South Africa's Taylor's Rule for Q2:2016 and Q3:2016

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Taylor's rule was developed and refined by economist John Taylor in 1993. It is used as a guide to show what nominal interest rates of a country should be based an various variables that include:
The actual formula being used: Interest Rates= CPI + Equilibrium Real Interest Rates+ab*(CPICPItarget)+xy*(RealGDPPotentialRealGDP). Where ab and xy are ratios (0.5 for both as recommended by Taylor). We take a look at what Taylor's Rule states South Africa's interest rates should currently be at. And how far off is the Reserve Bank from the suggested interest rate by Taylor's rule? 

The graphic to the left shows the repurchase rate (Repo rate) as set by the South African Reserve Bank (SARB) and our Taylor's rule calculation.
From the graphic it is clear that the underlying trends are very similar even though the level and magnitude of movements are different. Based on our estimates for Taylor's Rule South Africa's interest rates where way to high at end of 2003 (based on the big differential between the actual repo rate and Taylor's rule). This differential closed considerably and by the end of 2005 the two lines were pretty close. They remained very close until the first quarter of 2011, when divergence took place again. 
The divergence in 2011 continued and the two lines only started getting closer by the beginning of 2014. Perhaps this divergence between Taylor's rule and the actual repo rate is why the South African Reserve Bank (SARB) has been talking tough and continued with their interest rate increase cycle, even though inflation is currently driven by external factors (such as the drought in South Africa).
The average interest rate suggested by Taylor's rule over the period is 7.2% and the average Repo rate for the period is 7.17%, showing that the two series over the time span is very close, even though the magnitudes at different points in time differ significantly. Based on the graphic above South Africa's current interest rates are pretty much spot on right now. (As we mentioned in our previous post on Taylor's Rule, it suggested that interest rates will rise futher, and the average interest rate back in Q1:2016 has moved up from 6.2%, to sit at 7% in Q2:2016).
Based on Taylor's rule, South Africa's Repo rate should be at 7.4% for Q3:2016 (using available economic data and growth forecasts for variables for which economic data is not available yet for Q3:2016), and it is currently sitting at 7%, indicating that the South Africa interest rate setting policy is lagging behind the interest rate suggested by Taylor's Rule. But as we mentioned before over the long run the average interest rate suggested by Taylor's Rule and actual interest rates are very very close.
The biggest positive difference between Taylor's predicted interest rate and the actual Repo rate was 3.9%, when the Repo rate averaged 8.7% for the quarter (Q4: 2013), yet Taylor's rule suggested it be 4.8%, and the biggest negative difference was 2.5% when the Repo rate average 5% for the quarter (Q3:2013) yet Taylor's rule suggested it be 7.5%.
The average interest rate suggested by Taylor's rule over the period is 7.2% and the average Repo rate for the period is 7.17%, showing that the two series over the time span is very close, even though the magnitudes at different points in time differ significantly. Based on the graphic above South Africa's current interest rates are pretty much spot on right now. (As we mentioned in our previous post on Taylor's Rule, it suggested that interest rates will rise futher, and the average interest rate back in Q1:2016 has moved up from 6.2%, to sit at 7% in Q2:2016).
Based on Taylor's rule, South Africa's Repo rate should be at 7.4% for Q3:2016 (using available economic data and growth forecasts for variables for which economic data is not available yet for Q3:2016), and it is currently sitting at 7%, indicating that the South Africa interest rate setting policy is lagging behind the interest rate suggested by Taylor's Rule. But as we mentioned before over the long run the average interest rate suggested by Taylor's Rule and actual interest rates are very very close.
The biggest positive difference between Taylor's predicted interest rate and the actual Repo rate was 3.9%, when the Repo rate averaged 8.7% for the quarter (Q4: 2013), yet Taylor's rule suggested it be 4.8%, and the biggest negative difference was 2.5% when the Repo rate average 5% for the quarter (Q3:2013) yet Taylor's rule suggested it be 7.5%.
So how did we calculate Taylor's rule's estimates? All data was converted into quarterly data since the GPD data is published quarterly.
 Real GDP: 2010 Constant Prices GDP at Market Prices
 Potential Real GDP: We adjusted Real GDP by the percentage of manufacturing under utilisation (see our blog on this topic), to estimate South Africa's potential GDP if manufacturing was running at full capacity.
 Inflation Target: We used the upper band (6%) of the Reserve Bank's 3% to 6% inflation target.
 Equilibrium Real Interest Rates: We used the average interest rate over the period as the equilibrium interest rate (and adjusted it with inflation to get the Equilibrium Real Interest Rate)
 Ab and Xy: We used 0.5 as suggested by Taylor.
In summary
Due to all the uncertaintly regarding the future movements of inflation and the economic growth figures, SARB will from time to time be either ahead of behind what Taylor's rule suggest interest rates should be. But as mentioned in the post above, the average interest rate as suggested by Taylor's Rule over the period (Q4:2013 to Q2:2016) was 7.2% while the actual average interest rate over the same period was 7.17%. Therefore what Taylor's Rule is suggesting is very very close to actual interest rates. One wonders if SARB has someone calculating Taylor's Rule for them to give them a rough idea of what this economic theorem suggests interest rates should be.
Based on the fact that the estimated interest rates calculated using Taylor's Rule has been coming down in recent quarters (due to lower inflation and better GDP numbers (3.3% quarter on quarter annualised for Q2:2016), we expect that SARB will keep interest rates unchanged and continue with their "wait and see" policy as the difference between Taylor’s Rule suggested interest rate and actual interest rates is small and narrowing, it affords SARB the time to continue with their current “wait and see” policy.
Based on the fact that the estimated interest rates calculated using Taylor's Rule has been coming down in recent quarters (due to lower inflation and better GDP numbers (3.3% quarter on quarter annualised for Q2:2016), we expect that SARB will keep interest rates unchanged and continue with their "wait and see" policy as the difference between Taylor’s Rule suggested interest rate and actual interest rates is small and narrowing, it affords SARB the time to continue with their current “wait and see” policy.