versión On-line ISSN 1015-8812
S. Afr. j. econ. manag. sci. vol.13 no.1 Pretoria ene. 2010
Department of Economics, University of the Free State
This paper identifies the basic empirical characteristics and changes of the South African business cycle since 1960. As such, the paper examines changes in volatility as well as the co-movement between several national account variables and real GDP. To examine the co-movements the paper follows Kydland and Prescott, Gavin and Kydland as well as Bergman, Bordo and Jonung and uses correlation coefficients and Granger causality tests. Following Ramos, the paper extends the results of the Granger causality tests using variance decomposition analysis in the context of a VAR (vector auto regression) to establish the contribution that selected national account variables make to the h-period-ahead forecast error variance of themselves and the other variables included in the VARs. The paper indicates that since 1994 volatility in the South African economy decreased significantly, while durable consumption appears to lead the business cycle.
Keywords: Volatility, business cycle
JEL: E32, 53
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Accepted September 2009
1 A companion paper focuses on the relationship between the real GDP gap and variables other than national account variables.
2 Cyclical GDP can also be obtained using for instance a production function approach. However, this can only be applied to the GDP series and not the other series used. For the purposes of this paper, the same detrending technique had to be applied to all time-series used in the paper to ensure consistency. The Baxter-King BP filter could also be used, though the majority of the literature using statistical filters, selected the Hodrick-Prescott filter. As a result, this paper also uses the Hodrick-Prescott filter. This filter is a time-series smoothing technique where the smoothed time-series is obtained from selecting s so as to minimise where y is the time-series to smooth, s is smoothed series and λ is the smoothing parameter. For quarterly data the convention is to set λ = 1600. This convention is followed in this paper. Note that due to the endpoint problem of the HP filter, some observations at both ends have been dropped.
3 For the latter approach this paper ignored peaks and troughs smaller than 0.01 in absolute terms.
4 An alternative approach is to calculate the correlation coefficients between the growth rates of variables. However, as Barrel and Gottschalk (2004:101) note, the use of growth rates is problematic given that the long-term component of the data might pollute the cyclical pattern of the growth rates. The second alternative would be to remove the cyclical component of the growth rates before calculating the correlation coefficients between the growth cycles. In preparing this paper both the gap variables and the growth cycles were calculated and used for the correlations and the volatility measures. Because both sets of calculations yield very similar results this paper uses only the gap variables.
5 However, note that although there is no discernable correlation between the investment gap of the electricity sector and the GDP gap, Odhiambo (2009) found a strong bi-directional causal relationship between economic growth and electricity consumption.
6 My thanks to Meshach Aziakpono for bringing this paper to my attention.
7 However, the tables containing the VAR results are available from the author on request. Note that the VAR residual serial correlation LM Tests indicated no serial correlation problems at a 5 per cent level for any of the VARs. In addition, the joint test for heteroskedasticity indicates no hetero-skedasticity at a 5 per cent level in any of the VARs.
Granger causality tests
The columns headed by 'X Y' reports the probability of making a mistake by rejecting the null hypothesis that a variable such as the real consumption gap, denoted by X, does not Granger cause the real GDP gap, denoted by Y. The columns, headed by 'Y X' report the reverse causality result. Using a 5 per cent significance level, probability values of less than 0.05 indicate that there is evidence that, for instance, changes in the real consumption gap precede changes in the real GDP gap. These statistically significant results are shaded in grey.
Impulse-responses for period 2
Impulse-responses for period 3