test the above hypothesis. The test statistic is defined as;
(7)
Where; and
The above test statistic satisfies the inequality and , where is the k^{th} order serial correlation. If then , thus we fail to reject the null hypothesis implying that there is no serial correlation at the k^{th} order. Values of d close to 0 indicate positive serial autocorrelation, while values of d close to 4 imply negative serial autocorrelation [10].
2.5.2. Heteroscedasticity
If the OLS assumption that the variance of the error term is constant for all values does not hold, then we have the problem of heteroscedasticity.
Consider the model,
Where:
i. is normally distributed
ii.
iii.
iv.
With heteroscedasticity, the OLS estimates are still unbiased and consistent but inefficient (not BLUE) [10], [11].
Test for heteroscedasticity (Goldfelt-Quandt test)
The presence of heteroscedasticity in a two variable linear model can be tested by performing 2 separate regressions;
i For the small values of independent variable and
ii For large values of about of the total number of observations lying in the middle.
The ratio is tested to see if it’s significantly different from using the
Where;
a is the Error Sum of Squares of the 2^{nd}regression
b is the Error Sum of Squares of the 1^{st}regression
c and are the number of observations in the 2^{nd}and 1^{st} regression
d is the number of estimated parameters
The hypothesis is stated as;
The criterion will be to reject the null hypothesis of homoscedasticity if level of significance. If the hypothesis is not rejected, it implies that our model has unequal variance in the error term which can be corrected by transforming the linear model to obtain a homoscedasticity model; provided the assumption that holds, and consequently the OLS parameter estimates obtained using the new model will be a Best Linear Unbiased Estimator (BLUE) of [11].
Correcting for heteroscedasticity
The study will achieve this by transforming the above linear model by dividing it by to obtain a model which is free from heteroscedasticity.
Which we can denote as
(8)
Where
Where equation (8) is the new linear model free from heteroscedasticity i.e. homoscedastic model [9], [11].
3. Results and Discussion
3.1. Preliminary Analysis
GDP growth rate had a negative correlation with each of the three explanatory variables. As presented in Table1, every time crude oil price goes up by KSh 1,000, GDP growth rate dips by 0.165 percentage points. Similarly, if the Kenya shilling weakens against the US dollar by a single shilling and inflation rate goes up by 1 per cent, GDP growth rate decelerates by 0.059 and 0.470 percentage points respectively. If crude oil price goes up inflation also increases, if the shilling weakens against the US dollar, crude oil price goes up and finally if the shilling weakens against the US dollar the inflation goes up.
GDP growth rate | Crude oil price | Exchange rate | Inflation rate | |
GDP growth rate | 1.0000 | |||
Crude oil price | -0.1646 | 1.0000 | ||
Exchange rate | -0.0591 | 0.5878 | 1.0000 | |
Inflation rate | -0.4700 | 0.0992 | 0.1877 | 1.0000 |
3.2. Regression Analysis
3.2.1. Fitting Multivariate Regression Model
The fitted multivariate regression model was as follows;
(9)
Interpretation of the fitted model
When crude oil price increase by KSh 1,000 per barrel, the Kenya shilling weakens by a single Kenya shilling for every US dollar and the inflation rate goes up by 1 per cent, the GDP growth rate decreases by 0.132 percentage points (p=0.000). However, this decrease in GDP growth rate is 86.9 per cent of the actual decline as the model assumes in the absence of other indicators such as interest rates, the remaining 13.1 per cent is due to stochastic nature of the model.
3.2.2. Effect of Intervening Variables to the Multivariate Regression Model
Intervening variables were introduced to the regression model one at a time and the regression coefficient of the models tabulated in Table 2.
Model | Variables | R^{2} | Adjusted R^{2} | P-value |
Model1 | No intervening variable | 0.6816 | 0.6735 | 3.082e-11 |
Model2 | Inflation rate as the only intervening variable | 0.6829 | 0.6662 | 3.328e-10 |
Model3 | Exchange rate as the only intervening variable | 0.8315 | 0.8226 | 2.019e-15 |
Model4 | Both Exchange and Inflation rates as intervening variables | 0.8691 | 0.8585 | <2.2e-16 |
Analysis shows that fluctuation of crude oil price could only account for 68.2 per cent of the trend in GDP growth without any intervening variable being introduced in the model. Exchange rate was the most significant intervening variable to introduce to the model as compared to inflation rate. Regression coefficient shows that fluctuations in both the crude oil price and exchange rate explains 83.2 per cent of the behavior in GDP growth rate, while introducing the Inflation rate the adjusted R^{2} goes down by 1.3 percentage points meaning introducing inflation rate alone to the model was insignificant in explaining the trend in GDP growth rate. However 86.9 per cent of the trend in GDP growth rate was explained by fluctuation of crude oil price coupled with fluctuations in exchange rate and inflation rate.
3.3. Validating the Ordinary Least Square Parameter Estimates
In order to validate the OLS parameter estimates, a series of diagnostic tests were done.
