Inflation has received a disproportionate amount of attention in the South African macroeconomic literature. Empirically motivated papers on inflation in South Africa have shown a close adherence to theoretical priors. In particular, a core feature of the South African empirical studies has been a sustained search for a Phillips curve tradeoff between prices and demand-‐side inflationary pressure associated with real economic activity. A second constant that emerges from the empirical literature is the consistent failure to successfully support the Phillips curve trade off.
Instead, a far more pervasive finding in the South African empirical literature has been a strong association between inflation and wage costs.
Despite the ongoing struggle to generate any confirmatory evidence in support of the Phillips curve, it is surprising that the South African empirical inflation literature has executed a very limited search over alternative theoretical accounts of inflation. Few studies even consider monetary accounts of inflation. Nor is there much evidence of an exploitation of the well-‐established link between the first and second moments of the inflation time series. This is all the more surprising since a cursory consideration of South African inflation, suggests that ARCH structure is plausible both for the CPI and GDP deflator time series -‐ see Figure 1.
Our paper innovates in three distinct senses in relation to the South African debate.
First, we consider the relative performance of a range of alternative inflation models. This includes, but is not restricted to Phillips curve type models of inflation. We extend consideration to long-‐run structural models of price determination, a New Keynesian Phillips curve model, and monetary models of inflation.
Second, we consider the utility of incorporating ARCH structure into the modelling in improving the performance of inflation models. We do so across the full range of theoretical alternatives, with the exception of the structural model where econometric considerations preclude this possibility. A crucial means of considering the relative performance of the inflation models is not only goodness of fit of the models, but their forecast performance over a twelve (12) quarter window at the end of the sample period under consideration in this study.
Third, unlike previous studies we abandon theoretical purity. Instead we allow for all the potential covariates of inflation identified under the alternative theoretical models to compete empirically, in order to establish their relative robustness in modelling inflation.
Our core findings are as follows.
The single most robust covariate of inflation is unit labour cost. In our analysis we extend previous work which has noted the impact of unit labour cost, by decomposing unit labour cost into changes in the nominal wage and real labour productivity. The principal association is a strong positive relationship between inflation and nominal wage increases, while improvements in real labour productivity report a negative association with inflation. The implication of this finding is that South African inflation has a strong cost-‐push structure, with the principal driver being increases in nominal wage costs, while productivity growth exercising a moderate restraint on inflationary pressure. This accords well with established empirical findings on the pricing power of South African producers, and the existence of substantial mark-‐ups of price over the marginal cost of production in South African output markets.
Supply side shocks also consistently report an association with inflation.
As to demand-side shocks, the output gap does not return a robust statistical association with inflation. Instead, it is growth in the money supply and government expenditure which prove to return consistent associations with inflationary pressure, and these may prove to be more useful proxies for demand side shocks in inflation models than the output gap has proved to be.
1  See Aghion et al (2008, 2013) and Fedderke et al (2007).