Cointegration Analysis of Oil Prices and Consumer Price Index in South Africa using STATA Software
This paper investigates the concept of vector autoregression (VAR) and cointegration using a bivariate model of global oil prices and headline Consumer Price Index (CPI) in South Africa. The study aims to determine how much of inflation is driven by oil prices. Particular attention is paid to the theoretical underpinnings of cointergration analysis and the application of STATA software to undertake such analysis and perform test statistics. Contrary to the popular myth that a rise in global oil prices fuels inflation, this study has observed that global oil prices are not the drivers of inflation in South Africa. In this way, other macroeconomic indicators and policy developments need to be integrated in analyzing the determinants of South African inflation.
Key words: Consumer Price Index, Oil Prices, Vector Autoregression, Cointegration, STATA Software, South Africa
*Mphumuzi Sukati is an independent researcher working for the Ministry of Agriculture in the Kingdom of Swaziland. His research interests are in global food markets and drivers of food prices, mainly using CGE models and time series analysis. He holds a PhD in economics from the University of Nottingham.
Oil prices are a key driver of economic activities, with high prices perceived as being unfavorable for global economic growth. Popular myth is that high oil prices are generally associated with high consumer prices. The linkage between oil prices and CPI is especially important for the South African economy for two reasons. Firstly, in terms of income, South Africa is one of the most unequal countries in the world with a Gini coefficient of 63.1 in 20091. This means that inflation disproportionately affect larger sectors of the population that do not have enough income to keep up with rising prices. Further, South Africa is an oil importing country and as such it is exposed to external shocks of rising oil prices. For these reasons, it is important to determine the role of imported inflation (via rising global oil prices) in the economy.
Many studies have used the concept of VAR and cointegration to investigate the link between oil prices and inflation. For example, Cologni and Manera (2005) used a structural cointegrated VAR model to study the effects of oil price shocks on output and prices in G-7 countries. Their key finding was that for most of the countries considered, there seems to be an impact of unexpected oil price shocks on interest rates, suggesting a contractionary monetary policy response directed to fight inflation.
Çelik and Akgül (2011) studied the relationship between CPI and oil prices in Turkey using the Vector Error Correction Model (VECM). Their study revealed that a 1% increase in fuel prices caused the CPI to rise by 1.26% with an approximate one year lag.
Ansar and Asaghar (2013) analyzed the impact of oil prices on stock exchange and CPI in Pakistan and concluded that there was no strong relationship between oil prices, CPI and KSE- 100 Index.
LeBlanc and Chinn (2004) estimated the effects of oil price changes on inflation for the United States, United Kingdom, France, Germany and Japan using an augmented Phillips curve framework. Their study found that oil price increases of as much as 10 % will lead to direct inflationary increases of about 0.1-0.8 % in the U.S. and the E.U, which showed a modest response.
Cunado and Perezde (2003) analyzed the effect of oil prices on inflation and industrial manufacturing for several European countries for the period of 1960 to 1999. Their findings were that there is an asymmetric effect of oil price on production and inflation. Their findings suggest that there are expected differences in countries’ responses to changes in global oil
1 The Gini index measures the area between the Lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line. Thus a Gini index of 0 represents perfect equality, while an index of 100 implies perfect inequality (http://data.worldbank.org/indicator/SI.POV.GINI).
prices depending on their macroeconomic status, whether the country is an oil importer or exporter, and the monetary policies adopted by a given country in response to global oil prices and other trends like exchange rate variations.
Niyimbanira (2013) has analyzed the relationship between oil prices and inflation in South Africa. The difference between his work and ours is that in his paper he modeled inflation has the dependant variable which is driven by oil prices. However, our approach firstly uses headline CPI and not inflation. Secondly, our approach tests the myth that high oil prices drive up prices in the economy, such that oil prices are the dependant variables in our analysis. In this way, there is no need to conduct an Engle Granger causality test.
Our approach is also supported by the work of Lescaroux and Mignon (2008) who noted that concerning the short term analysis, results indicate that when causality exists between oil prices and other macroeconomic variables, it generally runs from oil prices to the other considered variables.