3.3.1. Durbin-Watson Test Statistics for Serial Autocorrelation
Hypothesis
Test statistics
Durbin Watson statistic=1.5034
Interpretation and Conclusion
Since 1.5034 is not significantly different from 2 than it is to either 0 or 4; we fail to reject the null hypothesis at 5% significance level. The model therefore had no serial autocorrelation implying that the error terms of the regression model for any given two different quarters were linearly uncorrelated.
3.3.2. Test Statistics for Heteroscedasticity
A plot of residuals vs the fitted values of GDP growth rates was done to study the presence of heteroscedasticity.
In Figure 2, the top-left plot graph of residuals vs the fitted values of GDP growth rate, the graph shows that the residuals are not equally distributed as they seem to increase as the fitted GDP growth rate values increase implying the presence of heteroscedasticity.
Goldfeld-Quandt test statistic
Hypothesis
Test statistics
Goldfeld-Quandt statistic=0.90611, df1=17, df2=17, p-value=0.5794
Interpretation and Conclusion
Since the calculated p-value for the Goldfeld-Quandt test is significantly higher than 5% or 1% significance levels, the null hypothesis of homoscedasticity is not rejected. This is despite graph of residuals vs the fitted values of GDP growth rate showing unequal distribution of residuals as the values of fitted GDP growth rate increased. Therefore traces of heteroscedasticity exist although very insignificant at the given significance levels. The Multivariate Regression linear model was therefore found to be homoscedastic i.e. free from heteroscedasticity.
4. Conclusions and Recommendations
The Government should focus on stabilizing the exchange rate. A stable exchange rate will prevent significant fluctuation of the oil import bill attributed to the unexpected changes in the exchange rate. Secondly, the Government should increase domestic energy production in order to reduce its reliance on imported oil. This could be achieved through increasing the production of cheap and reliable energy such as solar, wind, coal and geothermal energy. In addition, the recently discovered oil wells should be exploited to meet the country’s oil demand. This is likely to reduce oil imports, there by promoting economic growth through a stable supply of cheap energy. Finally, controlling the level of inflation is very key for a sustainable economic growth. Therefore, policymakers should put measures in place that would keep inflation rate at low level.
Acknowledgement
My acknowledgement goes to Dr. Waititu and Dr. Mung’atu of Jomo Kenyatta University of Agriculture and Technology (JKUAT) for the knowledge they have imparted on me. Mr. Etwasi and Ms. Mercylline for their moral support.
R-CODE
a1<-cor(GDP.growth,GDP.growth) a2<-cor(GDP.growth,Crude.Oil.Price) a3<-cor(GDP.growth,Exchange.Rate) a4<-cor(GDP.growth,Inflation.Rate) b1<-cor(Crude.Oil.Price,Crude.Oil.Price) b2<-cor(Crude.Oil.Price,Exchange.Rate) b3<-cor(Crude.Oil.Price,Inflation.Rate) c1<-cor(Exchange.Rate,Exchange.Rate) c2<-cor(Exchange.Rate,Inflation.Rate) d1<-cor(Inflation.Rate,Inflation.Rate) #Correlationmatrix m<-matrix(c(a1,a2,a3,a4,a2,b1,b2,b3,a3,b2,c1,c2,a4,b3,c2,d1),nrow=4,ncol=4,byrow=TRUE) m # par(mfrow=c(2,2)) plot(Crude.Oil.Price,type="l",lwd=2,col="red",main="VolatilityofCrudeoilPrices",xlab="Period",ylab="CrudePricesin'000'KSh",ylim=c(10,100)) plot(Exchange.Rate,type="l",lwd=2,col="blue",main="VolatilityofExchangeRate",xlab="Period",ylab="KShperUSDollar",ylim=c(60,100)) plot(GDP.growth,type="l",lwd=2,col="green",main="GDPgrowthrate",xlab="Period",ylab="Ratein%",ylim=c(0,10)) plot(Inflation.Rate,type="l",lwd=2,col="orange3",main="VolatilityofInflation",xlab="Period",ylab="Ratein%",ylim=c(0,20)) # #withoutinterveningvariables model1<-lm(GDP.growth~-1+Crude.Oil.Price) summary(model1) #withexchangerateasinterveningvariable model2<-lm(GDP.growth~-1+Crude.Oil.Price+Exchange.Rate) summary(model2) #withinflationrateasinterveningvariable model3<-lm(GDP.growth~-1+Crude.Oil.Price+Inflation.Rate) summary(model3) #withExchangeandInflationratesasinterveningvariables model4<-lm(GDP.growth~-1+Crude.Oil.Price+Exchange.Rate+Inflation.Rate) summary(model4) # #SerialCorrelation #Durbin&WatsontestforSerialCorrelation library(lmtest) dwtest(model4) # #Heteroscedasticity #GoldfeldQuandttestforHeteroscedasticity gqtest(model4) #plottingtheresidualsversusthepredictedvalues par(mfrow=c(2,2)) plot(model4) # |
References