Deriving an Optimal Monetary Policy Rule for South Africa

Andrea Masia1

in partial fulfilment of the Degree:

Master of Commerce (Economics)

University of the Witwatersrand July 2009

Thesis Supervisor: Dr. C. Malikane, Centre for Studies in Financial Markets and Macroeconomics, School of Economic and Business Sciences, University of the

Witwatersrand

1 Morgan Stanley & Co plc. The views expressed are attributable to the author and are not necessarily shared by Morgan Stanley or any of its subsidiaries. A particular word of thanks to Dr Brian Khan and Dr Greg Farrell of the South African Reserve Bank for providing the data that enabled this exposition; Danelee van Dyk; and an anonymous referee for insightful comments.

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Introduction South African monetary policy has undergone significant shifts in design over the last three decades. Policy regimes including ‘eclectic’ variants of monetary aggregate and exchange rate targeting often led to inflation and output outcomes which could be considered sub-optimal. For example, Aron & Muellbauer (2005) show that as such policy regimes evolved, the average rate and volatility of real GDP, and their own measure of the output gap, progressively improved over the period 1981 – 2004. Similarly, the average level of nominal interest rates declined over time as inflation tracked progressively lower, albeit the most recent era under the leadership of Governor Mboweni was shown to have been associated with a volatility in nominal interest rates comparable to the De Kock era of 1981Q1 – 1989Q2. The dissatisfaction with such eclectic styles of monetary policy is what subsequently led to the adoption of a more transparent and accountable inflation-forecast targeting framework in February 2000, in much the same spirit as that of the Central Bank of New Zealand, the Central Bank of Turkey and the Bank of Canada. Under this framework, the South African Reserve Bank has been assigned an inflation target2 to be maintained on a continuous basis. To achieve this, full instrument independence has been awarded to the central bank. The benefits of inflation targeting are well documented (see Svensson [1996], Bernanke et al [1999], Woodford [2004] and their references), suffice to say that they are generally characterised by increased transparency and predictability of the monetary policy process; the establishment of a framework which allows inflation expectations to anchor at a predetermined level; improved coordination between monetary and fiscal policy; as well as enhancing the accountability and ultimately the credibility of the central bank. For the most part, the South African Reserve Bank (SARB) has enjoyed these benefits. But, as has been highlighted in its recent experience (2006-2009), the inflation targeting regime is being stress-tested by a multiplicity of exogenous shocks. Indeed, after having achieved a target-consistent rate of inflation for approximately 50 percent of the period for which the SARB was mandated to do so, CPIX inflation exceeded the upper limit of the target range in 2007Q2, and is expected to remain out of target until 2010Q2 by most private sector economists. In fact, the most recent inflation data available implies that the SARB’s success ratio3 stands at a just 40 percent. This could fall further, to 39% if the SARB were to only meet their inflation objective by the second half of 2010, as most analysts expect. Understandably, South Africa is a small open economy that is vulnerable to shocks to the exchange rate and relative prices. The focus of monetary policy under such conditions should therefore be on anchoring inflation expectations and controlling the emergence of price pressures across other areas of the consumer price index (so called second round inflation). The challenge however, is that too long a period of above-target inflation readings

2 The target variable is the consumer price index, less mortgage repayment costs (CPIX). The target range for the CPIX is between 3 – 6 percent per annum, and was announced in the February 2000 National Budget Speech.

3 Defined as the proportion of time that the SARB has met its inflation mandate since inception in February 2000.

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may ultimately destabilise expectations and the monetary policy anchor, bringing into question the credibility and inflation fighting resolve of the central bank. The question we pose in this paper is as follows: In light of such shocks over the last two and-a-half decades, exogenous or endogenous, is it possible to define an optimal monetary policy rule for the SARB, and has the observed policy reaction been consistent with such an optimum? In this paper, a workhorse macro-model similar to that of Svensson (1996), Ball (1998) and Rudebusch & Svensson (1998) is used to assess the extent to which the SARB may or may not have responded optimally to aggregate shocks. To do this, an optimal monetary policy rule has been calibrated based on estimated parameters, with the corresponding costs and benefits of adhering to this rule presented. The advantage of such a stylised framework lies in the tractability of the analysis, its empirical consistency, and the reasonableness of its dynamics. In section 2 herein, a brief discussion of two well known model frameworks in the macroeconomic literature is provided, summarising the key tenets of each and the motivation for this study adopting its chosen approach. Section 3 provides the formal derivation of the model, while Section 4 handles its econometric estimation and calibration. Section 5 discusses the implications of the derived monetary policy rule and its impact on inflation and economic growth in the model economy. Section 6 provides a brief discussion on the implication of diverging from this derived optimum and the cost South Africa faces relative to several other economies. Section 7 concludes. 2. Competing Model Frameworks

In any such study that attempts to describe the economy within a stylised framework, a decision invariably has to be taken as to the modeling framework which will be followed, grounded in its ability to approximate the particular economy under study. Recent studies have adopted the Dynamic Stochastic General Equilibrium (DSGE) approach (McCallum & Nelson [1999], Clarida, Gali & Gertler [1999] and Rotemberg & Woodford [1997] among others), whose origins stem from the Real Business Cycle research program initiated by Kydland & Prescott (1982), and explained in detail by Stadler (1994), and Kremer (2006).

