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A Bayesian-Estimated Model of Inflation Targeting in South Africa

Author(s):
International Monetary Fund. Research Dept.
Published Date:
June 2010
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This paper estimates with Bayesian method a monetary model of the South African economy, which encompasses both open-economy features and forward-looking behavior of private agents and of the monetary authority. Such models are essential tools of monetary policy under an inflation-targeting regime, in order to meet the ongoing challenge of keeping the inflation expectations anchored in the fact of external shocks.

South Africa announced an inflation-targeting regime in 2000, which was implemented in 2002, with a target range in the low-moderate zone (generally 3-6 percent). Such regime has served South Africa well. Following the sharp depreciation at the end of 2001, inflation peaked at 11.3 percent in October 2002.1 The subsequent appreciation of the rand and monetary tightening led to a steady decline of inflation and inflation remained within the official target range of 3-6 percent for several years. At the same time, continuous improvements in the South African Reserve Bank’s (SARB) inflation-targeting framework strengthened its credibility and inflation expectations became much better anchored. More recently, however, rising global food and energy prices, together with a thriving economy, have contributed to higher inflation in 2007 and 2008.

Indeed, recent international experience with inflation targeting, as discussed, for example, in Roger and Stone (2005) and Mishkin and Schmidt-Hebbel (2007), provides some support for the view that inflation targeting is associated with an improvement in overall economic performance. Inflation targeting tends to help countries achieve lower inflation in the long run, experience smaller inflation response to oil-price and exchange-rate shocks, strengthen monetary policy independence, improve monetary policy efficiency, and obtain inflation outcomes closer to desired levels.

However, several authors, including Calvo (2001) and Mishkin (2004) have pointed to the specific difficulties that emerging market economies may face in conducting inflation targeting. First, credibility issues may weaken the design of optimal macroeconomic policy in these countries, and may reduce the effectiveness of monetary policy. Second, weak institutions may lead to currency substitution or liability dollarization, or even fiscal dominance, largely reducing the capability of the monetary authorities to effectively target inflation. Third, large exchange rate and other external shocks complicate the conduct of monetary policy, by introducing substantial volatility.

South Africa is not particularly affected by the first two types of issues. Macroeconomic polices have been impressive and currency substitution or liability dollarization are virtually absent. In particular, the sharp depreciation of the rand in 2001–02 has proven that there is certainly no “fear of floating.” However, like many other emerging market countries, South Africa implementation of the inflation-targeting strategy is often challenged by large exogenous—often external—shocks, as discussed above. In the typical environment in which many emerging markets operate—small open economies well integrated within a globalized world—an essential tool for policymaking lies in a coherent forward-looking framework for assessing the effect of external and domestic shocks on inflation, and for gauging the appropriate policy response.

To this purpose, this paper estimates with Bayesian methods a small dynamic macroeconomic model for the South African economy. The estimated model can help assess—within an inflation-targeting framework—the impact on inflation dynamics of the main domestic and external factors, such as those arising from exchange rates, domestic prices, and domestic as well as external demand. It is also able to display important empirical features of the monetary transmission mechanism in South Africa, and helps evaluate the policy response to shocks that affect inflation.

The model incorporates the central features of inflation targeting, including forward-looking behavior of private agents and of the monetary authority. As such, it embodies the basic principle that the fundamental role for monetary policy is to provide an anchor for inflation and inflation expectations. At the same time, it offers a consistent framework for understanding and interpreting inflation developments and for evaluating the central inflation forecast.2 Indeed, in an inflation-targeting framework, a sound inflation forecast is key to successful monetary policy.