Using the uncorrected or headline CPI and oil prices carries a risk of endogeneity. However, the direct link between oil price inflation and headline CPI is mainly through the price of petrol and this accounts for only 4.07% of the total CPI according to the CPI country weights of 2008 (Statistics South Africa, 2008)2. Further, cointegration analysis removes endogeneity and autocorrelation as we will discuss later.
Our analysis investigate the theoretical foundations of VAR processes and cointegration and their economic interpretation using the South African CPI monthly data from May 1987- 2013 and global oil prices for the same period.3 Our study approach specifically highlight the STATA commands used in such analysis and supported by the theoretical foundations of the analytical framework, STATA language and test statistics used4.
2 The complete contribution of goods and services to the CPI are as follows: Food and non alcoholic beverages 20.6%, alcoholic beverages and tobacco 6.26%, clothing and footwear 4.98%, housing and utilities 11.03%, household contents, equipment and maintenance 6.92%, health 1.67%, transport 20.04%, communication 3.52%, recreation and culture 4.43%, education 2.43%, restaurants and hotels 3.14% and miscellaneous goods and services 14.98%.
3 In January 2013, Statistics SA revised the basket of goods and services used to measure CPI, in order to measure consumer inflation more precisely. Among these changes are: food prices were gathered from rural areas, the fixed fruit basket was altered to a seasonal one, reduced weightings of automobiles, furniture and appliances whose prices have been falling in previous years, and increased weight was given to petrol, transport costs, electricity, education and medical insurance (Dhliwayo, 2013)
4 STATA statistical software is a complete, integrated statistical software package that is user friendly and readily available for purchase. It is versatile and has many techniques for data analysis for a wide range of fields. In economics it can be used to analyze for example survival models, panel data, generalized estimating equations, multilevel mixed models, models with sample selection, ARCH and GARCH, OLS, logit/probit regressions ANOVA/MANOVA, ARIMA and others. The software also facilitates the presentation of summary results in clear tabulated forms with strong graphical capabilities.
The rest of the paper is organized as follows; section 2 presents the modeling approach and tests for unit root. In section 3 we test for cointegration in the bivariate model and discuss the results. Section 4 presents the VECM estimates and discusses their implications while section 5 concludes.
Before working with our bivariate model we have to test the variables for unit root. Following Hendry and Juselius (2000), data can be unit root i.e. integrated of degree 1 (denoted as I(1)). Such data cannot be used to investigate relationships between the variables because of spurious regression and OLS estimates become invalid.
However, data showing such properties can be made stationary by first differencing. If a series is such that its first difference is stationary (and has positive spectrum at zero frequency) then the series has an exact (or pure) unit root (Granger and Swanson, 1996).
The test for unit root starts with Equation 1 below, which is an autoregressive process of degree one, denoted as AR(1) process.
π¦π‘ = π¦π‘−1 + sπ‘
(1)
With;
sπ‘ ∼πΌπ [0, π2]
From this equation it can be shown that subtracting π¦π‘ (as data) on both sides will result in a stationary process even though π¦π‘ is non stationary, i.e.
π¦π‘ − π¦π‘−1 = Δπ¦π‘ = sπ‘
(2)
Therefore;
Δπ¦π‘ ∼πΌπ [0, π2]
Such differencing can be extended to twice-integrated series i.e. I(2), in which case it must be differenced twice to deliver a stationary process etc.
It is visually difficult to predict the nature of variables in an economic process i.e. whether they are stationary or not. Figure 1 below is a plot of monthly data of oil prices and CPI for the South
African economy from 1987 to 2013 (changed to natural logarithm) with 309 observations and their first difference.
The oil prices data has been obtained from Europe Brent Spot Price FOB (Dollars per Barrel).
The headline CPI has been obtained from statistics South Africa, available at www.statssa.gov.za.
Figure 1: Monthly data of oil prices and consumer price index for the South African economy from 1987 to 2013 and their first difference
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