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The demand for gasoline in South Africa: An empirical analysis using co-integration techniques
Energy Economics 30 (2008) 3222–3229
Contents lists available at ScienceDirect
Energy Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e n e c o
The demand for gasoline in South Africa: An empirical analysis using co-integration techniques Oludele A. Akinboade ⁎, Emmanuel Ziramba, Wolassa L. Kumo Department of Economics, University of South Africa, P.O.Box 392, Pretoria 0003, South Africa
a r t i c l e
i n f o
Article history: Received 15 September 2007 Received in revised form 1 May 2008 Accepted 3 May 2008 Available online 16 May 2008 JEL classification: C22 R41 Keywords: Gasoline demand Bounds testing Co-integration
a b s t r a c t Using the recently developed Autoregressive Distributed Lag (ARDL) bound testing approach to co-integration, suggested by Pesaran et al. (Pesaran, M.H., Shin, Y., Smith, R.J. Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics 2001; 16(3) 289–326), we empirically analyzed the long-run relationship among the variables in the aggregate gasoline demand function over the period 1978–2005. Our study confirms the existence of a cointegrating relationship. The estimated price and income elasticities of −0.47 and 0.36 imply that gasoline demand in South Africa is price and income inelastic. © 2008 Elsevier B.V. All rights reserved.
1. Introduction South Africa is a middle income country and one of the most industrialized countries in Africa. Her economy is heavily dependent on energy. The urban population in South Africa has grown rapidly in recent years and in 2006 stood at about 58% of the total population in the country (World Bank, 2006). Given its relatively low average household income, South Africa has a high rate of car ownership. For every 1000 people, there are about 109 cars owned. This is high compared to 15 per 1000 in Lagos and 50 per 1000 in Nairobi (Satawu, 2006). The high car ownership means that 32% of commuters travel by private cars (Satawu, 2006). Table 1 contains the main energy indicators for South Africa. Gasoline consumption in South Africa has increased tremendously over the last three decades. From the table it can be seen that gasoline consumption more than doubled between 1975 and 2005. Over the same period oil supply to GDP ratio decreased from 12.9% to 9.8%. Overall, the economy's reliance on oil imports, as a proportion of GDP, decreased from 16.4% to 10.5% over the years. ⁎ Corresponding author. Tel.: +27 12 429 4782; fax: +27 12 429 3433. E-mail addresses: [email protected] (O.A. Akinboade), [email protected] (E. Ziramba), [email protected] (W.L. Kumo). 0140-9883/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.eneco.2008.05.002
O.A. Akinboade et al. / Energy Economics 30 (2008) 3222–3229
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Table 1 Oil indicators for South Africa
Gasoline consumption (thousand barrels per day) Oil supply/GDP (toe per thousand 2000 US$) Oil supply/population (toe per capita) Net oil imports/GDP (toe per thousand 2000 US$)
1975
1980
1985
1990
1995
2000
2005
96.4 0.129 0.429 0.164
88.6 0.111 0.383 0.158
109.3 0.093 0.304 0.123
146.1 0.095 0.301 0.102
188.5 0.099 0.293 0.112
178.7 0.088 0.266 0.101
191.5 0.098 0.332 0.105
Sources: International Energy Agency (various issues).
The main objective of this paper is to develop and test an econometric model to identify the main economic fundamentals that influence the behavior of motor gasoline consumption in South Africa. The empirical analysis is for the period 1978–2005, employing annual data. Income and price sensitivity of both the long- and the short-run demand for electricity are examined. The remainder of the paper is organized as follows: the next section reviews a selection of some of the empirical studies on gasoline demand. Section III outlines the empirical model specification used in this paper. The econometric techniques which are employed in this study are discussed in Section IV. Section V presents the empirical results of the study. The final section summarizes the main findings of the paper and gives their policy implications. 2. Literature review Empirical studies of the demand for gasoline have received considerable attention in both developed and developing countries (see Drollas, 1984; Graham and Glaister, 2002). There are several empirical studies that have examined the determinants of gasoline demand in a number of countries (see Table 2). Here we review only a few of the studies on the subject. A number of determinants for gasoline or energy demand have been considered in the empirical literature. In its simplest form, the demand for gasoline has been modelled as a function of real income and gasoline price (Eltony and Al-Mutairi, 1995; Birol and Guerer, 1993; Ramanathan, 1999). Bentzen (1994) in Denmark specifies gasoline demand as a function of a time trend (to capture the effect of increasing fuel efficiency), gasoline price and per capita vehicle stock. In such a specification, income only influences gasoline demand through the stock of vehicles. Eltony (1993), using a lagged endogenous model in a study of Gulf Cooperation Council countries, specifies gasoline demand as a function of real gasoline price, and per capita stock of automobiles. Birol and Guerer (1993), in a study of a number of developing countries, model gasoline demand as a function of income and price. Alves and Bueno (2003) in Brazil similarly estimate gasoline demand as a function of real per capita income, real gasoline price and real alcohol price. Polemis (2006) specifies gasoline demand for Greece as a function of a time trend, per capita income (GDP), real prices of gasoline and diesel as well as per capita vehicle fleet. The paper makes a methodological contribution to the literature on gasoline demand in South Africa. Using a more recent data set, this study uses the bounds test approach to co-integration to empirically isolate the price and income determinants of
