This Selected Issues paper for South Africa presents a quantitative analysis of inflation dynamics in the country. The conduct of monetary policy has been complicated by a variety of unanticipated events that have had important effects on inflation. Exposed to exchange rate and other shocks, the model confirms that a delayed policy response to inflation shocks leads to persistently higher inflation rates and, subsequently, to a sharp real contraction of the economy.

Abstract

This Selected Issues paper for South Africa presents a quantitative analysis of inflation dynamics in the country. The conduct of monetary policy has been complicated by a variety of unanticipated events that have had important effects on inflation. Exposed to exchange rate and other shocks, the model confirms that a delayed policy response to inflation shocks leads to persistently higher inflation rates and, subsequently, to a sharp real contraction of the economy.

I. A Quantitative Analysis of Inflation Dynamics in South Africa1

A. Introduction

1. Over the past decade, the South African Reserve Bank (SARB) has been remarkably successful in bringing inflation under control. Following the sharp depreciation at the end of 2001, inflation peaked at 11.3 percent in October 2002. The subsequent appreciation of the rand, monetary tightening and continuous improvements in the SARB’s inflation targeting framework led to a steady decline of inflation and, since September 2003, inflation has remained within the official target range of 3 to 6 percent. The conduct of monetary policy, however, has been complicated by a variety of unanticipated events that have had important effects on inflation. These include the recent sharp increase in petroleum prices, large fluctuations of the rand against other major currencies, but also the very benign development of food prices over the past years. Most of these unanticipated events or shocks tend to reflect exogenous factors which originated outside South Africa such as developments in international commodity prices, or portfolio rebalancing effects of international investors which may affect the exchange rate.2

2. This chapter applies a dynamic general equilibrium model, calibrated to the South African economy, to analyze inflation dynamics and risks to the inflation outlook in view of these shocks, including exchange rate shocks. A dynamic model that incorporates the central features of inflation targeting provides a consistent framework for understanding and interpreting inflation developments and for evaluating the central inflation forecast. In an inflation targeting framework, a sound inflation forecast is key to successful monetary policy. While the short-term outlook relies heavily on available high frequency data, the central forecast is usually based on various models.3 Most of these have, until recently, featured only backward looking behavior. The model applied in this chapter is a useful tool to integrate the short-term outlook into a medium-term framework that embodies the basic principle that the fundamental role for monetary policy is to provide an anchor for inflation and inflation expectations. We show that the model is able to display important empirical features of the monetary transmission mechanism. Exposed to exchange rate and other shocks, the model confirms that a delayed policy response to inflationary shocks leads to persistently higher inflation rates and, subsequently, to a sharp real contraction of the economy. The model can help to assess the policy response for exchange rate, other price and demand shocks that affect inflation.

B. A Small Open Economy Model

3. The model features a small open economy including forward-looking aggregate supply and demand with microfoundations, and with stylized (realistic) lags in the different monetary transmission channels.4 South Africa as the small economy faces internal shocks as well as external shocks from the rest of the world (here captured by the Euro area and the U.S). The rest of the world is not modeled and all variables related to it enter as exogenous variables. Output developments in the rest of the world feed directly into the small economy as they characterize foreign demand for South African products. Changes in foreign inflation and/or interest rates affect the exchange rate and, subsequently, demand and inflation in the South African economy.

4. Aggregate supply is described by a “New Keynesian Phillips” curve:5

πt=αππ4t+4+(1απ)π4t1++αYygapt+αz(ztzt1)+REStπ,πt=400[ln(cpit)ln(cpit1)]πt=100[ln(cpit)ln(cpit4)]zt=st+ln(cpit*)ln(cpit).

This augmented Phillips curve specification not only includes current inflation (π) and the output gap (ygap) but also expected and past inflation levels. The output gap is defined as the difference between actual and potential output. Expected inflation enters the equation due to the assumption of staggered price-setting (Calvo-style)6 while indexation schemes can rationalize the backward-looking inflation component. This somewhat stylized lag structure leads to a substantial degree of inertia in the inflation process which is observed empirically. The real exchange rate (z) reflects the effect of imported goods’ prices on inflation in an open economy.7 A residual captures other temporary exogenous effects that are not explicitly modeled.

5. Aggregate demand is modeled as follows:

ygapt=βygapLeadygapt+1+βygapLagygapt1βRRGAP(RRt1RRt1Equi)+βZGAPzgapt1+βygap*ygapt*+RESt1YGAP.