The adoption of DSGE techniques is most widely reflected in the “New Keynesian” literature, where explicit recognition of expectations by rational, utility maximising economic agents is incorporated; or as Kemp (2008) defines: “DSGE models can be described as small scale, structural simultaneous equation models firmly grounded in inter-temporal optimisation theory and micro economic principles.” The model economy is frequently set out in similar fashion to more traditional backward looking macroeconometric frameworks, whereby the economy is summarised by the output gap (or some other approximation of economic activity), a (New Keynesian) Phillips curve, a system of productivity and technology shocks, as well as the response of the central bank to the state of the economy (usually in the form of a Taylor rule). The relationships are derived from first principles and are of a forward looking nature (see: Clarida, Gali & Gertler [1999] for an excellent review of the New Keynesian approach to monetary policy).

Empirically however, the New Keynesian approximation of the observed response of output (or unemployment) and inflation to monetary policy shocks has been questioned due to its

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inconsistency with empirical evidence. In fact, the New Keynesian framework has been scathingly critiqued by Fuhrer & Moore (1995), Mankiw (2001) and Rudd & Whelan (2005), whereby the authors point out an inconsistent dynamic interaction of inflation and output, concluding that its specification is incapable of imparting the persistence to inflation commonly observed. Even after considering the theoretically rich New Keynesian Phillips curve (NKPC), Mankiw (2001) concludes that its impulse response function appears to suggest a dynamic path to unemployment in response to a contractionary monetary shock which is completely at odds with a priori expectations.

It is evident therefore, that the success of the forward looking New Keynesian model in replicating observed economic data is yet to be unquestionably achieved. Indeed, despite the principle motivation for “deep” structural parameters in this framework being to avoid the now infamous criticisms raised by Lucas (1976), the issues raised in the above (and in several other) studies all seem to point to the difficulty such models encounter when being reconciled with empirical data (see Estrella & Fuhrer [2002] for a further discussion).

In response to such short-comings of the DSGE framework, several researchers continue to subscribe to the more traditional, and admittedly more simplistic, backward looking framework’s of Svensson (1996), Ball (1997, 1998) and Rudebusch & Svensson (1998) among others. The underlying intuition here is similar to that of their forward looking contemporaries, except for the glaring absence of forward looking, expectation based parameters – precisely that which Lucas (1976) warned against! In his seminal critique, Lucas argued that the parameters of traditional macroeconometric models depended implicitly on agents’ expectations of the policy process, and were unlikely to remain stable as policy makers changed their behaviour. Nevertheless, such policy models remain widely used because the empirical significance of the Lucas Critique remains an academic debate (eg.: Rudebusch, [2002] and Linde [2001]).

The strong empirical consistency of the backward looking models has resulted in their widespread adoption by the world’s central banks. In fact, there may be reasons why such a framework would be better suited to the South African case in particular: Taylor (1993) discusses how the assumption of rational expectations may be inappropriate under monetary policy transition periods, particularly as economic agents are unlikely to fully comprehend the new policy, or perceive the central bank’s policy resolve as credible in its early stages. Because expectations only gradually converge during this transition period, the impact of the monetary policy rule on the economy may be quite different than projected by an analysis that assumes rational expectations (Taylor, 1993). This is an issue which Rudebusch (2002) attempts to control for in his exposition, by including in his model economy a perfect world scenario where economic agents are fully rational, with no information asymmetries between the monetary authorities and households. He then subjects the system to varying monetary policy rules in order to gauge the structural stability of the model parameters. The results suggest that although the Lucas Critique is unquestionable theoretically, there is little evidence that the Critique exerts an important statistical influence in the backward looking setting.

Consistent with these findings, the core forecasting model of the South African Reserve Bank (SARB, 2007) is entirely backward looking. The inflation target, a publicly unknown point estimate in the model of between 3 – 6 percent (4.5 percent, say), is the only (implicit)

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component which the SARB considers as an element of a forward looking nature, providing an anchor for inflation expectations. Nonetheless, the explicit recognition of forward-looking expectations does not feature in the model’s design. Indeed, ex-Federal Reserve Board Governor Frederic Mishkin affirms that “backward looking models seem to fit the data better, and this is one reason why a model like that used by Rudebusch & Svensson (1998) is taken more seriously by policy makers than models that rely on forward looking expectations” (Mishkin, 1998). This view is further supported by former Federal Reserve vice chairman Blinder (1998).