Table 2 Selected empirical long-run results of the gasoline demand function estimation Sources
Price elasticity
Income elasticity
Study period
Country(ies)
Polemis (2006) Alves and Bueno (2003) Belhaj (2002) Ramanathan (1999) Eltony (1996) Eltony and Al-Mutairi (1995) Samini (1995) Bentzen (1994) (Cloete and Smit, 1988) Petrol
−0.38 −0.464 −0.30 −0.319 −0.17 −0.463 −0.12 −0.41 −0.37
0.79 0.1217 0.50 2.682 0.48 0.919 0.52
1978–2003 1974–1999 1970–1996 1972/3–1993/4 1975–1993 1970–1989
Greece Brazil Morocco India GCC countries Kuwait Australia Denmark South Africa
0.43
1948–1991 1970–1983
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gasoline demand in South Africa. This is important given the dynamics of the socioeconomic changes that have taken place in the country since the end of apartheid in 1994. The bounds test approach is an innovative and more efficient econometric methodology compared with approaches used in earlier studies. 3. Empirical specification and data The reviewed literature reveals that the demand for gasoline has been modelled in a variety of ways. The lagged endogenous model has been used extensively in the literature. That formulation of the gasoline demand model does not recognize the non-stationarity nature of the time series data. However, it is now widely recognized that most economic data series tend to be non-stationary (Asche, 1997: 229). Ignoring the non-stationarity nature of the economic data series could result in spurious relationships (Stanley, 2000). The most common variables that have been included in the estimation of gasoline demand models include real income, real price of gasoline, price of substitute energy source and per capita vehicle fleet. Given data constraints on most of these variables we estimate a simple model of gasoline demand. We specify gasoline demand as a function of per capita income and the real price of gasoline. We do not include the price of a substitute fuel and vehicle fleet variables because data on these variables were not available for the study period. Following the specifications of Bentzen (1994), Alves and Bueno (2003), Ramanathan (1999), and Polemis (2006), we specify our model of gasoline demand in log-linear form. Therefore our long-run gasoline demand takes the following form: LnGt ¼ α 0 þ α 1 ln Yt þ α 2 ln Pt þ et :
ð1Þ
Where lnGt, is the natural log of the annual per capita gasoline consumption (kt per capita) at time t, lnYt is the natural log of the annual real per capita income at time t, lnPt is the natural log of the annual real gasoline price (R/litre) at time t, and ε is a random error which is assumed to be white noise and normally and identically distributed. According to economic theory α1 and α2 are expected to be positive and negative respectively. Higher real per capita income will increase purchases of motor vehicles and hence increase gasoline consumption. Our model was estimated using annual time series data for the period 1978–2005. The main reason for not using an extended period is that the International Energy Agency (IEA) provides statistical data for gasoline prices in South Africa from 1978 onwards. The per capita consumption of gasoline (G) is measured in litres. These data are available from the IEA. Per capita GDP is expressed in constant 2000 prices and are obtained from the South African reserve bank. The energy prices for gasoline (P) are taken from “Energy prices and Taxes” (IEA) and have been deflated by the consumer price index (2000 = 100). The data on the consumer price index were obtained from the South African reserve bank. The population data came from the International Energy Agency. 4. Econometric methodology In the literature a number of studies have applied co-integration analysis to the modelling of gasoline demand (see Bentzen, 1994; Samini, 1995; Eltony and Al-Mutairi, 1995; Ramanathan, 1999; Alves and Bueno (2003); De Vita et al., 2006; Polemis, 2006). This paper has chosen a methodology based on the estimation of an unrestricted error-correction model (UECM). This has certain preference over other co-integration tests. First, it can be applied to studies that have finite samples unlike the Engle and Granger (1987) approach, which suffers from considerable small sample bias (Mah, 2000: 240). Second, the bounds test procedure is applicable irrespective of whether the underlying explanatory variables are integrated of order zero (I(0)) or one (I(1)) (Mah, 2000: 240). In other words, it avoids the pre-testing problems associated with standard co-integration analysis which requires the classification of variables into I(0) and I(1) (Pesaran et al., 2001). Third, Pattichis (1999; 1062) has argued that the UECM is likely to have better statistical properties because it does not push the short-run dynamics into the residual term as in the Engle and Granger (1987) technique. Fourth, another important advantage of the bounds test procedure is that estimation is possible even when the explanatory variables are endogenous, and is sufficient to simultaneously correct for residual serial correlation (Tang, 2004,
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2005). However, it has to be pointed out that this procedure (method) is inappropriate if there is more than one co-integrating relationship involving the dependent variable. In the present study, we specifically follow De Vita et al. (2006) in applying the bounds testing approach to co-integration analysis in analyzing gasoline demand for the case of South Africa. The bounds test approach to co-integration does not require the knowledge of the order of integration or co-integration ranks of the variables. By adopting Pesaran et al.'s (2001) approach for co-integration analysis, a pre-test for unit root (degree of integration) of the interested series is not necessary. As such, our test consists of estimating the following unrestricted error-correction model (UECM): p n ΔLnGt ¼ α 0 þ ∑m i¼1 α 1i Δ ln Gt−i þ ∑i¼0 α 2i Δ ln Yt−i þ ∑i¼0 α 3i Δ ln Pt−i þ η1 ln Yt−1 þ η2 ln Pt−1 þ η3 ln Gt−1 þ et :