Fitting the parameters to the South African economy with conventional, classical estimation methods is a big challenge, given economic and political developments in South Africa over the past decades, involving several structural breaks. The preapartheid sample would not be particularly informative about today’s monetary transmission mechanism; the economy was characterized by prolonged periods of negative real interest rates as well as significant trade and capital restrictions. Currently, South Africa enjoys a much broader integration with world trade and capital markets, a flexible exchange rate regime, and a monetary transmission mechanism where the repurchase rate of the central bank has a key role.3

Therefore, the model is estimated employing Bayesian methods over the postapartheid period. Bayesian method present an advantage if the sample is short, to the extent the researcher brings to the exercise priors that are informative (for example, obtained from the experience of other countries, whose analysis maybe benefited from longer time series). Moreover, Bayesian methods do not need to rely on assumptions about distributions of estimators and test statistics over hypothetical repeated samples. They are less sensitive to econometric issues, such as unit root and cointegration, which heavily alter the frequentist approach.4

This paper is in line with a growing literature estimating with Bayesian method’s small macroeconomic models for specific countries, see, for example, Honjo (2007) and Iakova (2007) for the United Kingdom and Honjo and Hunt (2006) for Iceland. For recent applications of Bayesian estimation methods to much more comprehensive dynamic stochastic general equilibrium models, see, for example, Smets and Wouters (2003) for the euro area; Smets and Wouters (2005) and Iakova and others (2006) for the United States; Elekdag, Justiniano, and Tchakarov (2005) for Korea; Lubik and Schorfheide (2007) for Australia, Canada, New Zealand, and the United Kingdom; and Justiniano and Preston (2008) for Canada. For an application of Bayesian methods to estimate a macroeconomic model for South Africa, see Ortiz and Sturzenegger (2007).

I. A Small Open Economy Model

The model features a small open economy encompassing forward-looking aggregate supply and demand—as in the recent models with microfoun-dations developed by, among others, Woodford—as well as stylized lags in the monetary transmission channel. It includes internal shocks as well as external shocks from the rest of the world (here represented by the United States), which is kept exogenous. The particular specification of the model follows closely the one developed by Berg, Karam, and Laxton (2006a, 2006b) for the Canadian economy. The model is set up to represent the economy at a quarterly frequency and is mainly driven by four key equations: aggregate supply, aggregate demand, uncovered interest parity, and the monetary reaction function. Definitions and equilibrium relations complete the model. The properties of the key parameters are discussed in the Appendix, which also presents their values and the steady-state assumptions. These core equations are very close to standard ones in modern dynamic general equilibrium frameworks (Svensson, 2000; Walsh, 2003; and Woodford, 2003), although small modifications are in some cases necessary in order to bring the model to the data. Indeed, some features of the standard new Keynesian model have been persistently shown to be at odd with the data (the absence of a lag in the output gap in the Phillips curve ignores the higher persistence of this variable, while an uncovered interest parity with purely forward looking expectation would make the responsiveness of the exchange rate to shocks unrealistically high). Such modifications are discussed below.

The aggregate supply is described by a “New Keynesian Phillips” curve:

with

where π4t is the annual inflation rate, π4t+4 is the model-consistent inflation expectation four quarters ahead, πt is the annualized quarterly inflation rate, ygapt represents the output gap (defined as the difference between actual and potential output), zt is the log of the real exchange rate (an increase represents a real depreciation), cpit is the consumer price index, and st is the log of the nominal exchange rate (measured as local currency per 1 unit of foreign currency).5 A residual captures other temporary exogenous effects that are not explicitly modeled, such as supply or oil shocks. Thus, this augmented Phillips curve specification includes the output gap, the rate of real exchange rate depreciation, and both expected and past inflation levels. Expected inflation enters the equation due to the assumption of staggered price-setting (Calvo, 1983), while indexation schemes or the presence of irrational price setters can offer a rationale for the backward-looking inflation component (Steinsson, 2003). This somewhat stylized lag structure leads to a substantial degree of inertia in the inflation process, a phenomenon which is observed empirically. The real exchange rate reflects the effect of imported goods’ prices on inflation in an open economy.