3. A Small Macro Model Incorporating the framework specified in Svensson (1996), Ball (1998) and Rudebusch & Svensson (1998) a small macro model of the South African economy is specified as:

�� = ����� − ���� − ����� − ���� + � (1.1)

�� = ����� + ����� − ����� − ����� + �� (1.2)

�� = �� − ��� + �� (1.3)

All variables are expressed in logarithmic values. � represents the output gap, that is, the log of output relative to potential; i represents the nominal short term interest rate; and S

represents the real effective exchange rate (increase equals appreciation). � represents the deviation in the annual inflation rate from target (� = �� − � ∗� . � , � and � are i.i.d disturbances representing demand, supply and currency shocks, respectively. As in Svensson

(1996), the coefficients on � and � are assumed to be positive; all remaining coefficients are assumed to be non-negative. In addition, � and � fulfil � < 1, � < 1. Equation 1.1 is an open economy IS curve, relating output to lags of itself, the real interest rate and the real effective exchange rate. Here, output growth is proposed to decelerate in the real interest rate as consumption and investment stall under tighter monetary policy, whilst net exports contract under an appreciating exchange rate. Equation 1.2 represents an open economy Phillips curve, whereby inflation is determined by the lag of output and the lagged change in the exchange rate. A lag of itself is used to define the accelerationist version of the Phillips curve, capturing inflation persistence and adaptive expectations. The exchange rate captures the valuation effect of currency movements on import prices. Equation 1.3 is the real effective exchange rate, which supposes a positive relationship with the monetary policy instrument (the central bank repurchase rate, for example). This captures the notion that a rise in the interest rate makes domestic assets more attractive, as

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well as more costly to “short” on international currency markets.4 This therefore implies a positive relationship between the policy rate and the value of the real exchange rate. As in

Ball (1998), � captures all other influences on the exchange rate, such as expectations, risk premia, and foreign interest rates. Important to this model setup are the channels through which monetary policy affects inflation. Firstly, an increase in the nominal interest rate reduces the output gap with a periods lag. This contraction takes a further period lag before dampening inflation. Thus a monetary policy contraction takes a two period lag before impacting on inflation. This is the control lag imposed on the model. That the instrument affects inflation with a longer lag than it affects output is a crucial property, and is consistent with the results from a number of vector autoregression studies (Svensson, 1996). The second channel through which the monetary policy instrument affects inflation is through the exchange rate; the impact of a tightening in the policy rate raises the real interest rate contemporaneously. In accordance with Ball (1998), the direct exchange rate effect is the quickest channel from policy rates to inflation. In addition, output movements are persistent whilst inflation is inertial: once it rises, it stays high unless output contracts toward/further below potential (Ball, 1997). We now close the model by deriving the optimal monetary policy rule; which takes the form of a Taylor rule, such that the central bank responds optimally to developments in the output gap, the exchange rate, and the deviation of current inflation from its target. To do this, re-arrange equation (1.3) such that

� − �� = ������ (1.4)

By substituting (1.4) into (1.1), we obtain

�� = ������ − �� ���� − ����� − ���� + �� (1.5)

Shifting ahead one period, we illustrate how the central bank in period t determines the path of output and inflation in period t+1:

�� � = ���� − �� �� − ��� − �� + �� � (1.6)

�� � = ���� + ���� − ��� − ����� + �� � (1.7) By assuming the central bank exhibits some element of discretion5, we are able to derive the optimal criterion from a standard form of the central banks quadratic loss function. This is specified as a Lagrange problem which seeks to minimize the deviation of inflation and output from target, subject to the Phillips and IS curve constraints: 4 “Shorting” refers to a speculative trade in which financial market participants engage in a contract to sell a currency in the forward market. This requires the seller to borrow that currency at its own market rate (that economy’s policy rate), which when high proves as a disincentive.

5 Empirically supported in official SARB communiqué (SARB, 2000)

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min$�; &�

ℒ = (� ∑ �� *�� + +��,�-

�./ (1.8)

Subject to the constraints of equations (1.6) and (1.7); and where + represents the weight that the central bank places on the output gap in their reaction function. In later sections of this study, we investigate the implications of adjusting this weight towards more or less emphasis on the output gap6.

Given this problem, we use �� as a control variable to solve the central bank loss function. Therefore, differentiating with respect to �� results in the following first order condition: 0ℒ0��

= �� ��. � − +�� �. 2�� + 3 = 0 (1.9)

After substituting (1.6) and (1.7) into (1.9) and taking expectations, we can solve for St. This is shown as:

�� = 56&��7 + 58 9:;�$�

7 + 5<���=7 +

9:2��> 3?�

7 (2.0)

Where @ = 2�� + 3 and A = �� + @�+�

Using equation (1.3), we solve for and obtain the optimal reaction function/Taylor rule:

� = 256 �7� 3 �� + 258 9:;

7� 3 �� + 25<

7�3 ���� + 29:���7�< 3 �� (2.1)

The Taylor rule describes the optimal level of interest rates in the model economy. The central bank observes the deviation of inflation from target, the level of the output gap, the previous period’s exchange rate and its variation which is not explained by the real interest rate. Observing this criterion yields the optimal level of nominal interest rates. As the coefficients accompanying such variables are the structural coefficients derived from a stable IS curve, Phillips curve, and real exchange rate relation, the variation in the interest rate is

determined solely by the value of + chosen by the central bank and shocks to the real exchange rate. 4. Estimation and Calibration

The equations specified above have been estimated via ordinary least squares regression using quarterly time series data sourced from the SARB, spanning from 1980Q1 – 2008Q3. Before presenting the data, we find it necessary to highlight certain challenges experienced with sourcing the appropriate historical values. Firstly, monetary policy in South Africa aims

6 This provides an indication of the trade-off between strict inflation targeting, flexible inflation targeting, and a monetary policy that aims to minimize the output gap.