ð2Þ
Where Δ denotes first difference, the other variables are as defined above. The co-integration equation is defined as ηˆ 1 ln Yt−1 þ ηˆ 2 ln Pt−1 þ ηˆ 3 ln Gt−1 ¼ 0:
ð3Þ
The bounds test methodology suggests analyzing the null hypothesis of no co-integration through a joint significance test of the lagged variables lnYt − 1, lnPt − 1, and lnGt − 1 based on the Wald or F-statistic: Ho : η1 ¼ η2 ¼ η3 ¼ 0 H1 : η1 ≠ 0; or η2 ≠ 0; or η3 ≠ 0: We test the null hypothesis of no co-integration by means of the F-test. Pesaran et al. (2001) have established that, under the null hypothesis of no co-integration and regardless of the degree of integration of the variables, the asymptotic distribution of the obtained F-statistic is non-standard. It follows an asymptotic χ2(m) under the null, where m is the number of restrictions. They develop two bounds of critical values for the different model specifications: upper bound applies when all variables are integrated of order one, I(1) and the lower bound applies when all the variables are stationary, I(0). If the computed F-statistic, for a chosen level of significance, exceeds the upper bound, the null hypothesis of no co-integration is rejected. If the F-statistic is lower than the lower bound then the null hypothesis cannot be rejected. If the F-statistic lies between the lower and the upper bounds, conclusive inference cannot be made. We adopt Hendry's ‘general to specific’ approach (Hendry et al., 1984) to determine the different lag lengths of the variables in the unrestricted error-correction model (UECM. First we introduce a relatively long lag length in the model. Next we gradually drop statistically insignificant variables in order to end up with a parsimonious model. Specification and diagnostic tests are presented to assess the appropriateness of the selected parsimonious model. From the estimated UECM, the long-run coefficients are the coefficients of the one-lagged explanatory variables (multiplied by a negative sign) divided by the coefficient of the lagged dependent variable (Bardsen, 1989). The respective long-run income and price coefficients are — (η1 / η3) and — (η2 / η3). These coefficients can be interpreted directly as elasticities. They are the focus of our empirical analysis. 5. Empirical results 5.1. Co-integration tests In order to perform bounds test we estimate a parsimonious UECM. Given our sample size, we start by introducing a lag length of three for the differenced variables. Following Hendry et al. (1984), we successively drop statistically non-significant variables. The preferred parsimonious UECM is presented in Table 3. The adequacy of this UECM is checked through a set of specification and diagnostic tests. The results of such tests are reported in Table 4 which shows that the parsimonious UECM passes all specification and diagnostic tests. The Ramsey RESET (2) test does not reject the null hypothesis of no misspecification in the functional form. The Jarque Bera test confirms the normality of the residuals. The Breusch–Godfrey LM test does not reject the null hypothesis of no serial correlation in the residuals. The
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Table 3 UECM for gasoline demand (dependent variable: (ΔlnGt) Regressor
Coefficient
t-statistic
ΔLNP ΔLNG(−2) ΔLNP(−3) ΔLNY(−3) LNG(−1) LNP(− 1) LNY(− 1) R2 adjusted DW
0.143774 0.375055 0.195794 −0.696987 −0.422971 −0.197311 0.151238 0.659 1.45
2.326856⁎⁎ 1.948892⁎ 2.368499⁎⁎ − 2.229179⁎⁎ − 5.854524⁎⁎⁎ − 3.852913⁎⁎⁎ 5.393208⁎⁎⁎
⁎⁎⁎, ⁎⁎, ⁎ indicate 1%, 5% and 10% significance level, respectively.
Table 4 Specification and diagnostic tests for the gasoline demand function Ramsey RESET (2) Jarque-Bera test Breusch–Godfrey LM test White's test ARCH test (2)
F-statistic: 2.34 (0.13) JB-statistic: 1.55 (0.46) F-statistic: 0.77 (0.48) Test statistic: 19.7 (0.10) F-statistic: 0.05 (0.95)
ARCH (2) test confirms that there is no evidence of autoregressive conditional heteroscedasticity. White's test does not reject the null hypothesis of no heteroscedasticity. Based on the estimated parsimonious UECM, we performed the bounds test using the following model specifications: no intercept and no trend (case I). We used the F-test to test for the significance of η1, η2 and η3 in Eq. (2). The results of the bounds test are presented in Table 5. The computed F-statistic is larger than the upper critical value. Thus, the null hypothesis of no co-integration, that is, η1 = η2 = η3 = 0, is rejected and we conclude that there is a stable long-run relationship among gasoline demand, income and price. The critical values come from Pesaran et al. (2001). Based on the variance–covariance matrix of coefficients in the UECM drawn from econometrics view software version 5 (Eviews 5), the variances of each long-run coefficient are computed using the method suggested by Bardsen (1989). The t-statistics of income and price elasticities are, respectively 12.0896 and −5.34747. 5.2. Income and price elasticity of gasoline demand The income elasticity of demand has a positive sign as is expected and is statistically significant in the long-run. The income variable is statistically significant at 1% level of significance. The long-run elasticity is 0.36. The sign of the computed income elasticity is in line with the theoretical expectations and is statistically significant. The results indicate that gasoline consumption is a normal good as it increases with income. The magnitude of the long-run income elasticity estimate is within the range of previous studies in other countries. Alves and Bueno (2003) found a long-run income elasticity estimate of 0.12 for Brazil. Cloete and Smit (1988) found an income elasticity estimate of 0.43 for petrol demand in South Africa. An
Table 5 Bounds tests co-integration test results Dependent variable
ΔlnGt ⁎⁎⁎Statistical significance at 1% level.
