Our specification now provides a reasonable enough fit for both periods for us to make some more confident observations. First, as expected, the simpler specifications provide a poor fit for the pre-IT period, when monetary policy was known to be eclectic. Only whenwe control for the real exchange rate and some other asset prices does the fit of the model improve significantly, with both the real exchange rate and the other asset prices significant at conventional levels. The output gap is insignificant in all of the pre-IT regressions, suggesting that monetary policy paid little or no attention to output, focussing rather on other target variables.
For the IT period, the basic Taylor Rule provides a good fit, and even more so when we augment it to account for interest rate smoothing. The coefficient on the output gap is significantly positive, suggesting that the inflation targeting regime followed by the SARB has indeed been flexible. As previously noted, a positive coefficient on the output gap is also evidence that the Reserve Bank has tended to react countercyclically to demand shocks but has tended to accommodate supply shocks. In the IT regressions, the coefficient on the real exchange rate is weakly statistically significant but small in magnitude, while those on asset prices are not significant, suggesting that monetary policy has paid little attention to these variables under inflation targeting. CPI and CPIX inflation provide similarly good fits, while the fit of the specification using core inflation is relatively worse, despite core inflation’s tendency to be a better predictor of future headline inflation.
The differences between the regimes are thus fairly clear. Broadly, the pre-IT regime focussed on exchange rates and possibly asset prices, and not on output. The IT regime has focussed strongly on output, but not on exchange rates and asset prices. The SARB focussed on inflation in both periods, and its instrument setting behaviour seems to have been influenced by a tendency to systematically smooth interest rates in both periods.
The major concern raised throughout our analysis has been that the weight on the inflation gap is low in both periods. (It is also noteworthy that the weight on the inflation gap seems paradoxically to have decreased under inflation targeting.) A weight on the inflation gap lower than unity has been shown to result in an unstable inflation process in a wide range of macroeconomic models; in all of our regressions (both pre-IT and IT), the short run and (inplied) long run weights on the inflation gap are substantially and
statisti-cally significantly lower than unity. This would appear to contravene the Taylor principle that these weights should be greater than unity, and suggests that the monetary policy of the SARB has been conducive to inflation instability in both periods, perversely allowing the real interest rate to rise in response to decreases in inflation, and vice versa. This result warrants more investigation; in particular, it necessitates a discussion of whether our low estimates of the inflation weights might be driven by specification or other econometric issues, rather than a truly low inflation emphasis.
A plausible explanation lies in the relation between the original forward-looking speci-fication (1) and its contemporaneous counterpart (2), which was the specispeci-fication we used in our estimations. The Taylor principle, applied to (1), advises that the coefficient on the expected future inflation gap be larger than unity. We noted that our proxy for expected future inflation, viz. current inflation, was likely an oversimplification, since the Reserve Bank considers many more variables than current inflation in forming its expectation of fu-ture inflation. The small coefficient on current inflation in our regressions might therefore reflect the small weight placed on this variable in the SARB’s formation of its expectation of future inflation, rather than a low weight placed on expected future inflation in the first place. To illustrate, suppose the SARB’s forecast model for future inflation is of the simple linear form
Etπt+T|t=γ0+γ1πt+γ2yt+γ3et+ψ·xt, (13) where theγi and the elements ofψare constants, andxtis a vector of other variables the SARB might consider in forecasting future inflation. Keeping the proxy for the SARB’s forecast of the future output gap as the output gap’s contemporaneous level, and substi-tuting (13) into (1), yields a reaction function of the same general form as (2):
it=k+γ1φππt+ (γ2φπ+φy)yt+ (γ3φπ+φe)et+. . . (14) wherekis a constant. Note that the coefficient on the inflation gap is the product of two coefficients: the coefficient on expected future inflation in the Taylor-like rule, and the weight on current inflation in the forecast model for future inflation. Ifφπ is greater than unity, in line with the Taylor principle, but smaller than 1/γ1, then the overall coefficient on the inflation gap will be less than unity, and would be expected to be estimated as such in an unbiased regression. For example, our point estimate ofφπ in the IT regression (vi) is 0.237. If the true φπ>1, and any attenuation of our estimate ofφπ stems solely from the above problem, it would be required thatγ1<0.237.