Demand for domestic goods depends on real interest rates (RR), the gap (zgap) between the real exchange rate and its equilibrium, the foreign output gap (ygap*) and expected and past demand. Only deviations of real interest rates, the exchange rate and foreign demand from long-run equilibrium levels matter, not their levels. Past demand affects current demand if habit persistence in consumption or adjustment costs of investment is assumed. A residual captures other temporary, exogenous effects.

6. The uncovered interest rate parity condition determines the exchange rate:

zt=zt+1(RRtRRt*RiskPtEqui.)/400+REStLZ.

The model displays Dornbusch-style overshooting due to the assumption of uncovered interest rate parity. In contrast to the foreign real return, the domestic return is assumed to be subject to some risk and, therefore, a risk premium is introduced. As the exchange rate in this model refers to quarterly data while interest rates are expressed in annual terms, some normalization is required. A residual captures other temporary, exogenous effects.

7. The monetary authorities are assumed to set nominal interest rates (RS) according to the following monetary policy rule (or reaction function):

RSt=γRLagRSt1+(1γRLag)[(RRtEqui.+π4t+γπ(π4t+4π4t4Target)+γYGAPygapt]+REStRS.

In an inflation targeting framework, the inflation forecast plays a crucial role in determining the policy rate. Any expected deviation of inflation from its target triggers a response of the nominal policy rate. The respective coefficient of these deviations has to be larger than one (Taylor Principle) to ensure stability of the model.8 In this case, real interest rates increase if inflation is expected to be above target, and vice versa. While inflation is the primary target, the output gap is also included in the reaction function reflecting the fact that the monetary authorities are not indifferent to output developments.9 Past levels of the policy rate are included in the reaction function to account for the fact that there is also some degree of partial-adjustment dynamics for the interest rate.

C. Parameterization of the Model

8. The parameters of the model can be determined in several different ways including: (i) by simultaneous estimation of the four equations using historical data; (ii) estimation of the structural parameters related to preferences and technology of the underlying general equilibrium model which determine the parameters above, and (iii) calibrating the model to display stylized facts of the monetary transmission mechanism.

9. Reliable estimation is complicated by several issues including; misspecification, nonobservability of some variables and structural breaks in the data.

  • The simple structure of the model is useful for tractability and understanding of the key transmission of and reaction to various shocks; however, it may imply misspecification, as important variable are omitted, such as commodity prices and production, fiscal variables, etc.

  • Some variables are not observable or very hard to proxy, such as the output gap and inflation expectations.

  • South Africa underwent major structural changes in the past decades, including the recent introduction of an inflation targeting regime. Inflation targeting aims precisely at altering the formation of inflation expectations, thus exacerbating the issue of structural breaks. In addition, the usual problems of data measurement error and frequent data revisions further complicate the analysis. While it is a future goal to formally estimate the parameters of the model, at present, only a calibration exercise is being performed.

10. The calibration exercise is performed on the basis of several criteria. First, country-specific knowledge about structural parameters or estimates available in other studies are employed. Second, model parameters are chosen to reflect some stylized facts of the monetary transmission mechanism. Third, parameters for similar models of other countries might provide a benchmark; in particular, the Canadian model prepared by Berg, Karam, and Laxton (2005), which has been refined over several years, serves as a benchmark. The properties of the key parameters, their values and the steady-state values of the model variables are discussed in Appendix A.

D. Shock Scenarios

The monetary transmission mechanism

11. The response of inflation, the output gap and the exchange rate to a monetary policy shock in the model concurs with the facts found in other empirical studies on the monetary transmission mechanism (Figure I.1).10 Two monetary policy shocks describing monetary tightening are analyzed: (a) a purely transitory shock that raises the policy rate by 100 basis points for one quarter above the baseline, and (b) a more persistent shock that raises the policy rate by 100 basis points for one year above the baseline.11 The temporary increase in interest rate will lower domestic demand and appreciate the exchange rate. Consequently, output drops and prices fall. The main effect of a monetary policy shock on inflation occurs in the quarters following those in which the output response is strongest. The effect on inflation peaks after about five to eight quarters while the impact on the output gap peaks after two to five quarters. The effect on the exchange rate is relatively small. Even the more persistent shock results in an immediate nominal appreciation of less than one percent.12

Figure I.1.
Figure I.1.

The Monetary Transmission Mechanism. Response of Inflation, Output and the Exchange Rate to Interest Rate Shocks

Citation: IMF Staff Country Reports 2005, 345; 10.5089/9781451966763.002.A001

Source: Fund staff calculations.

