Do we need a global VAR model to forecast inflation and output in South Africa?

Abstract

This study determines whether the global vector autoregressive (GVAR) approach provides better forecasts of key South African variables than a vector error correction model (VECM) and a Bayesian vector autoregressive (BVAR) model augmented with foreign variables. The article considers both a small GVAR model and a large GVAR model in determining the most appropriate model for forecasting South African variables. We compare the recursive out-of-sample forecasts for South African GDP and inflation from six types of models: a general 33 country (large) GVAR, a customized small GVAR for South Africa, a VECM for South Africa with weakly exogenous foreign variables, a BVAR model, autoregressive (AR) models and random walk models. The results show that the forecast performance of the large GVAR is generally superior to the performance of the customized small GVAR for South Africa. The forecasts of both the GVAR models tend to be better than the forecasts of the augmented VECM, especially at longer forecast horizons. Importantly, however, on average, the BVAR model performs the best when it comes to forecasting output, while the AR(1) model outperforms all the other models in predicting inflation. We also conduct ex ante forecasts from the BVAR and AR(1) models over 2010:Q1–2013:Q4 to highlight their ability to track turning points in output and inflation, respectively.

Keywords:

• South Africa
• global vector autoregressive (GVAR) model
• Bayesian vector autoregressive (BVAR) model
• forecasting

JEL Classification:

• C51
• C53

Notes

¹ We considered the inclusion of more trading partners to represent 80% of South Africa’s average trade with the countries included in the 33 country GVAR. However, due to South Africa’s diverse trade, we would have had to include at least five more trading partners, and the GVAR model would then have included almost half of the countries in the original 33 country (‘large’) GVAR, thus it would not have been a ‘small’ model.

² The results of the weighted symmetric augmented Dickey Fuller test are available from the authors on request.

³ The real exchange rate definition differs from the usual definition of ($e-p-p^{\ast }$). The definition used here is standard to the GVAR literature (e.g., Pesaran et al., 2004; Pesaran and Smith, 2006; Dées et al., 2007a; Eickmeier and Ng, 2011; Cesa-Bianchi et al., 2012; Assenmacher-Wesche and Geissmann, 2013). The definition enables the separation of the domestic (endogenous) variables from the foreign (weakly exogenous) variables, which is important in VECX* and GVAR models.

⁴ We experimented with higher and lower interaction values, in comparison to those specified above, to the star variables in both the star and circle equations, but the rank ordering of the alternative forecasts remained the same.

⁵ The h-quarter ahead forecast error for each variable of each model is $e_t\left(h\right)=y_{t+h}-{\hat{y}}_{t+h|t}$, where $y_{t+h}$ is the actual value of the variable and ${\hat{y}}_{t+h|t}$ is the forecast of the variable. The h-quarter ahead RMSFE is $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{F}\mathrm{E}(h,R)=100\sqrt{R^{-1}\sum _{t=T}^{T+n-1}{e}_t^2(h)}$ and the h-quarter ahead MAE is $M\mathrm{A}\mathrm{E}(h,R)=100R^{-1}\sum _{t=T}^{T+n-1}\left|e_t(h)\right| ,$ with R the forecast sample size.

⁶ One of the anonymous referees inquired about the possibility of structural breaks. In this regard, it is important to point out the following three issues: (1) since all models are estimated recursively over the out-of-sample periods: 2005:1–2009:4, the parameter estimates are updated at each recursion and hence, this allows us to account for any structural breaks, for instance, due to the global financial crisis over this period; (2) also, the GVAR (as well as the other models) accounts for possible structural breaks that might have occurred across various economies over the entire sample, by using time-varying trade weights, which allows us to capture the change in the relationship among the South African variables with the variables from of its trading partners. Possibly, this is the primary reason one observes that the time-varying GVAR outperforms the fixed weight-based GVAR consistently; (3) finally, the CUSUM test conducted on the relationship between the South African GDP and the domestic and foreign variables indicate no breaks for inflation and one for GDP, with the break corresponding exactly with 2005:Q1, from which period we estimate the models recursively in any case. Furthermore, the Bai and Perron (2003) tests of multiple structural breaks conducted on a VAR(2) involving GDP and inflation – our two variables of concern also depict no structural breaks. Further details on the test conducted here are available upon request from the authors.

⁷ The MSE-F statistic uses the loss differential and is given as: $\mathrm{M}\mathrm{S}\mathrm{E}-F=(T-R-h+1)\left(\bar{d}/\mathrm{M}\mathrm{S}{\mathrm{E}}_1\right),$ where T represents the number of observations in the total sample, R represents the number of observations used to estimate the model from which we calculate the first forecast (i.e., the in-sample portion of T), h, the forecast horizon, $\bar{d}=\mathrm{M}\hat{\mathrm{S}}{\mathrm{E}}_0-\mathrm{M}\hat{\mathrm{S}}{\mathrm{E}}_1$, $\mathrm{M}\hat{\mathrm{S}}{\mathrm{E}}_i=(T-R-h+1{)}^{-1}\sum _{t=R}^{T-h}{(u_{i,t+1})}^2$ with $i=1, 0$, $\mathrm{M}\hat{\mathrm{S}}{\mathrm{E}}_1$ represents the MSE of the unrestricted model and $\mathrm{M}\hat{\mathrm{S}}{\mathrm{E}}_0$ represents MSE of the restricted model.

Additional information

Funding

Annari de Waal acknowledges financial support from the Commonwealth Scholarship Commission in the UK and the Cambridge Commonwealth Trust.