In fact, (14) highlights a general difficulty in interpreting the results of our regression:
Is the significance of a coefficient on a variable the result of the SARB’s targeting that variable separately, or is it a result of that variable forming part of the SARB’s forecast of future inflation? On this question, our regressions are necessarily ambiguous. One point that can be made is that the two terms in each coefficient on the non-inflation variables are unlikely to cancel each other out; they should be of the same sign.
Our low estimates of the SARB’s inflation weights could also be the result of attenuation bias stemming from our inflation variable being mismeasured. Since we are attempting to characterise the behaviour of the Reserve Bank, it would be most advisable to use real-time data rather than revised ex-post data, since it is obviously real-real-time data that the Reserve Bank uses in its decision-making (Orphanides, 2001). To the extent that revised
data is a mismeasured form of real-time data, there is a possibility of attenuation bias in our estimate of the weights on inflation. If the real-time inflation rate and its revised ex-post form are related by
πrt=πep+ν,
and the classical measurement error acondition, E(ν|πep) = 0, holds, then we would expect our estimate of the weight on inflation to be biased towards zero if we use πep in our regression, rather thanπrt.
These caveats notwithstanding, there remain strong reasons to believe that our results represent evidence that the SARB has been ‘soft on inflation’. First, the estimated co-efficient on the inflation gap is lower for the IT period than for the pre-IT period. It is unlikely that structural changes (for example, in the formation of inflation forecasts) can account for this paradoxical change in apparent emphasis. Second, similar studies (using current inflation and OLS, and as such, subject to the same general objections as those raised above) carried out for other countries have yielded estimates of inflation weights that are significantly above unity.
6 Conclusions
Under inflation targeting, the SARB has missed its official inflation target in 19 of the 37 quarters since the year for which the target was first set. While this gives the lie to the accusations of COSATU and others that the Reserve Bank focusses too much on meeting its inflation targets, it also raises serious doubts around how successful the regime has been with respect to its primary goal, price stability. Indeed, the volatility of inflation seems to have increased under inflation targeting, relative to the previous monetary targeting regime. This contrasts with most international experiences of inflation targeting; the regime has in general been associated with a greater degree of macroeconomic stability.
In this paper, we have sought to explain these anomalies by empirically analysing the behaviour of the SARB before and after the adoption of inflation targeting, making use of Taylor-like rules to gain insight into what variables the SARB focussed on (and with what weightings) when setting its interest rates in the two periods.
Our approximation of an instrument rule for the pre-IT period suggested that the SARB reacted primarily to changes in inflation, the real exchange rate and other asset prices in this period; we found no evidence of a tendency to smooth interest rates. The emphasis on the real exchange rate and other asset prices is consistent with the eclectic focus this regime is known to have had.
In contrast, our approximation of a rule for the IT period revealed that the SARB has reacted to changes in inflation and the output gap under inflation targeting, and has exhibited little or no targeting of the exchange rate or other asset prices. The significance of the output gap in our IT regressions, along with its relatively large weight, points to a large degree of flexibility exercised by the SARB (in contrast to COSATU’s claims).
Evidence of a tendency to smooth interest rates in this period was found.
Of major concern is the very low coefficient on inflation in our regressions for both periods. Theory suggests that a weighting lower than unity for inflation in an instrument rule could lead to an unstable inflation process, and in every regression our estimate of this
weight was both substantially and statistically significantly smaller than this threshold.
This is a particularly disturbing result for the IT period (for which the estimated weighting was actually lower than that for the pre-IT period), and casts further doubt on the SARB’s insistence that price stability is its overriding objective.
This low coefficient could be explained away if the SARB places a low weight on current inflation in its forecast for future inflation, since it is actually the forecast for which it has a target. The low coefficient on current inflation in our regressions might reflect this, rather than a weak focus on keeping inflation within the target band. Also, because instrument decisions in the period under study would have been made making use of real-time data, while we use ex-post data in our estimations, our results could suffer from the problems associated with mismeasured variables, and in particular, attenuation bias.
Still, that the coefficient on inflation in our regressions was smaller for the IT period than for the pre-IT period, and that in similar estimations for other countries, inflation coefficients significantly greater than unity have been found, support the suspicion that the SARB has tended to respond more timidly to changes in inflation than theory suggests it should have.
Thus, we have found evidence that the SARB places too low a weight on its inflation target when setting the interest rate, which may explain the high volatility of inflation observed in the IT period.
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Appendix
Table 1: List of variables used
Variable Symbol used Source Description
repo rate it SARB The rate at which the SARB repurchases
government securities.