Aggregate demand is modeled as follows:

Domestic output gap (ygapt) depends on both expected and past realizations of the domestic output gap, the lagged gap between the real interest rates (RRt) and its equilibrium value (RRequi), the lagged gap (zgapt) between the real exchange rate and its equilibrium value, and the foreign output gap (ygapt*). A residual captures other temporary, exogenous effects (such as fiscal policy or other demand shocks).6 Only deviations of real interest rates, the exchange rate, and domestic and foreign demand from long-run equilibrium levels matter (not their levels). The effect of past demand on current demand can be ascribed to, for example, habit persistence in consumption (Fuhrer, 2000) or adjustment costs of investment. Future domestic demand can reflect the effect of intertemporal smoothing, or of forward-looking investment choices.

The uncovered interest rate parity condition in real terms determines the real exchange rate:

with

and RiskptEqui. reflecting the equilibrium level of the domestic risk premium (the foreign real return, RRt* , is assumed to be risk-free).7 A residual captures other temporary, exogenous effects, such as exogenous exchange rate shocks. The model displays Dornbusch-style overshooting with δ = 1. However, in this case, the exchange rate predicted by the model would tend to be excessively volatile compared with the data. Therefore, it is common to assign to δ a value less than one, although this would imply a deviation from fully rational expectations.

The monetary authorities are assumed to set the short-term nominal interest rates (RSt) according to the following monetary policy rule (or reaction function):

where RRtEqui is the equilibrium real interest rate (see the Appendix for a derivation) and π4t+4Target is the inflation target four quarters ahead. A residual captures other temporary, exogenous effects, such as policy mistakes.

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 (γπ) has to be larger than 1 (Taylor principle) to ensure stability of the model.8 In this case, the real interest rate increases if inflation is expected to be above target, and vice versa. Although 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. Past levels of the policy rate are included in the reaction function to account for partial-adjustment dynamics in the interest rate, resulting, for example, from the preference of the monetary authorities for interest rate smoothing. Such a preference has been empirically found to be high (high γRLag) in estimations of these models, possibly reflecting the resilience to respond aggressively to shocks in light of the uncertainty surrounding the persistence of the shocks.

II. Bayesian Estimation of the Model

This section estimates the model using Bayesian methods.9 The main estimation sample is 1994–2005, to capture the full postapartheid period, but results are quite similar when replicated only for the more recent period since the announcement of the inflation-targeting regime in 2000. We use data for nine series. CPIX inflation (πt) is from the SARB. Three other series are derived from the IMF’s International Financial Statistics data set: the short-term nominal interest rate (RSt, three-month government bonds), the bilateral real exchange rate vs. the United States (zt), and the U.S. short-term real interest rate (RRt*, the nominal interest rate on the three-month U.S. treasury bills minus the one-year inflation rate). The model is expressed in terms of gaps, for example, the gap between actual and potential output in the absence of nominal rigidities influences inflation. The output gap, in turn is also determined by the gap between the real interest rate and the natural rate, or equilibrium rate prevailing in absence of nominal rigidities. We follow the common approach in the literature for the canonical model of Woodford (2003) and estimate potential output, the natural rate of interest and other long-run equilibrium values with the use of simple linear filters (Lubik and Schorfheide, 2007).10 The Appendix describes how we derived the remaining five series: the domestic output gap (ygapt), the U.S. output gap (ygapt*), the real exchange rate gap (zgapt), the equilibrium domestic real interest rate (RRtEqui), and the inflation target (π4t+4Target).

Given a set of observables YT over a sample period T and a set of priors p (θ), the posterior density of the model parameters θ is given by:

where YT is the above set of nine variables and θ is the vector of eighteen parameters.11

A summary of the assumptions regarding the distribution of the priors for the parameters of the model and for the shocks can be found in Table 1. The type of distribution is chosen on the basis of the range of admissible values for the parameters (the beta distribution ranges between 0 and 1, whereas the gamma and inverted gamma ones are positive). The prior values for mean and standard deviations are guided by the following criteria (a deeper discussion of the choice of other priors is provided in the Appendix). 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 provide a benchmark (in particular, the U.S. and Canadian models prepared by Berg, Karam, and Laxton, 2006a and 2006b, which have been refined over several years). Fourth, the intuition behind the economic effect of the parameters of the model (described in the Appendix) has also guided the assessment of the suitability of the priors for the South African economy.