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to maintain the CPIX within a predefined target band7. Therefore, the CPIX would be the obvious definition of the price level in the SARB’s reaction function. Unfortunately, the CPIX was only first calculated and published by Statistics South Africa in January 1997. For the purpose of model consistency, a CPIX equivalent would therefore have to be used for the period 1980 – 1996. However, simply chain-linking (or “splicing”) the CPIX onto any previously available price measure, such as the headline CPI, may result in a structural break problem in the series as a result of combining two different price indices. To resolve this constraint, the SARB has kindly provided a “re-calculated” CPIX dating back to 1980, thus ensuring the underlying composition of the basket remains consistent with that which is being measured in the most recent CPIX index8.

The policy rate employed is the prime lending rate charged by commercial banks, which the SARB indirectly controls through changes to its policy rate (the repurchase rate). For the exchange rate, South Africa’s real effective exchange rate has been employed, whilst the output gap is measured as the ratio between expenditure on GDP, at seasonally adjusted and annualised constant prices, to potential GDP (derived from a Hodrick-Prescott filtered GDP series with the smoothing parameter set to 1600)9. Besides the central bank policy rate, all variables share a base year of 2000 and are specified in natural logarithms.

Table 1: Data Description

Variable Description

π Consumer Price Index excluding the cost of mortgage repayments

x Output gap; measured as the ratio of real GDP to potential GDP

s Real Effective Exchange Rate

i Prime lending rate

Source: South African Reserve Bank

7 As from January 2009, the targeted measure of inflation became the CPI. As this exposition considers the period 1980 - 2008, we will continue to focus on the CPIX as the price measure.

8 This measure simply excludes the mortgage repayment component from the headline CPI. As with any other form of economic time series, the index is still susceptible to changes in component weights in the CPI due to changes in consumer expenditure patterns.

9 Du Plessis & Burger (2006) discuss the drawbacks of assuming potential output in South Africa is well approximated by a smoothed output series. Although cognizance is taken of their critique, the results provided herein provide sufficient support that this measure - which is widely employed in the literature (including that from which this model derives) - provides the required theoretical implications. Further support for this technique is found in Aron & Muellbauer (2009) and their (2008) investigations into the core forecasting model of the SARB. Elsewhere, Du Toit (2008) discusses the appropriateness of setting the quarterly smoothing parameter to 352 for the South African business cycle. The above specified model has been re-estimated using Du Toit’s suggestion, the results of which are available upon request. Suffice to say that the final recommendations remain broadly similar.

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In estimating equations (1.1) – (1.3) the standard checks on ordinary least squares regression were performed, ensuring all estimations reflected the best linear and unbiased estimates of the structural parameters. Standard errors are calculated using the Newey-West (1987) covariance matrix to control for the autocorrelation of the residuals. The regression output from these equations is presented in Table 2 below:

Table 2: Parameter Estimates Equation/Parameter �� �� ��

α 0.81 [0.07]

β -0.96 [0.36]

θ 0.01** [0.01]

λ 0.97 [0.01]

γ 0.12* [0.06]

φ -0.05 [0.01]

ζ 1.16 [0.07]

Adj- R2 0.68 0.94 0.86

Regression S.E 0.95 0.99 5.26

F-Stat (p-value) 0.00 0.00 0.00

LM-test statistic 0.40 0.67 0.99

Source: Author’s estimates; Standard errors in parenthesis; * at the 5% significance level; ** at the 10% significance level

It is encouraging to note that the coefficient estimates are broadly similar to those found by similar studies [DeLong & Summers (1988), Rudebusch (1995), and Ball (1997)]. Unit root tests on each variable provided balanced regressions integrated of order I(0); π is I(1) however. As πt and πt-1 result in a cointegrated I(0) vector in the Phillips curve, addition of the output gap and real effective exchange rate to the resulting I(0) vector merely add explanatory power. Results of the unit root tests are summarised in Table 3 overleaf.