CPI inflation πCP It SARB The year-on-year rate of change of the consumer price index.
CPIX inflation πtCP IX SARB The year-on-year rate of change of the consumer price index, excluding the mortgage interest rate cost.
core inflation πtcore SARB The year-on-year rate of change of the consumer price index, excluding certain food products, the mortgage interest rate cost, overdrafts and personal loans, value-added tax and property taxes.
output gap yt SARB/own calc. The percentage difference between ac-tual and trend real (seasonally adjusted) GDP, with the trend level determined us-ing a Hodrick-Prescott filter (λ= 1600).
REER et IMF IFS The real effective exchange rate,
CPI-based, with PPP whenet= 100.
share price gap sharegapt IMF IFS/own calc. The percentage difference between the actual and trend level of the All Share In-dex, with the trend level determined us-ing a Hodrick-Prescott filter (λ= 1600).
house price gap housegapt ABSA/own calc. The percentage difference between the actual and trend level of the ABSA Average House Price Index, with the trend level determined using a Hodrick-Prescott filter (λ= 1600).
Table 2: Summary of inflation statistics for pre-IT and IT periods
Pre-IT IT
1990Q1-1999Q4 2000Q1 -2011Q1
Mean (%) 9.91 5.92
Minimum (%) 1.96 0.44
Maximum (%) 16.11 12.75
Standard deviation (%) 3.62 3.12
Standard deviation
around linear trend (%) 1.86 3.11
Source: Authors’ calculations, using data as described in Table 1.
Table 3: Results of tests for unit root processes in the variables
H0: variable has a unit root
Standard DF test Aug. DF test - 1 lag Aug. DF test - 2 lags
θ |t| θ |t| θ |t|
repot −0.032 1.07 −0.053 1.89 −0.041 1.46
repot(pre-IT) −0.136 1.56 −0.211 2.45 −0.179 1.93
repot(IT) −0.049 0.88 −0.104 2.28 −0.093 1.97 πCP It −0.082 2.07 −0.109∗∗ 3.10 −0.103∗ 2.79 πCP It (pre-IT) −0.038 0.58 −0.069 1.04 −0.061 0.90 πCP It (IT) −0.128 1.81 −0.205∗∗∗ 3.84 −0.199∗∗ 3.14
πCP IXt (IT) −0.037 0.50 −0.156 2.09 −0.190 2.32
πcoret (IT) −0.040 0.51 −0.140 1.63 −0.174 1.87 yt −0.090 2.13 −0.126∗∗∗ 3.75 −0.122∗∗ 3.40
yt(pre-IT) −0.095 1.58 −0.114 2.29 −0.112 2.11
yt(IT) −0.085 1.38 −0.143∗∗ 3.06 −0.138∗ 2.65 et −0.054 1.61 −0.062 1.86 −0.057 1.69
et(pre-IT) −0.054 0.77 −0.066 0.88 −0.039 0.50
et(IT) −0.119 1.58 −0.164 2.15 −0.167 2.02
sharegapt −0.215∗∗ 3.15 −0.270∗∗∗ 3.85 −0.271∗∗ 3.54
sharegapt(pre-IT) −0.332∗ 2.78 −0.422∗∗ 3.33 −0.397∗ 2.72
sharegapt(IT) −0.171 1.98 −0.218 2.47 −0.235 2.47
housegapt −0.065 1.60 −0.117∗∗∗ 3.87 −0.082∗ 2.61
housegapt(pre-IT) −0.140 1.53 −0.294∗∗∗ 4.44 −0.291∗∗∗ 3.55
housegapt(IT) −0.054 1.07 −0.095 2.57 −0.059 1.59
The standard Dickey-Fuller (DF) test is applied by estimating the regression:
∆xt=α+θxt−1+et, so that θ is the first order autocorrelation of x. The augmented DF tests add lags of ∆xto the above regression. A value for θ that is statistically sig-nificantly different from zero is evidence against xbeing a unit root process. The values forθ, as well as their correspondingt-values, are reported. ∗,∗∗,∗∗∗ represent statistically significant difference from zero at the 10%, 5% and 1% levels respectively, according to the Dickey-Fuller distribution (Dickey and Fuller, 1979).