Table 1.Priors
ParameterMeanDistributionSD
απ0.250Beta0.10
αy0.300Gamma0.10
αz0.150Beta0.05
βyld0.050Beta0.02
βylg0.700Beta0.05
βrr0.120Gamma0.03
βz0.050Gamma0.01
βf0.200Gamma0.05
γlg0.500Beta0.10
γπ2.000Gamma0.30
γy0.300Beta0.05
δ0.500Beta0.10
λ10.800Beta0.05
λ20.800Beta0.05
λ30.800Beta0.05
λ40.500Beta0.25
λ50.700Beta0.10
RR steady state3.500Gamma1.00
SD of supply shock2.000Inv. gamma
SD of interest shock2.000Inv. gamma
SD of demand shock1.000Inv. gamma
SD of exchange rate shock3.000Inv. gamma
SD of ygap*0.500Inv. gamma
SD of RR*1.000Inv. gamma
SD of zgap5.000Inv. gamma
SD of RRequi0.300Inv. gamma
SD of π4target0.500Inv. gamma
Note: See Appendix for the choice of priors and an explanation of the λs. “SD” stands for standard deviation and “Inv.” for inverse.
Note: See Appendix for the choice of priors and an explanation of the λs. “SD” stands for standard deviation and “Inv.” for inverse.

The task was particularly difficult for the priors related to the monetary policy reaction function, as reliable estimates of the corresponding parameters are notoriously difficult to achieve. Moreover, the time period over which South Africa has implemented inflation targeting is relatively short. As priors for the weights on the lagged interest rate term and inflation, we use the values suggested by Berg, Karam, and Laxton (2006b) for the United States and Canada, which are close to those chosen by Lubik and Schorfheide (2007) for Australia, Canada, New Zealand, and the United Kingdom. We assign a somewhat smaller value to the output gap term in view of the greater potential of measurement error in real time (Orphanides, 2001). In contrast to some other recent studies on monetary policy in small open economies (Justiniano and Preston, 2008), we do not include the nominal exchange rate directly in the monetary reaction function. This is consistent with the evidence found by Ortiz and Sturzenegger (2007, Figure 3), who find a coefficient close to zero for the exchange rate fluctuations in the monetary reaction function of South Africa in 1997–2006. More broadly, empirical evidence in this regard is mixed, according to Lubik and Schorfheide (2007), who find evidence suggesting that the central banks of Australia and New Zealand do not target the exchange rate explicitly, whereas the Bank of Canada and the Bank of England do include the nominal exchange rate in their policy rule. Augmenting the policy rule in this regard could be an interesting area for future research.

Figure 1.Prior and Posterior Distributions: Selected Parameters

Note: The dotted line represents the prior point estimate, the gray and black lines represent the prior and posterior distributions, respectively, obtained using the Metropolis-Hastings algorithm.

Figure 2.Interest Rate Shock

(Deviations from control)

Note: Dynamic responses of output, interest rates, and inflation and exchange rates to a 100 basis point rise in the policy rate for one quarter.

Figure 3.Exchange Rate Shock

(Deviations from control)

Note: Dynamic responses of output, interest rates, and inflation and exchange rates to a 10 percent nominal depreciation for one quarter.

On the basis of the priors, we search for the posterior modes using Sims’ algorithm and check that a local optimum is found at these modes. Starting from these modes, we estimate the parameters by drawing from the posterior density using the Metropolis-Hastings algorithm with 500,000 replications. The acceptance rate for each draw was around 30 percent and convergence was achieved on the basis of the Brooks and Gelman (1998) criterion.