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Table 3: Unit Root Summary

Variable Augmented Dickey Fuller

Dickey Fuller GLS Test

Phillips- Perron

Kwiatkowski-Phillips-Schmidt-Shin

Elliot-Rothenberg Stock

x I(0) I(0) I(0) I(0) I(0)

(i- π) I(0)* I(0)** I(0)** I(1) I(0)

s I(1) I(0) I(1) I(0)** I(1)

π I(1) I(1) I(1) I(0) I(1)

(st - st-1) I(0) I(0) I(0) I(0) I(0) Source: Author’s estimates; * at the 5% significance level; ** at the 10% significance level

As previously highlighted, the model setup in this exposition is in contrast to developments in New Keynesian economics, whose benefit is derived from micro-foundations which circumvent the Lucas Critique. Although Rudebusch (2002) investigates its empirical statistical significance, some insight into the susceptibility of the model estimated herein is constructive. Figure 1 provides a plot of the parameter values obtained through recursive estimation. Were the Lucas Critique to be relevant in the estimated model, clear shifts in the parameter values would be recorded as economic agents alter their response to changes in economic policy. The results herein however suggest that after the initial period of regression instability, the coefficients converge to their estimated long run averages, and remain stable over the sample period. The exception here appears to be the clear adjustment in the pass through from the output gap to inflation (γ), and of the real interest rate to the exchange rate (ζ) in the first half of the estimation sample. As this was a period where South Africa suffered from the restrictive nature of trade and financial sanctions, as well as a shifting currency regime, it is likely that the structural nature of these coefficients were relatively unstable over this period.

A more statistically orientated test has also been performed to determine the structural stability of the model parameters, by means of the Chow (1960) breakpoint test. For this test, an explicit assumption as to the possible breakpoint date must be made. In light of the discrete periods of excess volatility in the Rand in the latter half of the estimation sample, we first investigated the possibility of structural breaks in the REER (ζ), particularly over the period 1996, 1998, and 2002, where private sector economic commentators believed the Rand to have suffered a currency crisis. The test finds no evidence of structural breaks in these periods. Similar investigations for the output gap and Phillips curve equations were also performed; however without explicit knowledge of possible breakpoints, the Quandt-Andrews test which allows one to test for several unknown breaks over the sample period was performed. The results corroborate those obtained by the Chow test, providing no evidence of a structural break. We conclude that the Lucas Critique does not appear to pose a significant challenge to the estimation of the structural parameters.

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-0.8

-0.4

0.0

0.4

0.8

1.2

-0.8

-0.4

0.0

0.4

0.8

1.2

1980 1985 1990 1995 2000 2005

Alpha

-5

0

5

10

15

20

25

-5

0

5

10

15

20

25

1980 1985 1990 1995 2000 2005

Beta

-.10

-.05

.00

.05

.10

-.10

-.05

.00

.05

.10

1980 1985 1990 1995 2000 2005

Theta

0.2

0.4

0.6

0.8

1.0

1.2

0.2

0.4

0.6

0.8

1.0

1.2

1980 1985 1990 1995 2000 2005

Lambda

-.4

-.2

.0

.2

.4

-.4

-.2

.0

.2

.4

1980 1985 1990 1995 2000 2005

Gamma

-.2

-.1

.0

.1

.2

.3

.4

-.2

-.1

.0

.1

.2

.3

.4

1980 1985 1990 1995 2000 2005

Phi (low er case)

0.7

0.8

0.9

1.0

1.1

1.2

1.3

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1980 1985 1990 1995 2000 2005

Zeta

Figure 1: Recursive Estimation Results

Source: Author’s estimates

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The results from a calibration exercise of the derived monetary policy rule using the earlier estimated parameters are now reported, and the correlations and deviations of this theoretically implied optimum compared to the actual out-turn of monetary policy observed.

Of importance however, is the assumption made for ϕ, which determines the weight on the output gap, as well as the rate assumed for �∗, in the monetary policy rule. Regarding the former, four purely subjective scenarios for ϕ within a range of 0.5 – 2.0 have been analysed, each representing a differing concern by the SARB for the output gap. In the case of

determining �∗, far more uncertainty exists. The ambiguity lies in the changing monetary policy regime of the SARB, whereby inflation was only explicitly targeted from the first quarter of 2000, with the objective of being within the 3- 6 percent range by the year 2002. This therefore leaves the period 1980 quarter 1 to 2001 quarter 4 open to assumption10. To determine the target specified in equation (1.2) therefore, we assume that at equilibrium, there is a long run constant rate of inflation, the output gap is closed, and the REER remains steady. Through recursive estimation of the Phillips curve including a constant, we are able

to derive an estimate of this long run rate of inflation. Combining this with � shown in Figure 1, results in a dynamic rate of �∗ over time11. Due to the natural instability of these parameters in the early, small sample regressions, we rely only on the derived long run relationship from 1985 onwards (Figure 2). Figure 2: Implied “Inflation Target”

Source: Author’s estimates

10 Previous monetary policy regimes would implicitly have attempted to maintain a degree of price stability, with inflation somewhere near its equilibrium rate. Indeed, even monetary aggregate and exchange rate targeting regimes still acknowledge low and stable inflation as characteristics of responsible central banking. Comments made by SARB Governor T.T. Mboweni that “any central bank worthy of its mandate will pursue low inflation anyway” (Mboweni, 2009) reaffirm this notion.