F-statistic
9.12⁎⁎⁎⁎
Critical bounds at 1% Lower bound I(0)
Upper bound (1)
3.88
5.30
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Table 6 Long-run elasticities of gasoline demand Income elasticity
Price elasticity
0.36 (12.0896)⁎⁎⁎
−0.47 (−5.34747)⁎⁎⁎
Numbers in the parentheses indicate t-statistics. The elasticities and variances (hence t-statistics) are computed using the methodology developed by Bardsen (1989). ⁎⁎⁎ indicates a 1% significance level.
increase in income will bring about a gradual increase in the derived demand for gasoline in the long-run as consumers buy more cars or move to bigger ones. However, our results suggest that demand for gasoline is both price and income inelastic (Table 6). The price elasticity is negative and statistically significant. The long-run price elasticity is −0.47. The sign of the computed price elasticity is in line with the theoretical expectations and is highly significant statistically. The price elasticity value is within range of previous studies in other countries. Eltony and Al-Mutairi (1995), in Kuwait, found a long-run price elasticity estimate of −0.46. The absence of reliable public transport and high costs of public transport could be an explanation for the low elasticity estimate. 5.3. Constancy of co-integration space After estimating the parsimonious model, the cumulative sum of recursive residuals (CUSUM) and the CUSUM of squares (CUSUMSQ) tests were applied to test for parameter constancy. Figs. 1 and 2 plot the CUSUM and CUSUM of squares statistics for Eq. (2). The results clearly indicate the absence of any instability of the coefficients during the investigated period because the plots of the two statistics are confined within the 5% critical bounds of parameter stability. 6. Summary and policy implications Econometric studies of the demand for gasoline for South Africa are few. It is important to estimate the price and income elasticities of gasoline for the possible relevance to the development of an appropriate energy policy for the country. Therefore, using the recently developed Autoregressive Distributed Lag (ARDL) bound testing approach to co-integration, suggested by Pesaran et al. (2001), we empirically analyzed the long-run relationship among the variables in the aggregate gasoline demand function over the period 1978–2005. Our study confirms the existence of a co-integrating relationship. The respective long-run price and income elasticities are −0.47 and 0.36. The signs of the computed elasticities are in line with the theoretical expectations. In order to perform bounds test a parsimonious UECM was estimated.
Fig. 1. CUSUM graph for the model.
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Fig. 2. CUSUM squares graph for the model.
The suitability of this UECM was assessed through a set of specification and diagnostic tests. The model passes these tests. The stability of the parameter estimates was also assessed. Gasoline demand studies have important practical implications. The results indicate that the estimated gasoline demand function can be used for policy purposes since it is stable. The finding that a stable aggregate gasoline demand function seems to exist, would make forecasting of gasoline need at the national level possible. The estimated price and income elasticities of −0.47 and 0.36 imply that gasoline demand in South Africa is price and income inelastic. Public transport system in South Africa is unreliable and inefficient. This forces households to rely on private vehicles for their mobility. Our results hence show that price increases alone will not discourage gasoline consumption and that the increases in income will only induce small increases in gasoline demand. These results could assist policy makers in isolating the distributional impact of their energy policy in South Africa. References Alves, D.C.O., Bueno, R.D., 2003. Short-run, long-run and cross elasticities of gasoline demand in Brazil. Energy Economics 25, 191–199. Asche, F., 1997. Dynamic adjustment in demand equations. Marine Resource Economics 12, 221–237. Bardsen, G., 1989. Estimation of long-run coefficients in error correction models. Oxford Bulletin of Economics and Statistics 51 (3), 345–350. Belhaj, M., 2002. Vehicle and fuel demand in Morocco. Energy Policy 30 (2), 1163–1171. Bentzen, J., 1994. An empirical analysis of gasoline demand in Denmark using co integration techniques. Energy Economics 16,139–143. Birol, F., Guerer, N., 1993. Modelling the transport sector fuel demand for developing economies. Energy Policy 1163–1172 (December). Cloete, S.A., Smit, E. vd. M., 1988. Policy implications of the price elasticity of demand for petrol in South Africa. South African Journal of Science 84, 227–229. De Vita, G., Endresen, K., Hunt, L.C., 2006. An empirical analysis of energy demand in Namibia. Energy Economics 34, 3447–3463. Drollas, L.P., 1984. The demand for gasoline: further evidence. Energy Economics 71–82. Eltony, M.N., 1993. The demand for gasoline in the GCC: an application of pooling and testing procedures. Energy Economics 18 (3), 203–209. Eltony, M.N., 1996. Demand for Gasoline in the GCC: An Application of Pooling and Testing Procedures. Eltony, M.N., Al-Mutairi, N.H., 1995. Demand for gasoline in Kuwait: an empirical analysis using co integration techniques. Energy Economics 17 (3), 249–253. Engle, R.F., Granger, C.W.J., 1987. Cointegration and error correction: representation, estimation and testing. Econometrica 55, 251–276. Graham, D.J., Glaister, S., 2002. The demand for automobile fuel: a survey of elasticities. Journal of transport Economics and Policy 36 (1), 1–26. Hendry, D.F., Pagan, A., Sargan, J.D., 1984. Dynamic specification. In: Griliches, Z., Intrilligator, M. (Eds.), Handbook of Econometrics, vol. 2. North Holland, Amsterdam. International Energy Agency, several years,. Energy Statistics and Balances of non-OECD countries (various issues). Mah, J.S., 2000. An empirical examination of the disaggregated import demand of Korea — the case of information technology products. Journal of Asian Economics 11, 237–244. Pattichis, C.A., 1999. Price and income elasticities of disaggregated import demand: results from UECMs and an application. Applied Economics 31, 1061–1071. Pesaran, M.H., Shin, Y., Smith, R.J., 2001. Bounds testing approaches to the analysis of level relationships. Journal of Applied Econometrics 16 (3), 289–326.