Table 2 reports the estimates for the posterior mean and the 90 percent confidence interval (for the reader interested in the frequentist interpretation of the result). The results should obviously be interpreted as a Bayesian updating of the authors’ priors. Figure 1 presents the prior and posterior distributions for selected parameters. The most notable characteristics of the estimation are inflation is reasonably forward looking (0.44 is the coefficient of lead inflation); and interest rates are highly sluggish (0.75 is the coefficient of lagged interest rate in the monetary reaction function). Data seem to be informative about most parameters, apart from the ones reflecting the inflation and output weights in the monetary reaction function. This is not surprising as the inflation-targeting regime has been adopted only recently, and implies that the monetary reaction function is mainly calibrated by priors than estimated by the data. The calibration for such a function is based on the Taylor rule, evidence for other countries adopting inflation targeting, and the objective of obtaining a reasonable policy and economic response to shocks. Nonetheless, the estimated parameters are quite close to those obtained from Ortiz and Sturzenegger (2007, Figure 3) for the 1996–2006 sample.

Table 2.Estimates: Posterior Distribution
Parameter90% Confidence Interval
απ0.4340.2330.631
αy0.2280.1050.339
αz0.1460.0760.208
βyld0.0430.0160.068
βylg0.7460.6820.809
βrr0.0860.0550.117
βz0.0270.0190.035
βf0.1430.0910.194
γlg0.7000.6070.793
γπ1.9321.4332.401
γy0.2830.2070.360
Δ0.4340.3720.498
λ10.8770.8300.922
λ20.8790.8380.921
λ30.8040.7390.872
λ40.9820.9670.998
λ50.9910.9860.996
RR steady state3.4222.2634.540
SD of supply shock2.6572.1723.104
SD of interest shock1.2861.0581.513
SD of demand shock0.5790.4710.687
SD of exchange rate shock6.2915.1577.346
SD of ygap*0.4820.4010.559
SD of RR*0.5410.4510.628
SD of zgap5.5574.6516.414
SD of RRequi0.2120.1760.246
SD of π4target0.2050.1690.241
Note: The posterior distribution is obtained using the Metropolis-Hastings algorithm. See the Appendix for an explanation of the λs. “SD” stands for standard deviation.
Note: The posterior distribution is obtained using the Metropolis-Hastings algorithm. See the Appendix for an explanation of the λs. “SD” stands for standard deviation.

We also checked whether the results were robust to a different sample, a richer lag structure, or different priors. First, we estimated the model in a more recent sample (2000–05), given that the inflation-targeting regime was announced in 2000. Most parameters were very similar; the main difference, quite surprisingly, is visible in the less forward-looking component of inflation in the 2000–05 sample. The data are again not particularly informative about the monetary reaction function. Second, we also estimate a model with richer dynamic structure, to check whether the simulated response to shocks would be substantially different (see the Appendix for details on the richer dynamic structure). The parameters are generally similar, but the richer model has a lower marginal data density, which suggest that the more parsimonious model is preferred (as the two models are estimated on the basis of the same dataset, the marginal data density can allow us to compare them, by providing a summary indication of whether the use of additional parameters is justified on the basis of a better fit). Third, we tried different priors and the final results were generally similar.