11 In equilibrium, �∗ = ���� ∴ �∗ = D + ��∗

∴ �∗ = D1 − ��

2

4

6

8

10

12

14

16

18

20

2

4

6

8

10

12

14

16

18

20

86 88 90 92 94 96 98 00

Pie *% %

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The resulting rate of target inflation fluctuates within a band of 4% and 19% year-on-year (standard deviation of 3.7); the range of which appears to have been artificially widened by a sharp spike to 18.9% in the third quarter of 1988. The mean of this derived target is 10.7% year-on-year. Finally, the apparent structural shift to a lower mean level of target inflation from 1995 onwards as the economy “opened” to the rest of the world is also noteworthy. Indeed, Aron & Muellbauer (2008) discuss the importance of this event and its impact on structural inflation forecasting models for South Africa. After the formal introduction of inflation targeting however, we assume that the target rate of inflation settles at 6% year-on-year12.

We now use this target rate of inflation, together with differing values for ϕ in equation 2.1, to examine how the optimal monetary policy rule compares with the actual observed policy

rate set by the SARB. In our analysis, an increasing (decreasing) value of ϕ represents higher (lower) concern for the output gap in the central banks loss function. The results are reported in Figure 3 and Table 4. Figure 3: Implied Monetary Policy Rule vs. Observed Policy Rate

Source: South African Reserve Bank, Author’s estimates. * To account for the apparent smoothing of monetary policy, a 3-quarter moving average of the derived policy rate has been reported.

12 It unknown whether the SARB has an implicit preference for a point estimate within the mandated 3 – 6 percent range. It is also worth noting that the target was initially set to 3 - 6 percent in for 2002 and 2003, and 3 - 5 percent for 2004 and 2005. The 2004 target was later revised to 3 - 6 percent, and has been maintained since.

0

10

20

30

40

50

60

0

10

20

30

40

50

60

1980 1985 1990 1995 2000 2005

Actual Policy Rate Phi = 0.5

Phi = 1.0 Phi = 1.5

Phi = 2.0

% %

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Table 4: The Optimal Rule Under Varying ϕ Assumptions

Φ = 0.5 1.0 1.5 2.0

Reduced form coefficients: �� 2.974 1.492 0.996 0.748

�� 0.845 0.841 0.839 0.839

���� 0.006 0.003 0.002 0.002

�� -1.261 -0.210 0.142 0.318

�: � ratio 3.5:1 1.8:1 1.2:1 0.9:1 Correlation to Actual 0.434 0.405 0.355 0.295 RMSE (from actual) 15.136 5.528 7.796 9.704 Theil Statistic 0.341 0.179 0.296 0.403 Actual less Derived (mean) -11.497 2.019 6.543 8.817 Source: Author’s estimates

After examining the above results one could argue that a value of ϕ = 1.0 yields the closest fit to the actual out-turn of monetary policy over the sample period, as this is the value of ϕ which results in the lowest RMSE and Theil statistic, whilst the mean difference between the implied policy rate and actual is the least. This corresponds with a coefficient on the inflation gap in the Taylor rule of 1.492, whilst the coefficient on the output gap is 0.841. Expressed as a ratio, this translates into a response to inflation relative to output of 1.8:1. That the response of the policy rule to inflation is greater than 1 is a critical property and is consistent with the Taylor Principle, whereby the central bank should avoid a decline in real interest rates in times of rising inflation. Taylor (1999) explains: “A slope below one would lead to poor economic performance according to a variety of models. With the slope less than one, an increase in inflation would bring about a decrease in the real interest rate. This would increase demand and add to upward pressures on inflation. This is exactly the wrong policy response to an increase in inflation because it would lead to ever increasing inflation. In contrast, if the slope of the policy rule were greater than one, an increase in inflation would bring about an increase in the real interest rate, which would be stabilising.” It is also worth mentioning that the estimated coefficients in our version of the SARB’s reaction function are similar to those reported in a recent working paper released by the SARB (Steinbach, Mathuloe & Smit [2009]), which attempts to model an open, New Keynesian model of the South African economy. Although we earlier discussed our reservations with the use of such models in South Africa, it is nonetheless noteworthy that the micro-founded parameters estimated via Bayesian techniques in their paper of 1.4 on the inflation variable (within a 90% confidence interval of 1.2 – 1.5) and 0.6 on the output gap (within a 90% confidence interval of 0.4 – 0.9), are not dissimilar to those parameters estimated herein. 5. Implications of the Optimal Rule Although a comparison of the optimal rule with the actually observed monetary policy rate is constructive, its fit to the empirical series should not guide the decision as to which policy rate is optimal from an inflation and growth perspective. This is because the very objective of this study is to highlight how the observed policy rate may or may not have deviated from

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its derived optimum, and it is this optimum that provides the appropriate growth/inflation trade-off, even if only in the short run.