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Polemis, M.L., 2006. Empirical assessment of the determinants of road energy demand in Greece. Energy Economics 28, 385–403. Ramanathan, R., 1999. Short- and long-run elasticities of gasoline demand in India: an empirical analysis using co integration techniques. Energy Economics 21, 321–330. Samini, R., 1995. Road transport energy demand in Australia. Energy economics 17 (4), 329–339. Satawu. Notes on the transport industry in South Africa. The 41st Congress of the ITF. Information and Document Centre. 2006; available from http://www.itfglobal.org/congress/SAtransport.cfm, accessed 16 November 2007. Stanley, T.D., 2000. An empirical critique of the Lucas critique. Journal of Socio-Economics 29 (1), 91–107. Tang, T.C., 2004. Demand for broad money and expenditure components in Japan: an empirical study. Japan and the World Economy 16, 487–502. Tang, T.C., 2005. Revisiting South Korea's import demand behaviour: a co integration analysis. Asian Economic Journal 19 (1), 29–50. World Bank, 2006. The Little Green Data Book. World Bank, Washington DC.
Contents lists available at ScienceDirect
Energy Economics j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e n e c o
The demand for gasoline in South Africa: An empirical analysis using co-integration techniques Oludele A. Akinboade ⁎, Emmanuel Ziramba, Wolassa L. Kumo Department of Economics, University of South Africa, P.O.Box 392, Pretoria 0003, South Africa
a r t i c l e
i n f o
Article history: Received 15 September 2007 Received in revised form 1 May 2008 Accepted 3 May 2008 Available online 16 May 2008 JEL classification: C22 R41 Keywords: Gasoline demand Bounds testing Co-integration
a b s t r a c t Using the recently developed Autoregressive Distributed Lag (ARDL) bound testing approach to co-integration, suggested by Pesaran et al. (Pesaran, M.H., Shin, Y., Smith, R.J. Bounds Testing Approaches to the Analysis of Level Relationships. Journal of Applied Econometrics 2001; 16(3) 289–326), we empirically analyzed the long-run relationship among the variables in the aggregate gasoline demand function over the period 1978–2005. Our study confirms the existence of a cointegrating relationship. The estimated price and income elasticities of −0.47 and 0.36 imply that gasoline demand in South Africa is price and income inelastic. © 2008 Elsevier B.V. All rights reserved.
1. Introduction South Africa is a middle income country and one of the most industrialized countries in Africa. Her economy is heavily dependent on energy. The urban population in South Africa has grown rapidly in recent years and in 2006 stood at about 58% of the total population in the country (World Bank, 2006). Given its relatively low average household income, South Africa has a high rate of car ownership. For every 1000 people, there are about 109 cars owned. This is high compared to 15 per 1000 in Lagos and 50 per 1000 in Nairobi (Satawu, 2006). The high car ownership means that 32% of commuters travel by private cars (Satawu, 2006). Table 1 contains the main energy indicators for South Africa. Gasoline consumption in South Africa has increased tremendously over the last three decades. From the table it can be seen that gasoline consumption more than doubled between 1975 and 2005. Over the same period oil supply to GDP ratio decreased from 12.9% to 9.8%. Overall, the economy's reliance on oil imports, as a proportion of GDP, decreased from 16.4% to 10.5% over the years. ⁎ Corresponding author. Tel.: +27 12 429 4782; fax: +27 12 429 3433. E-mail addresses: [email protected] (O.A. Akinboade), [email protected] (E. Ziramba), [email protected] (W.L. Kumo). 0140-9883/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.eneco.2008.05.002
O.A. Akinboade et al. / Energy Economics 30 (2008) 3222–3229
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Table 1 Oil indicators for South Africa
Gasoline consumption (thousand barrels per day) Oil supply/GDP (toe per thousand 2000 US$) Oil supply/population (toe per capita) Net oil imports/GDP (toe per thousand 2000 US$)
1975
1980
1985
1990
1995
2000
2005
96.4 0.129 0.429 0.164
88.6 0.111 0.383 0.158
109.3 0.093 0.304 0.123
146.1 0.095 0.301 0.102
188.5 0.099 0.293 0.112
178.7 0.088 0.266 0.101
191.5 0.098 0.332 0.105
Sources: International Energy Agency (various issues).