III. Shock Scenarios

The Monetary Transmission Mechanism

The response of inflation, the output gap, and the exchange rate to a monetary policy shock in the model is consistent with the evidence found in other empirical studies of the monetary transmission mechanism (Figure 2).12 In particular, the model’s features are broadly consistent with the core forecasting model of the SARB (2007), which is a macroeconometric model with 18 structural equations. Considering deviations from the equilibrium solution of the model (control), a 100-basis point shock to the interest rate lowers domestic demand, appreciates the exchange rate, and, consequently, prices fall. To counter the fall in prices and the slowdown in output, the central bank lowers interest rates that fall below control about a year after the shock occurred. The effects on inflation and output peak several quarters after the initial monetary contraction. The effect on the exchange rate is relatively small. The monetary tightening results in an immediate nominal appreciation of less than one percent and nominal appreciation peaks at about 1.5 percent two quarters later.13

Exchange Rate, Price, and Demand Shocks

Shocks to the exchange rate have relatively moderate effects on inflation (Figure 3).14 An exchange rate shock that causes an unanticipated immediate appreciation of ten percent lowers inflation by about 0.6 percentage points one year later. Monetary policy reacts immediately by lowering interest rates by about 30 basis points, and the cumulative response amounts to 100 basis points after one year. Output falls by about 0.6 percentage points below potential, also with about a one-year lag and then recovers.

A price shock would require a relatively strong policy response (Figure 4). Exogenous price shocks could be interpreted as international oil or food price shocks. A price shock that initially raises the annualized quarterly inflation rate by 1 percentage point requires an increase in the nominal interest rate of about 140 basis points above the baseline after three quarters. This would increase the real interest rate by about 1 percentage points for several quarters. The associated output cost would be quite sizable, with the output gap peaking at about a negative 1 percentage point of GDP after two years and remaining in negative territory for about five years. This is mainly due to the inflation inertia in the model.

Figure 4.Price Shock

(Deviations from control)

Note: Dynamic responses of output, interest rates, and inflation and exchange rates to a 1 percentage point increase in inflation for one quarter.

Exogenous demand shocks could be interpreted as changes in the fiscal policy stance that is not explicitly modeled here. A positive demand shock of one percent of GDP (Figure 5) will raise the output gap. Inflation would increase only moderately (0.2 percent after about one year), as a tightening of the monetary policy stance would bring the policy rate by almost half of a percent. This would dampen demand and lead to a (nominal and real) exchange rate appreciation by about 2 percent in two years.

Figure 5.Demand Shock

(Deviations from control)

Note: Dynamic responses of output, interest rates, and inflation and exchange rates to a 1 percentage point increase in the output gap for one quarter.

IV. Conclusion

This paper employs Bayesian methods to estimate a dynamic small open economy model for the South African economy. The model is tailored to the analysis of the effect on inflation of domestic and foreign shocks under an inflation-targeting regime. It embodies the basic principle that the fundamental role for monetary policy is to provide an anchor for inflation and inflation expectations. Although model and estimation uncertainties are bound to be large in these exercises, the estimated model is able to display important empirical features of the monetary transmission mechanism and can help assess the dynamic response of the main macroeconomic variables to shocks. Overall, the model can serve as a useful policy tool: it helps to integrate the short-term inflation outlook into a consistent medium-term forward-looking framework, and to design the policy response for various shocks that affect inflation.15,16

Appendix

The Role of Parameters in the Model

Phillips Curve

  • απ(1–απ) determines the importance of forward (backward)-looking components in inflation expectations. For example, a larger wage indexation to past developments would imply a lower απ. Note that the lower απ, the more difficult it is for the monetary authorities to change inflationary patterns, as the effect of inertial inflationary behavior is stronger. Given that South Africa has experienced high and volatile inflation in the recent past than Canada and the United States, we pick a slightly higher value, 0.25, than Berg, Karam, and Laxton (2006b) used for Canada and the United States.

  • αY, the slope of the Phillips curve, increases with the responsiveness of inflation to the output gap (it increases, for example, with the number of firms that adjust prices every period).15 Hence, the larger αY, the smaller would be the sacrifice ratio (that is, the cumulative loss in output as a percent of potential output necessary to permanently bring down inflation by 1 percentage point).16 We choose αY equal to 0.3, consistent with values reported in the literature (Gali and Gertler, 1999).