A scenario analysis of the various ϕ assumptions would need to be fed through the model to determine which value of ϕ minimises the volatility of inflation and the output gap, whilst also minimising the rate of inflation, and maximising the rate of economic output. To simplify the interpretation, we present the resulting rate of economic growth as measured by real GDP (as opposed to the output gap). To achieve this, the calibrated version of the economy has been solved in a dynamic setting that evolves from the forecast produced for each variable in period t-1. Table 5: Model Simulation Results Parameter Mean Median Maximum Minimum Standard

Deviation

/ = actual 10.59 10.32 19.70 3.43 4.28

π when Φ=

0.5 12.06 11.56 16.16 9.42 1.76 1.0 11.49 10.98 16.16 8.02 2.20 1.5 10.60 9.72 16.16 6.44 2.77 2.0 12.70 12.57 17.33 8.77 2.11

GDP = actual 2.54 3.18 10.77 -4.19 2.70

GDP when

Φ= 0.5 2.52 2.40 10.77 -1.61 1.93 1.0 2.52 2.34 10.77 -1.61 1.94 1.5 2.51 2.34 10.77 -1.69 1.97 2.0 2.53 2.61 10.77 -1.76 2.04

Source: South African Reserve Bank; Author’s estimates

The results suggest that a more stringent focus on inflation (ϕ = 0.5) is not efficient in that, perversely, monetary policy becomes sufficiently volatile to destabilise the economy, ultimately resulting in a mean rate of inflation greater than that actually recorded whilst economic growth remains broadly unchanged relative to the remaining policy options. This is because inflation volatility is a significant form of growth-impeding uncertainty (Aron and Muellbauer, 2007). This result is consistent with the SARB’s (2005) own view that “...the stricter inflation targeting is, the more variable output will be. Too narrow a focus on inflation will result in interest rate and output instability”. Similarly, an excessive focus on

minimising the output gap, (ϕ = 2.0) indeed results in GDP growth matching actual recorded growth with less volatility that actual, however the resulting mean rate of inflation is a full 2.1 percentage points higher than actual. That the mean rate of economic growth is not significantly higher in this scenario is clearly inefficient when considering the inflation

trade-off. Furthermore, the implication for the Taylor Principle under ϕ = 2.0 is destabilising, as shown in Table 4 earlier. Some combination of targeting price stability and maximising economic growth is therefore optimal in this model, whereby acknowledgement of real economy indicators such as the output gap is awarded meaningful weight in the central bank’s loss function, although not at

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the expense of the Taylor Principle. For this we look toward the intermediate options of ϕ = 1.0 and ϕ = 1.513. Recall, that ϕ = 1.0 bore the most resemblance to what has actually been observed in South African monetary policy. Under that option, inflation volatility is indeed shown to be approximately 2.1 standard deviations lower than actual; however its

mean rate is 0.9 percentage points higher. With ϕ = 1.5 however, inflation volatility is 1.5 standard deviations lower, with a mean rate that is essentially equal. Less disparity is

observed with regards to real economic growth however, with ϕ = 1.0 and ϕ = 1.5 yielding mean rates of GDP growth in line with actual; and a volatility of 0.76 and 0.73 standard deviations less than actual, respectively.

A value of ϕ = 1.5 therefore appears to provide the optimal result, with its benefit over ϕ = 1.0 being primarily derived from its lower implied mean rate of inflation. To be sure, the optimal Taylor rule awards greater attention to the output gap compared to what most

closely resembles observed SARB behaviour, in this model. The optimal choice of ϕ would therefore be skewed toward 1.5. While it is encouraging that the SARB’s policy rule appears to share many similarities with this proposed reaction, there have been periods of large divergence between the observed and optimal policy rate (see shaded areas in the bottom left pane of Figure 4). This divergence may be explained by a host of unique factors that may have occupied monetary policy maker’s minds at the time; such as distress in financial markets, socio economic pressures, or a shift in monetary policy strategy away from the formal use of the policy interest rate (an example of one such strategy being quantitative easing; see Miles & Baker [2009] for an intuitive description and Ugai [2006] for a more technical review).

13 The tightness of the implied economic growth rates across the scenarios suggest that long run economic growth potential of South Africa over the sample period was probably in the region of 2.5% per annum. This is in accordance our measure of potential growth used in the calculation of the output gap earlier on. The indifference of potential growth to monetary policy in the long run may be evidence of a vertical long run-Phillips curve in South Africa. This is an area for future research.

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Figure 4: Model Simulation Results (ϕ=1.5)

6. The Deviation from Optimality The shaded regions in the lower left pane of Figure 4 above highlight the periods in which

the deviation of the actual policy rate from optimum (with ϕ set at 1.5) was particularly acute. Over the sample period, the average deviation amounts to 6.55 percentage points, suggesting that, on average, monetary policy in South Africa over the last two and a half decades has been too tight relative to what the optimal rule would have implied. Admittedly,

