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Theoretical model
The central bank’s monetary policy design problem is a targeting rule following Svensson (1999) and draws from Boinet and Martin (2008). The monetary policy reaction function is an adaptation of the New Keynesian setup that is modelled as an intertemporal optimisation problem where the central bank is assumed to use all available information available at any point in time to bring the target variables in line with their desired values.
Data description
Monthly data for South Africa spanning the period January 2000 to December 2008 is used in the analysis. The three month treasury bill rate is used to measure the rate of interest. The short term Treasury bill rate has commonly been used to proxy the official policy rate, particularly in similar studies such as Martin and Boinet (2008), Nelson (2003) for the United Kingdom. We prefer using this interest rate rather than the key policy rate, the repurchase rate, given that it contains more variation. The correlation between the repurchase rate and treasury bill rate during the sample period is sufficiently high at about 98 percent and drops to about 96 percent after 2007. This drop in correlation can be explained by the disruption of the close relationship between policy rates and money market interest rates during the recent financial crisis. Inflation gap is measured by the difference between the annual change in consumer price index and 4.5, which is the midpoint of the inflation target in South Africa.
Output gap is measured by the difference (in logarithms) between coincident business cycle indicator and its Hodrick and Prescott (1997) trend. Industrial production is often used as the measure of the output gap at the monthly frequency. However, this runs into operational problems because industrial production is not official data in South Africa. We also found that the coincident business cycle indicator is a better proxy for output because it is a much broader index and has a higher correlation with gross domestic product than industrial production at levels and in deviations from trend. The coincident business cycle indicator is the composite index comprising the following equally weighted components; Gross value added, Value of wholesale, retail and new vehicle sales, Utilisation of production capacity in manufacturing, Total formal non-agricultural employment and Industrial production index. The autoregressive (n) model with n set at 4 is applied to the output measure eliminate serial correlation and to tackle the end-point problem in calculating the Hodrick Prescott trend as in Mise et al. (2005a,b). This model was used to forecast twelve additional months that were then added to the series before applying the Hodrick Prescott filter.
The instrument set includes the lags of the independent variables, the long term government bond yield, annual change in M3 and the index of financial conditions gap. All the data is sourced from the South African Reserve Bank database. The main variables are depicted in Figure 2.3. The inflation rate is showing a persistent increase towards the end of the sample together with an accompanying increase in interest rate. The output gap is showing a severe downturn by the end of 2008.
Estimates for the non-linear monetary policy rule
The diagnostic tests show no serious misspecification except for a heteroscedasticity issue in the linear model. We implement two statistical tests to support the nonlinear results. The estimates of the linear model fail a Chow test of parameter stability. This conclusion is robust even when other dates for the break point of the stability test are used. This implies that the Taylor rule is inadequate as a model of monetary policy and provides further support for the model with target zones and asymmetries. The estimates of the preferred model with a symmetric zone response to inflation and a nonlinear response to output do not suffer from parameter instability. The Ramsey RESET test further concludes that the general specification of the linear regression model is not appropriate.
The results for both models show statistically significant coefficients for inflation gap and the output gap. The optimal monetary policy preferences implied by these estimates are illustrated in Figure 2.4. The preferred model shows a negligible response to inflation when it deviates by about 0.5 percent from the inflation target mid-point of 4.5 percent. The results show that the monetary authorities increase the nominal interest rates by 0.4 percent when inflation hits the upper threshold of the inflation target band so that the desired nominal interest rate is at 8.7 percent compared with the equilibrium interest rate of 8.4 percent. When inflation deviates by one percent outside the upper bound of the inflation target, the monetary authorities increase the nominal interest rates by 2.9 percent so that the desired nominal interest rate is 11.4 percent.
The benchmark model implies a constant response of interest rates to changes in inflation regardless of its deviation from the target. The results show that the monetary authorities move interest rates by 0.8 percent when inflation deviates from the inflation target range midpoint of 4.5 percent by 1 percent. The response of nominal interest rates to changes in inflation implied by the benchmark model is stronger than that which is implied by the preferred model when inflation is between 1.6 and 7.4 percent.
With regard to output, the estimated optimal monetary policy rule for the preferred model shows that the monetary authorities cut nominal interest rates by 1 percent when output undershoots the potential by 0.8 percent. The negative coefficient on the parameter that governs asymmetry implies that monetary authorities’ are more aggressive when output falls below that when it overshoots the potential. This implies that monetary authorities’ preferences’ are biased towards output expansions in that they weigh negative deviations of output more heavily than output expansions. The results for the benchmark model show a constant response to output contractions and expansions as discussed above. The estimated results show that the monetary authorities move the nominal interest rates by 0.4 percent when output deviates from the desired level by 1 percent. The preferred model implies a stronger reaction to output fluctuations compared with the benchmark model whenever output is below its potential.
Chapter 1
Introduction
Chapter 2
Optimal monetary policy reaction function with target zones and asymmetric preferences for South Africa
2.1 Introduction
2.2 Theoretical model
2.3 Data description
2.4 Empirical results
2.5 Conclusion
Chapter 3
Financial market conditions, target zones and asymmetries: a flexible optimal monetary policy reaction function for South Africa
3.1 Introduction
3.2 Theoretical model
3.3 Data description
3.4 Empirical results
3.5 Conclusion
Chapter 4
Financial market conditions and the response of monetary policy to uncertainty with asymmetric and zone targeting preferences in South Africa
4.1 Introduction
4.2 Theoretical model
4.3 Data description
4.4 Empirical Results
4.5 Conclusion
Chapter 5
Conclusion
References