Exchange rate, other price and demand shocks

12. Shocks to the exchange rate have persistent effects on inflation and output only if the shock itself is serially correlated (Figure I.2). In this scenario, two different policy responses are analyzed: (a) interest rates are adjusted immediately according to the policy reaction function, and (b) the policy response is delayed and interest rates are kept at the baseline levels for two quarters before they are adjusted. An exchange rate shock that causes an unanticipated immediate depreciation of ten percent and displays some serial correlation13 raises inflation by about 0.6 percentage points one year later if monetary policy reacts immediately. Output rises by about 0.5 percentage points above potential three quarters later and then recedes, falling slightly below potential two years after the shock. If the policy response is delayed by half a year, inflation goes up by 0.8 percentage points a year later and the positive output response is stronger. The following output contraction, however, is more severe and inflation more persistently remains above the baseline.

Figure I.2.
Figure I.2.

Response of Inflation, Output and the Interest Rate to Exchange Rate Shocks

Citation: IMF Staff Country Reports 2005, 345; 10.5089/9781451966763.002.A001

Source: Fund staff calculations.

13. A persistent price shock would require a relatively strong policy response (Figure I.3). Exogenous price shocks could be interpreted as international oil or food price shocks. Even a temporary (lasting for a single quarter) price shock that raises the annualized quarterly inflation rate by one percentage point, requires a persistent increase in the interest rate which would peak at about 70 basis points above the baseline after three quarters. This is mainly due to the inflation inertia in the model. A delayed policy response would require a very sharp upward adjustment in interest rates.

Figure I.3.
Figure I.3.

Response of Output, the Interest Rate and the Exchange Rate to Price Shocks

Citation: IMF Staff Country Reports 2005, 345; 10.5089/9781451966763.002.A001

Source: Fund staff calculations.
Figure I.4.
Figure I.4.

Response of Output, the Interest Rate and the Exchange Rate to Demand Shocks

Citation: IMF Staff Country Reports 2005, 345; 10.5089/9781451966763.002.A001

Source: Fund staff calculations.

14. Exogenous demand shocks could be interpreted as changes in the fiscal policy stance that is not explicitly modeled here. A positive demand shock will raise output and consequently the output gap and will gradually put upward pressure on prices. This would require a tighter monetary policy stance that would lower demand and appreciate the exchange rate. Depending on the persistence of the shock, inflations would peak after 4–6 quarters. Again, a delayed policy response would result in a more severe adjustment.

E. Conclusion

15. This chapter has analyzed a dynamic small open economy model that is calibrated to the South African economy and embodies the basic principle that the fundamental role for monetary policy is to provide an anchor for inflation and inflation expectations. The model is able to display important empirical features of the monetary transmission mechanism that have been found in other studies. Exposed to exchange rate and other price shocks, the model confirms that a delayed policy response to inflationary shocks triggers persistently higher inflation rates and will eventually lead to a sharp real contraction of the economy. The model can serve as a useful policy tool. It helps to integrate the short-term inflation outlook into a consistent medium-term framework and to design the policy response for various shocks that affect inflation.

F. References

  • Berg, A., P. Karam and D. Laxton, 2005, “Model-Based Monetary Policy Analysis: A Practical Guide”, unpublished manuscript (Washington: International Monetary Fund).

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  • Calvo, G., 1983, “Staggered Prices in a Utility-Maximizing Framework”, Journal of Monetary Economics (12), pp. 383 -398.

  • Coats, W., D. Laxton and D. Rose, 2003, The Czech National Bank’s Forecasting and Policy Analysis System (Prague: Czech National Bank).

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  • Kearns, J. and P. Manners, 2005, “The Impact of Monetary Policy on the Exchange Rate: A Study Using Intraday Data”, Research Discussion Paper (Sydney: Reserve Bank of Australia).

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  • Orphanides, A., 2001, “Monetary Policy Rules Based on Real-Time Data”, American Economic Review (91), pp. 964 -985.

  • Smal, M. and S. de Jager, 2001, “The monetary transmission mechanism in South Africa”, Occasional Paper (16) (Pretoria: South African Reserve Bank).

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  • Svensson, L., 2000, “Open-economy inflation targeting”, Journal of International Economics (50), pp. 155 -183.

  • Woodford, M., 2003, Interest and Prices: Foundations of a Theory of Monetary Policy, (Princeton University Press, Princeton, NJ).