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the average is skewed by two periods of sharp policy tightening: 1983Q3 - 1985Q1 and 1994Q4 – 1998Q3. The mean deviation over these two periods combined was as large as 11.1 percentage points; excluding these two periods results in a mean deviation of some 5.4 percentage points over the adjusted sample. What is particularly encouraging is the downward trend in this deviation since the introduction of the inflation targeting regime in 2000. The explicit targeting of inflation and the clearly defined policy framework likely explains this improvement. Overall however, the results do suggest that the SARB may have committed a persistent policy error, where the cost of pursuing an overly restrictive monetary policy resulted in losses to potential and actual output. This “cost” is known as the sacrifice ratio, that is, the output lost by reducing inflation via an aggregate demand contraction. While the sacrifice ratio is a key consideration for policy makers, estimating its size is often complex as it requires the precise identification of the impact of monetary policy changes on output and inflation. More specifically, it is crucial to be able to differentiate between those movements in output and inflation that were policy induced and those that were not. To provide a simple indication of this cost however, one could rely on the method proposed by Ball (1997), who defines the sacrifice ratio simply as the inverse of the slope of the Phillips curve (parameter γ in equation 1.2 above, i.e. 1/0.116). This method provides a sacrifice ratio of 8.6% for South Africa. That is, an 8.6% reduction in GDP growth would have to be engineered to provide a purely demand-led reduction in inflation14. Alternatively, assuming quarter-on-quarter GDP growth of 5%, a deceleration to 4.57% would be required to reduce CPI by 1%. This result is comparable to countries such as Italy (7.0%) and the United States (9.6%) in the 1971 -1988 sample considered by Ball (1993), with Germany producing a high 11.7%, and the United Kingdom a low 3.1%. Using the Phillips curve slope estimates for a number of emerging market economies estimated by Mohanty & Klau (2001), South Africa holds the 6th highest sacrifice ratio in their sample of 14 economies, according to the Ball (1997) methodology. In fact, the results are similar those reported in our study, with South Africa’s sacrifice ratio shown to be 9.4%. The average ratio in their sample is 33.7%, which appears to be skewed however by the outlier readings of Malaysia and the Czech Republic (333% and 91%, respectively), and the Philippines and Mexico (-7.6% and -8.1%, respectively). Excluding those outliers provides an average sacrifice ratio of 6.3%. As Cecchetti & Rich (1999) highlight in their study for the US however, it is crucial for policy makers to be aware of the range around which computed sacrifice ratios fluctuate. The scope and nature of South African monetary policy would undoubtedly have the potential to explain the divergence between actual monetary policy and that proposed by the derived rule. The objective of this exposition however, is not to dissect the idiosyncrasies of monetary policy decision making over the last three decades, but rather to remain focused on defining its optimum. Cognisance should also be taken of the fact this optimum criterion is model-specific, although coming from a very popular framework, with potentially different results obtained under a different specification of the economy. The importance of

14 See Ball (1993) for results from a cross section estimation of OECD sacrifice ratios. Ball’s results suggest that the sacrifice ratio across those countries declines the more aggressive the central bank is in reigning in inflation; and is more costly in the presence of nominal rigidities and inflexible wage setting institutions.

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robustness across methodological divides is highlighted in McCallum (1999). It is also important to note, that the explicit use of short term interest rates as the monetary policy instrument was not always the primary tool of the SARB in influencing the demand for money. An example would be in the early 1980’s where controls over commercial banks liquid asset and cash reserve ratios were the primary avenue in which market liquidity was manipulated. From 1990, monetary guidelines were supplemented by an eclectic set of indicators, including the exchange rate, asset prices, the output gap, balance of payments, wage settlements, total credit extension, and the fiscal stance (Aron & Muellbauer, 2008). In fact, the move toward the repurchase rate as the de facto monetary policy anchor only occurred in 1998. The reader is referred to Aron & Muellbauer (2000) and (2008) for an excellent discussion on the nature of the various regimes. 7. Conclusion This study uses a small macro model a la Svensson (1996), Ball (1998) and Rudebusch & Svensson (1998) to derive an optimal monetary policy rule for South Africa, based on fluctuations in the output gap, inflation and real effective exchange rate. By comparing the model implied interest rate to that which the SARB has actually implemented affords some insight into the SARB’s historical response to these variables, and the importance it may have assigned to them. In the current landscape, where inflation targeting central banks are being stress tested by a multiplicity of exogenous shocks, the results from the calibration and simulation exercise of this study suggest that a shift in emphasis is required compared to what appears to have been the case historically. Specifically, greater concern for the deviation of output from potential is proposed herein. The results confirm that inflation targets do have a positive role to play in the central bank’s reaction function, but in the case of South Africa, the SARB policy rule is optimised when greater attention is paid to the deviation in output from its defined potential, in conjunction to the inflation target. According to our model framework, the closest approximation of the actual policy rate response to inflation and the output gap is a ratio of 1.8:1. This study suggests that the optimal response need be closer to 1.2:1, which implies a coefficient of 1 on the inflation gap, and 0.8 on the output gap in our estimated Taylor rule. That the SARB appears to have deviated from the feasible set of guidelines proposed from the popular framework employed herein, suggests that some element of judgement/discretion enters the monetary policy decision making process. Alternatively, a broader set of macroeconomic considerations are entering the decision function, outside of the inflation target, output gap and real effective exchange rate. The robustness of these results, across alternative modelling frameworks and broader macroeconomic considerations, is certainly an area for further research.

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