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In today's blog we calculate Taylor's rule for South Africa. 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: Interest Rates= CPI + Equilibrium Real Interest Rates+ab*(CPI-CPItarget)+xy*(RealGDP-PotentialRealGDP). 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.
Updated 20 May 2016:
Yesterday we published the above blog with Taylor's rule and what it suggests interest rates should be. The MPC of the Reserve Bank decided to keep the Repo Rate unchanged. We made a few quick assumptions regarding quarter 2 of 2016 and recalculated Taylor's Rule below, adding quarter 2 of 2016 with our assumptions made for this quarter to the graphic. Based on the graphic below the Reserve Bank was right in keeping rates unchaged. And it seems our interest rates are set at levels very close to where Taylor's rule suggests it should be.
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The assumptions regarding quarter 2: 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. |