G. Appendix

Phillips curve:

  • απ determines the importance of forward (and backward) looking components in inflation expectations. For example, a larger wage indexation to past developments would imply a lower απ. It is important to note that the lower απ, the more difficult it is for the monetary authorities to change inflationary patterns. αy characterizes the relation between the output gap and inflation. It increases, for example, with the number of firms that adjust prices every period.14 The larger αy, the less output responds to price level fluctuations. Hence, the larger αy, the smaller would be the sacrifice ratio (i.e. the cumulative loss in output as a percent of potential output necessary to permanently bring down inflation by 1 percentage point).15

  • αz relates directly to the weight of imported goods in the CPI basket and the pass-through of foreign-currency prices (and hence the nominal exchange rate) on to the domestic-currency prices of imports.16

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Aggregate demand (IS) curve:

  • The output gap tends to exhibit substantial inertia (high βygapLag) which is normally lower in developing than in industrial countries, and the effect from lead output (βygapLead) is usually limited. The effect of interest rates is crucial for the monetary transmission mechanism, as a larger βRRgap would imply a more effective monetary policy. The effects of exchange rates (βZgap) and of foreign output (βygap*) tend to be larger in more open economies. Significant lags in the transmission of monetary policy imply that the sum of βRRgap and βZgap should be relatively small compared to βyagapLag.

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Monetary policy reaction function:

A reliable policy function for South Africa has not yet been estimated and would be difficult to obtain given the short time period during which inflation targeting is practiced. In fact, these parameters represent the policy choices about a temporary trade-off between inflation and output fluctuations rather than empirical laws. A key parameter in this function is γπ, which captures the degree of aggressiveness of monetary authorities. Hence, a higher value for γπ implies that the authorities will respond to a given shock with a larger change in interest rate. This normally tends to frontload the output costs. The parameter γRLag measures he degree of aversion of authorities to alter the interest rates, so that a higher coefficients implies a slower monetary reaction to a given shock. Orphanides (2003) and others have argued that in light of the high degree of uncertainty about the output gap and substantial real-time measurement errors in output, the parameter on the output gap (γYGAP) should be rather small.

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The long-run steady state values for the variables of the model are as follows:

π4tTarget = 5.0 percent,

RRt* = 2.25 percent (historic average for the U.S. real short-term interest rate),

RiskPtEqui. = 1.75 percent.

The previous two figures imply a long-run equilibrium real interest rate of about 4 percent and a nominal short-term rate of about 9 percent. All gaps that measure deviations of actual variables from their long-run equilibria are by definition zero. Equilibria for the exchange rate and potential output are defined statistically through use of an HP filter. For the forecast period, potential output growth is set equal to 3.5 percent and the real equilibrium exchange rate is held constant.

1

Prepared by Thomas Harjes (AFR) with Luca Ricci (RES).

2

It is unclear, however, if and to what extent the sharp depreciation of the rand at the end of 2001 may have been due to the monetary policy stance in 2001.

3

Amongst others, the SARB employs econometric time series models, structural inflation models, and macroeconometric models.

4

The particular specification of the model follows closely the one developed by Berg, Karam and Laxton (2005) for the Canadian economy.

5

For a detailed derivation of the following equations within a dynamic general equilibrium framework, see Woodford (2003) and Svensson (2000).

6

See, G. Calvo (1983).

7

An increase in the real exchange rate (z) corresponds here to a real depreciation.

8

This strictly holds if there is no interest rate smoothing.

9

In this model, the exchange rate is a forward-looking variable determined on the basis of rational expectations and, at time t, does not offer additional information to that included in the output gap and inflation. It, therefore, does not need to be included in the monetary reaction function.

10

Smal and de Jager (2001) find a transmission lag of a monetary policy shock to inflation in South Africa of about 6–8 quarters.

11

The baseline refers to the basic model forecast without the shock.

12

In an empirical study for Australia, Canada, New Zealand and the U.K., Kearns and Manners (2005) find that an unanticipated tightening of 25 basis points immediately appreciates the nominal exchange rate by 0.2 to 0.4 percent.

13

This shock is modeled as an AR(1) process and the AR(1) parameter is 0.75, that is, after a year the shock is at about 30 percent of its initial level.

14

Woodford (2003) shows also how it would decrease with the degree of strategic complementarity of pricing decisions amongst producers, as more firms would tend to mimic price stickiness behavior.

15

The sacrifice ratio is 0.75 percent in this model.

16

A coefficient of about 0.15 can be derived from a weight of imports in the CPI of about 30 percent and an immediate pass-through to domestic prices of imports of about 40 percent.

South Africa: Selected Issues
Author: International Monetary Fund
  • View in gallery

    The Monetary Transmission Mechanism. Response of Inflation, Output and the Exchange Rate to Interest Rate Shocks

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    Response of Inflation, Output and the Interest Rate to Exchange Rate Shocks

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    Response of Output, the Interest Rate and the Exchange Rate to Price Shocks

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    Response of Output, the Interest Rate and the Exchange Rate to Demand Shocks