The main objective of this paper is to develop and test an econometric model to identify the main economic fundamentals that influence the behavior of motor gasoline consumption in South Africa. The empirical analysis is for the period 1978–2005, employing annual data. Income and price sensitivity of both the long- and the short-run demand for electricity are examined. The remainder of the paper is organized as follows: the next section reviews a selection of some of the empirical studies on gasoline demand. Section III outlines the empirical model specification used in this paper. The econometric techniques which are employed in this study are discussed in Section IV. Section V presents the empirical results of the study. The final section summarizes the main findings of the paper and gives their policy implications. 2. Literature review Empirical studies of the demand for gasoline have received considerable attention in both developed and developing countries (see Drollas, 1984; Graham and Glaister, 2002). There are several empirical studies that have examined the determinants of gasoline demand in a number of countries (see Table 2). Here we review only a few of the studies on the subject. A number of determinants for gasoline or energy demand have been considered in the empirical literature. In its simplest form, the demand for gasoline has been modelled as a function of real income and gasoline price (Eltony and Al-Mutairi, 1995; Birol and Guerer, 1993; Ramanathan, 1999). Bentzen (1994) in Denmark specifies gasoline demand as a function of a time trend (to capture the effect of increasing fuel efficiency), gasoline price and per capita vehicle stock. In such a specification, income only influences gasoline demand through the stock of vehicles. Eltony (1993), using a lagged endogenous model in a study of Gulf Cooperation Council countries, specifies gasoline demand as a function of real gasoline price, and per capita stock of automobiles. Birol and Guerer (1993), in a study of a number of developing countries, model gasoline demand as a function of income and price. Alves and Bueno (2003) in Brazil similarly estimate gasoline demand as a function of real per capita income, real gasoline price and real alcohol price. Polemis (2006) specifies gasoline demand for Greece as a function of a time trend, per capita income (GDP), real prices of gasoline and diesel as well as per capita vehicle fleet. The paper makes a methodological contribution to the literature on gasoline demand in South Africa. Using a more recent data set, this study uses the bounds test approach to co-integration to empirically isolate the price and income determinants of
Table 2 Selected empirical long-run results of the gasoline demand function estimation Sources
Price elasticity
Income elasticity
Study period
Country(ies)
Polemis (2006) Alves and Bueno (2003) Belhaj (2002) Ramanathan (1999) Eltony (1996) Eltony and Al-Mutairi (1995) Samini (1995) Bentzen (1994) (Cloete and Smit, 1988) Petrol
−0.38 −0.464 −0.30 −0.319 −0.17 −0.463 −0.12 −0.41 −0.37
0.79 0.1217 0.50 2.682 0.48 0.919 0.52
1978–2003 1974–1999 1970–1996 1972/3–1993/4 1975–1993 1970–1989
Greece Brazil Morocco India GCC countries Kuwait Australia Denmark South Africa
0.43
1948–1991 1970–1983
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gasoline demand in South Africa. This is important given the dynamics of the socioeconomic changes that have taken place in the country since the end of apartheid in 1994. The bounds test approach is an innovative and more efficient econometric methodology compared with approaches used in earlier studies. 3. Empirical specification and data The reviewed literature reveals that the demand for gasoline has been modelled in a variety of ways. The lagged endogenous model has been used extensively in the literature. That formulation of the gasoline demand model does not recognize the non-stationarity nature of the time series data. However, it is now widely recognized that most economic data series tend to be non-stationary (Asche, 1997: 229). Ignoring the non-stationarity nature of the economic data series could result in spurious relationships (Stanley, 2000). The most common variables that have been included in the estimation of gasoline demand models include real income, real price of gasoline, price of substitute energy source and per capita vehicle fleet. Given data constraints on most of these variables we estimate a simple model of gasoline demand. We specify gasoline demand as a function of per capita income and the real price of gasoline. We do not include the price of a substitute fuel and vehicle fleet variables because data on these variables were not available for the study period. Following the specifications of Bentzen (1994), Alves and Bueno (2003), Ramanathan (1999), and Polemis (2006), we specify our model of gasoline demand in log-linear form. Therefore our long-run gasoline demand takes the following form: LnGt ¼ α 0 þ α 1 ln Yt þ α 2 ln Pt þ et :
ð1Þ
Where lnGt, is the natural log of the annual per capita gasoline consumption (kt per capita) at time t, lnYt is the natural log of the annual real per capita income at time t, lnPt is the natural log of the annual real gasoline price (R/litre) at time t, and ε is a random error which is assumed to be white noise and normally and identically distributed. According to economic theory α1 and α2 are expected to be positive and negative respectively. Higher real per capita income will increase purchases of motor vehicles and hence increase gasoline consumption. Our model was estimated using annual time series data for the period 1978–2005. The main reason for not using an extended period is that the International Energy Agency (IEA) provides statistical data for gasoline prices in South Africa from 1978 onwards. The per capita consumption of gasoline (G) is measured in litres. These data are available from the IEA. Per capita GDP is expressed in constant 2000 prices and are obtained from the South African reserve bank. The energy prices for gasoline (P) are taken from “Energy prices and Taxes” (IEA) and have been deflated by the consumer price index (2000 = 100). The data on the consumer price index were obtained from the South African reserve bank. The population data came from the International Energy Agency. 