South Africa's Taylor's Rule Calculated

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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). 

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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 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 7.14% 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 too low ( and they have been since the first quarter of 2011).
Based on Taylor's rule, South Africa's Repo rate should be at 7.7% (average interest rate for quarter one 2016), yet it is currently sitting at 6.6%, indicating that the South Africa is behind the so called "8 ball" when it comes to interest rate setting policy. Further proof of this can be seen by the fact that the Repo rate was slow to come down in 2003 when Taylor's rule's estimate was showing that interest rates should have been a lot lower than they actually were.
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 (Fourth quarter of 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 (Third quarter 2013) yet Taylor's rule suggested it be 7.5%.
The average interest rate suggested by Taylor's rule over the period is 7.14% 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 too low ( and they have been since the first quarter of 2011).
Based on Taylor's rule, South Africa's Repo rate should be at 7.7% (average interest rate for quarter one 2016), yet it is currently sitting at 6.6%, indicating that the South Africa is behind the so called "8 ball" when it comes to interest rate setting policy. Further proof of this can be seen by the fact that the Repo rate was slow to come down in 2003 when Taylor's rule's estimate was showing that interest rates should have been a lot lower than they actually were.
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 (Fourth quarter of 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 (Third quarter 2013) yet Taylor's rule suggested it be 7.5%.
So what is Taylor's rule telling us about the future movements of the Repo rate? Based on the current graphic the South African Reserve Bank is behind where they should be in terms of interest rate setting targets. We therefore suspec that the South African Reserve Bank will continue to incrementally increase interest rates until such time that the gap between Taylor's rule and the Repo rate has been narrowed down again.
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.
So what is Taylor saying about our interest rate future?
In order to answer this we need to make a few assumptions regarding 2nd quarter 2016 and recalculate Taylor's Rule based on these assumptions. The graphic below shows the value of Taylor's rule for 2nd quarter 2016, and the descriptions next to it discuss the assumptions made to get the Taylor's rule for 2nd quarter 2016

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The assumptions regarding 2nd quarter 2016 (for the light blue line) CPI to average 6.2% for the quarter Repo Rate to remain at current level GDP for 1st and 2nd quarter to grow at 0.6% quarter on quarter annualised. Same growth rate as reported in last quarter of 2015. Assumption 2: The assumptions regarding 2nd quarter 2016 (for the red line) CPI to average 6.5% for the quarter Repo Rate to remain at current level GDP for 1st and 2nd quarter to grow at 0.6% quarter on quarter annualised. Assumption 3: The assumptions regarding 2nd quarter 2016 (for the orange line) CPI to average 6.7% for the quarter Repo Rate to remain at current level GDP for 1st and 2nd quarter to grow at 0% quarter on quarter annualised. 
From the graphic and descriptions above it's clear that any further increases in the inflation rate will imply that South Africa's interest rates are too low, as Taylor suggests it be at 7.5% or 7.8% if inflation for the 2nd quarter 2016 averages 6.5% or 6.7% respectively. But if inflation averages the same as the previous quarter and economic growth remains the same for 1st quarter 2016 and 2nd quarter 2016 as it was at end of 2015, then the Reserve Bank's interest rate setting is spot on.
Due to all the uncertaintly regarding the future movements of inflation and the economic growth figure, the Reserve Bank in all honesty did the right thing by keeping rates constant and assume the "wait and see" position before increasing interest rates any further. Any further rate hikes at this point in time could have severe consequencies on South Africa's economy, as already struggling and indebted South African consumers would find it even harder to pay the bills. And as consumers are a major driving force behind South Africa's economy, a slow down in their spending would naturally filter through to the economy that would slow down as a result too.