Table 4: Results of Engle-Granger tests for cointegration
Pre-IT IT
Variable set 1990Q1-1999Q4 2000Q1 -2011Q1
{it, it−1, πt, yt, et} t-statistic 4.56 3.81
Critical value 10% 4.02 4.00
5% 4.38 4.35
1% 5.12 5.06
{it, it−1, πt, et} t-statistic 4.17 3.37
Critical value 10% 3.61 3.59
5% 3.96 3.94
1% 4.67 4.63
The Engle-Granger test is carried out by obtaining the residuals from a regression of one of the variables in the set of variables being tested for cointegration on the others, and using the residuals to test for a unit root in the error process. (The null hypothesis is that there is a unit root in the error process, and therefore that the variables are not cointegrated.) The unit root test is identical in procedure to the simple Dickey-Fuller test carried out above, but the critical values are different; we use the estimates provided by MacKinnon (2010).
Table 5: Regression results
Dependent variable: ∆repot
Regression: (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix)
Start: 1990Q1 2000Q1 1990Q1 2000Q1 1990Q1 2000Q1 2000Q1 2000Q1 2000Q1
End: 1999Q4 2011Q1 1999Q4 2011Q1 1999Q4 2011Q1 2008Q4 2008Q4 2008Q4
Obs: 40 45 40 45 40 45 36 36 36
∆repot−1 - - 0.175 0.252∗∗ 0.235 0.306∗∗ 0.225 0.349∗∗ 0.405∗∗
(0.173) (0.113) (0.197) (0.132) (0.177) (0.155) (0.163)
∆πtCP I 0.322∗∗ 0.302∗∗∗ 0.247 0.218∗∗∗ 0.272∗ 0.199∗∗∗ 0.205∗∗ -
-(0.137) (0.063) (0.156) (0.071) (0.141) (0.070) (0.083)
∆πtCP IX - - - - - - - 0.271∗∗
-(0.108)
∆πtcore - - - - - - - - 0.150
(0.102)
∆yt −0.014 0.574∗∗∗ 0.055 0.570∗∗∗ −0.394 0.476∗∗ 0.636∗ 0.548 0.693∗ (0.327) (0.167) (0.334) (0.160) (0.324) (0.207) (0.324) (0.334) (0.347)
∆et - - - - −0.135∗∗∗ −0.030∗ −0.018 −0.028 −0.034
(0.047) (0.016) (0.020) (0.020) (0.021)
∆sharegapt - - - - 0.066∗∗ 0.012 0.012 0.013 0.013
(0.031) (0.011) (0.012) (0.012) (0.013)
∆housegapt - - - - 0.123 −0.019 −0.117 −0.057 −0.068
(0.118) (0.060) (0.086) (0.080) (0.092)
φˆπ 0.322∗∗ 0.302∗∗∗ 0.299∗ 0.292∗∗∗ 0.356∗∗ 0.286∗∗∗ 0.265∗∗∗ 0.417∗∗ 0.253 φˆπ−1 −0.678∗∗∗ −0.698∗∗∗ −0.701∗∗∗ −0.708∗∗∗ −0.644∗∗∗ −0.714∗∗∗ −0.735∗∗∗ −0.583∗∗∗ −0.747∗∗∗
(0.137) (0.063) (0.169) (0.080) (0.162) (0.087) (0.086) (0.163) (0.165) φˆy −0.014 0.574∗∗∗ 0.066 0.762∗∗∗ −0.514 0.685∗∗ 0.820∗∗ 0.842∗ 1.165∗∗
(0.327) (0.167) (0.408) (0.242) (0.439) (0.280) (0.393) (0.465) (0.516)
R2 0.127 0.599 0.150 0.642 0.388 0.680 0.659 0.658 0.614
adj.R2 0.081 0.581 0.081 0.616 0.280 0.630 0.591 0.590 0.536
ρˆ 0.224 0.058 0.122 −0.114 0.088 −0.146 −0.117 −0.185 −0.078
P >|t| 0.161 0.705 0.447 0.452 0.581 0.333 0.502 0.289 0.651
DWd-stat. 1.542 1.691 1.738 2.061 1.733 2.121 2.100 2.216 2.066
Standard errors are reported in parentheses. Statistical significance at the 10%, 5% and 1% significance levels represented by∗,∗∗and∗∗∗
respectively. Output, share price, oil price and house price gaps calculated using a Hodrick-Prescott filter,λ= 1600, and are represented as percentages of the trend. ˆρis the estimated coefficient in a regression of the residual on its lagged value; a value for ˆρthat is statistically
31