  • αZ relates directly to the weight of imported goods in the consumer price index (CPIX) basket and the pass-through of foreign currency prices (and hence also the nominal exchange rate) onto the domestic-currency prices of imports. A prior of about 0.15 can be derived from a weight of imports in the CPI of about 30 percent and an immediate pass-through of about 50 percent.

Aggregate Demand Curve

  • The output gap tends to exhibit substantial inertia (high βygapLag), as mentioned above possibly because of habit persistence. But, consumption smoothing is likely to be more constrained in developing than in industrial countries, although the effect from lead output (βygapLag) is usually limited. Accordingly, our priors for βygapLag and βygapLag are somewhat lower than values commonly applied for industrial countries (Berg, Karam and Laxton, 2006b).

  • 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 with βygapLag. Our priors for βRRgap, βZgap and βygap* (0.12; 0.05; and 0.2) are consistent with values reported in the literature (Lubik and Schorfheide, 2007), once our prior for the effect of the lagged output gap is accounted for.

The Uncovered Interest Parity

  • The parameter δ (with 0<δ<1) determines the degree to which exchange rate expectations are forward looking as opposed to backward looking. A value closer to 1 implies much more forward-looking expectations and make the exchange rate react much more in response to anticipated changes in fundamentals. As discussed in the text, a value equal to 1 delivers a standard uncovered interest parity condition and Dornbusch style overshooting.

Steady State and Forecast Assumptions

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

  • π4tTarget = 4.5 percent (the midpoint of the inflation-targeting range),

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

  • RiskptEqui. = 1.25 percent, close to the spread in the last few years of the sample.

In steady state, these figures imply a real interest rate of about 3.5 percent and a nominal short-term rate of about 8 percent. All gaps that measure deviations of actual variables from their long-run equilibria are by definition zero. The real equilibrium exchange rate is held constant.

Estimation Assumptions about Nonobservables

  • The domestic and foreign output gaps (ygapt and ygapt*) are calculated as the respective difference between actual and the HP trend (with a smoothing parameter of 1600). To avoid the notorious end-of-sample problems of the HP filters, the series for actual output in South Africa is assumed to converge to a long-run potential output growth of 4 percent.

  • The real exchange rate gap (zgapt) is calculated as the difference between the actual real exchange rate and the equilibrium one. The latter is evaluated as the HP filter of the real exchange rate, but it is imposed that the gap is zero in 2005:Q2, by using the LRX filter (a more sophisticated version of the HP filter) described in Berg, Karam, and Laxton (2006b, Appendix IV).

  • The South African equilibrium real interest rate (RRtEqui.) is assumed to be equal to 1 percent in 1994 because of capital control (1 percent is approximately the average since 1970) and to reach 3.5 percent from 2007:Q4 onwards. In between these dates, it is smoothed using the using the LRX filter.

  • The South African risk premium (RiskptEqui.) is assumed to be the gap between the South African and the U.S. equilibrium real interest rate (the latter being assumed at 2.25, the historical average).

  • The inflation-targeting regime was announced in 2000 and started in 2002 with a target range of 3-6 percent. For the estimation purposes, we implicitly assume that the monetary authorities have been setting the interest rate with a criterion that is similar to inflation targeting throughout the sample. The inflation target (π4tTarget) is assumed to be given by the HP filter of actual inflation until end-2000 (by then, the actual inflation was close to the upper side of the range, 6 percent). Since 2001, it is assumed that the target progressively declines towards the middle of the range, 4.5 percent (more precisely, the inflation target is given by the LRX filter passing through: 6 percent in 2001:Q1, 5.5 percent in 2003:Q1, 5 percent in 2004:Q1, 4.5 percent in 2005:Q1). Note that in the estimation based on the 2000–05 sample, assumptions related to years before 2000 are irrelevant.