4. Econometric methodology In the literature a number of studies have applied co-integration analysis to the modelling of gasoline demand (see Bentzen, 1994; Samini, 1995; Eltony and Al-Mutairi, 1995; Ramanathan, 1999; Alves and Bueno (2003); De Vita et al., 2006; Polemis, 2006). This paper has chosen a methodology based on the estimation of an unrestricted error-correction model (UECM). This has certain preference over other co-integration tests. First, it can be applied to studies that have finite samples unlike the Engle and Granger (1987) approach, which suffers from considerable small sample bias (Mah, 2000: 240). Second, the bounds test procedure is applicable irrespective of whether the underlying explanatory variables are integrated of order zero (I(0)) or one (I(1)) (Mah, 2000: 240). In other words, it avoids the pre-testing problems associated with standard co-integration analysis which requires the classification of variables into I(0) and I(1) (Pesaran et al., 2001). Third, Pattichis (1999; 1062) has argued that the UECM is likely to have better statistical properties because it does not push the short-run dynamics into the residual term as in the Engle and Granger (1987) technique. Fourth, another important advantage of the bounds test procedure is that estimation is possible even when the explanatory variables are endogenous, and is sufficient to simultaneously correct for residual serial correlation (Tang, 2004,
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2005). However, it has to be pointed out that this procedure (method) is inappropriate if there is more than one co-integrating relationship involving the dependent variable. In the present study, we specifically follow De Vita et al. (2006) in applying the bounds testing approach to co-integration analysis in analyzing gasoline demand for the case of South Africa. The bounds test approach to co-integration does not require the knowledge of the order of integration or co-integration ranks of the variables. By adopting Pesaran et al.'s (2001) approach for co-integration analysis, a pre-test for unit root (degree of integration) of the interested series is not necessary. As such, our test consists of estimating the following unrestricted error-correction model (UECM): p n ΔLnGt ¼ α 0 þ ∑m i¼1 α 1i Δ ln Gt−i þ ∑i¼0 α 2i Δ ln Yt−i þ ∑i¼0 α 3i Δ ln Pt−i þ η1 ln Yt−1 þ η2 ln Pt−1 þ η3 ln Gt−1 þ et :
ð2Þ
Where Δ denotes first difference, the other variables are as defined above. The co-integration equation is defined as ηˆ 1 ln Yt−1 þ ηˆ 2 ln Pt−1 þ ηˆ 3 ln Gt−1 ¼ 0:
ð3Þ
The bounds test methodology suggests analyzing the null hypothesis of no co-integration through a joint significance test of the lagged variables lnYt − 1, lnPt − 1, and lnGt − 1 based on the Wald or F-statistic: Ho : η1 ¼ η2 ¼ η3 ¼ 0 H1 : η1 ≠ 0; or η2 ≠ 0; or η3 ≠ 0: We test the null hypothesis of no co-integration by means of the F-test. Pesaran et al. (2001) have established that, under the null hypothesis of no co-integration and regardless of the degree of integration of the variables, the asymptotic distribution of the obtained F-statistic is non-standard. It follows an asymptotic χ2(m) under the null, where m is the number of restrictions. They develop two bounds of critical values for the different model specifications: upper bound applies when all variables are integrated of order one, I(1) and the lower bound applies when all the variables are stationary, I(0). If the computed F-statistic, for a chosen level of significance, exceeds the upper bound, the null hypothesis of no co-integration is rejected. If the F-statistic is lower than the lower bound then the null hypothesis cannot be rejected. If the F-statistic lies between the lower and the upper bounds, conclusive inference cannot be made. We adopt Hendry's ‘general to specific’ approach (Hendry et al., 1984) to determine the different lag lengths of the variables in the unrestricted error-correction model (UECM. First we introduce a relatively long lag length in the model. Next we gradually drop statistically insignificant variables in order to end up with a parsimonious model. Specification and diagnostic tests are presented to assess the appropriateness of the selected parsimonious model. From the estimated UECM, the long-run coefficients are the coefficients of the one-lagged explanatory variables (multiplied by a negative sign) divided by the coefficient of the lagged dependent variable (Bardsen, 1989). The respective long-run income and price coefficients are — (η1 / η3) and — (η2 / η3). These coefficients can be interpreted directly as elasticities. They are the focus of our empirical analysis. 5. Empirical results 5.1. Co-integration tests In order to perform bounds test we estimate a parsimonious UECM. Given our sample size, we start by introducing a lag length of three for the differenced variables. Following Hendry et al. (1984), we successively drop statistically non-significant variables. The preferred parsimonious UECM is presented in Table 3. The adequacy of this UECM is checked through a set of specification and diagnostic tests. The results of such tests are reported in Table 4 which shows that the parsimonious UECM passes all specification and diagnostic tests. The Ramsey RESET (2) test does not reject the null hypothesis of no misspecification in the functional form. The Jarque Bera test confirms the normality of the residuals. The Breusch–Godfrey LM test does not reject the null hypothesis of no serial correlation in the residuals. The
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Table 3 UECM for gasoline demand (dependent variable: (ΔlnGt) Regressor
Coefficient
t-statistic
ΔLNP ΔLNG(−2) ΔLNP(−3) ΔLNY(−3) LNG(−1) LNP(− 1) LNY(− 1) R2 adjusted DW
0.143774 0.375055 0.195794 −0.696987 −0.422971 −0.197311 0.151238 0.659 1.45
2.326856⁎⁎ 1.948892⁎ 2.368499⁎⁎ − 2.229179⁎⁎ − 5.854524⁎⁎⁎ − 3.852913⁎⁎⁎ 5.393208⁎⁎⁎
⁎⁎⁎, ⁎⁎, ⁎ indicate 1%, 5% and 10% significance level, respectively.