Estimation Assumptions about Variables Exogenous to the Theoretical Model

In the Bayesian estimation, the variables that are exogenous to the theoretical model (foreign output gap, foreign interest rate, real exchange rate gap, the equilibrium real interest rate, and the inflation target) are assumed to mean revert to their equilibrium or steady state value by an autoregressive pattern: X = λ*X (–1) + (1–λ)*Xbar, where X represents the five variables above and Xbar their steady state. Hence, in addition to the 12 parameters of the model, we also estimate five λ autoregressive terms, one for each variable, λ1 to λ5 respectively. As a consistency check, we also allow for the steady state real interest rate (toward which the equilibrium real interest rate converges at a rate equal to λ4) to be stochastic, and we estimate it (RR steady state in Tables 1 and 2); the estimation confirms a figure close to 3.5, consistent with the forecast assumptions. Hence, we estimate a total of 18 parameters.

The Model with Richer Dynamics

The richer model encompasses three additional terms: a second lag for inflation in the aggregate supply equation, to better account for inflation inertia; a lag of the change in the real exchange rate into the same equation, to better account for pass-through; a second lag of the real interest rate gap into the aggregate demand equation, to better capture the monetary policy transmission mechanism.

References

Thomas Harjes is a senior economist in the IMF European Department and Luca Antonio Ricci is a deputy division chief in the IMF Research Department. The authors started this project when they were desk economists for South Africa. The authors are highly indebted to Andy Berg, Philippe Karam, and Douglas Laxton for sharing their programs and also thank Peter Gakunu, Manuela Goretti, Nikolay Gueorguiev, Alejandro Justiniano, Ondrej Kamenik, Daniel Leigh, Papa N’Diaye, Sean Nolan, Frank Schorfheide, Theo Van Rensburg, Werner Schule, and participants in the presentation at the South Africa Reserve Bank and in the IMF Small Modeling Group seminars for very helpful discussions and comments. The Bayesian estimation is programmed in Dynare, a software kindly provided by Michel Juillard and his team.

It is unclear, however, if and to what extent the sharp depreciation of the rand at the end of 2001 was a fully exogenous event or may have been in part due to the monetary policy stance in 2001.

Woodford (2003) presents comprehensive theoretical foundations for models encompassing these features.

It would be an interesting exercise to explore change in regime, but this is beyond the scope of the paper and is left for future work.

On the advantages of Bayesian methods, see Koop (2003), Lancaster (2004), and Koop, Poirier, and Tobias (2007).

The consumer price index employed in the paper is the measure targeted by the SARB, which excludes interest payments on mortgage loans (CPIX).

As the model is tailored to represent short-run dynamics and the monetary transmission mechanism, there is no explicit formalization of the supply side of the economy. Hence, the dynamics of the output gap mainly reflect movements in the demand side of the economy.

Some normalization is required: the interest rate term needs to be divided by 400, because the interest rates and the risk premium are measured in percent at annual rates, whereas changes in the logarithms of the exchange rate are quarterly.

This strictly holds if there is no interest rate smoothing.

A broad discussion of the methodology and related issues is offered by Geweke (1999), Schorfheide (2000), and An and Schorfeide (2007). For general references on Bayesian estimation, see Koop (2003) and Lancaster (2004). The estimation is implemented using Dynare (see http://www.cepremap.cnrs.fr/dynare/).

In models with fully specified preferences and technology, such as the model of Smets and Wouters (2003), a model-based output and real interest rate gap can be derived. Smets and Wouters argue that for monetary policy purposes, the appropriate estimate of potential output and the natural interest rate should only take into account the parts of the natural level of output and the interest rate that are driven by shocks arising from preferences and technologies. They derive a model-based output and real interest rate gap but show that there is considerable uncertainty around it.

In addition to the 12 parameters of the model, we also estimate the steady state real interest rate and the autoregressive terms for the five observable variables that are exogenous to the theoretical model (see the Appendix).

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

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

With Dornbusch-style overshooting (δ = 1), the effects of exchange rate shocks on inflation and output would be even less persistent.

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

The sacrifice ratio is about one in this model.

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