Table 4 Specification and diagnostic tests for the gasoline demand function Ramsey RESET (2) Jarque-Bera test Breusch–Godfrey LM test White's test ARCH test (2)
F-statistic: 2.34 (0.13) JB-statistic: 1.55 (0.46) F-statistic: 0.77 (0.48) Test statistic: 19.7 (0.10) F-statistic: 0.05 (0.95)
ARCH (2) test confirms that there is no evidence of autoregressive conditional heteroscedasticity. White's test does not reject the null hypothesis of no heteroscedasticity. Based on the estimated parsimonious UECM, we performed the bounds test using the following model specifications: no intercept and no trend (case I). We used the F-test to test for the significance of η1, η2 and η3 in Eq. (2). The results of the bounds test are presented in Table 5. The computed F-statistic is larger than the upper critical value. Thus, the null hypothesis of no co-integration, that is, η1 = η2 = η3 = 0, is rejected and we conclude that there is a stable long-run relationship among gasoline demand, income and price. The critical values come from Pesaran et al. (2001). Based on the variance–covariance matrix of coefficients in the UECM drawn from econometrics view software version 5 (Eviews 5), the variances of each long-run coefficient are computed using the method suggested by Bardsen (1989). The t-statistics of income and price elasticities are, respectively 12.0896 and −5.34747. 5.2. Income and price elasticity of gasoline demand The income elasticity of demand has a positive sign as is expected and is statistically significant in the long-run. The income variable is statistically significant at 1% level of significance. The long-run elasticity is 0.36. The sign of the computed income elasticity is in line with the theoretical expectations and is statistically significant. The results indicate that gasoline consumption is a normal good as it increases with income. The magnitude of the long-run income elasticity estimate is within the range of previous studies in other countries. Alves and Bueno (2003) found a long-run income elasticity estimate of 0.12 for Brazil. Cloete and Smit (1988) found an income elasticity estimate of 0.43 for petrol demand in South Africa. An
Table 5 Bounds tests co-integration test results Dependent variable
ΔlnGt ⁎⁎⁎Statistical significance at 1% level.
F-statistic
9.12⁎⁎⁎⁎
Critical bounds at 1% Lower bound I(0)
Upper bound (1)
3.88
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Table 6 Long-run elasticities of gasoline demand Income elasticity
Price elasticity
0.36 (12.0896)⁎⁎⁎
−0.47 (−5.34747)⁎⁎⁎
Numbers in the parentheses indicate t-statistics. The elasticities and variances (hence t-statistics) are computed using the methodology developed by Bardsen (1989). ⁎⁎⁎ indicates a 1% significance level.
increase in income will bring about a gradual increase in the derived demand for gasoline in the long-run as consumers buy more cars or move to bigger ones. However, our results suggest that demand for gasoline is both price and income inelastic (Table 6). The price elasticity is negative and statistically significant. The long-run price elasticity is −0.47. The sign of the computed price elasticity is in line with the theoretical expectations and is highly significant statistically. The price elasticity value is within range of previous studies in other countries. Eltony and Al-Mutairi (1995), in Kuwait, found a long-run price elasticity estimate of −0.46. The absence of reliable public transport and high costs of public transport could be an explanation for the low elasticity estimate. 5.3. Constancy of co-integration space After estimating the parsimonious model, the cumulative sum of recursive residuals (CUSUM) and the CUSUM of squares (CUSUMSQ) tests were applied to test for parameter constancy. Figs. 1 and 2 plot the CUSUM and CUSUM of squares statistics for Eq. (2). The results clearly indicate the absence of any instability of the coefficients during the investigated period because the plots of the two statistics are confined within the 5% critical bounds of parameter stability. 6. Summary and policy implications Econometric studies of the demand for gasoline for South Africa are few. It is important to estimate the price and income elasticities of gasoline for the possible relevance to the development of an appropriate energy policy for the country. Therefore, using the recently developed Autoregressive Distributed Lag (ARDL) bound testing approach to co-integration, suggested by Pesaran et al. (2001), we empirically analyzed the long-run relationship among the variables in the aggregate gasoline demand function over the period 1978–2005. Our study confirms the existence of a co-integrating relationship. The respective long-run price and income elasticities are −0.47 and 0.36. The signs of the computed elasticities are in line with the theoretical expectations. In order to perform bounds test a parsimonious UECM was estimated.
Fig. 1. CUSUM graph for the model.
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Fig. 2. CUSUM squares graph for the model.
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