Chapter

5 Estimation of the Equilibrium Real Exchange Rate for South Africa

Author(s):
Charalambos Tsangarides, Carlo Cottarelli, Gian Milesi-Ferretti, and Atish Ghosh
Published Date:
September 2008
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In the first quarter of 2002, the real effective exchange rate of the South African rand was 25 percent less than in the same period of the previous year and 45 percent more depreciated than its average 1995 level. A depreciation of this magnitude raises the question as to what extent it can be considered an equilibrium phenomenon (that is, consistent with persistent movements in economic variables that regularly affect the real exchange rate), rather than a temporary deviation from equilibrium. The depreciation also raises the question of how long it would take for any temporary deviation to dissipate. In this chapter, we address these questions by estimating an equilibrium path for South Africa’s real effective exchange rate over the period from 1970 to the first quarter of 2002.

The outline of the remainder of this chapter is as follows. After reviewing the existing literature, the chapter briefly describes the dynamics of the real exchange rate and its determinants. Subsequently it investigates the presence of a long-run cointegrating relationship between the real exchange rate and certain explanatory variables and estimates the speed at which the real exchange rate converges toward its equilibrium level. It then derives measures for the equilibrium real exchange rate and, correspondingly, the gap between the actual and the equilibrium levels.

Brief Review of the Literature

There is a considerable body of literature on estimation of the equilibrium real exchange rate, some of which has been surveyed in MacDonald (1995) and Rogoff (1996). This literature indicates that purchasing power parity is not an appropriate model for the determination of equilibrium exchange rates because of the slow mean reversion of real exchange rates to a constant level (which is the long-run equilibrium implied by the purchasing power parity assumption). This has resulted in a shift away from purchasing power parity—based measures of the equilibrium exchange rate to ones that focus on the link between the real exchange rate and various so-called real determinants, such as productivity and net foreign assets (see MacDonald and Stein, 1999, and Hinkle and Montiel, 1999). Most of this recent work uses cointegration techniques to identify persistent patterns of comovements among variables.

The main explanatory variables identified in the literature for developing countries are commodity price movements (or terms of trade), productivity and real interest rates differentials vis-à-vis trading-partner countries, measures of openness of the trade and exchange system, the size of the fiscal balance, and the extent of net foreign assets.1 The rationale for most variables is based on a simple neoclassical theoretical framework that assumes that the prices of tradable goods are equalized across countries and investigates how changes in the real exchange rate arise mainly from relative movements in the price of nontradables across countries. Relaxing the assumption of price equalization should provide richer insights into the transmission mechanisms: as in the presence of imperfectly substitutable traded goods across countries, the real exchange rate would also be affected through the relative price of traded goods—but this leads to broadly similar conclusions (see MacDonald and Ricci, 2002). In either case, the chosen variables explain why the real exchange rate can be expected to vary over time and provide a rationale for deviations from purchasing power parity.

The classic example of an equilibrium deviation from purchasing power parity is the Balassa-Samuelson effect (see Balassa, 1964, and Samuelson, 1964). If a country were to experience an increase in the productivity of its tradables sector (relative to those of its trading partners), its real exchange rate would tend to appreciate. For given prices of tradables, such stronger productivity would induce higher wages in the tradables sector; if wages are equalized across sectors, this would be reflected in higher prices of nontradables, and hence an increase in the consumer price index relative to that of trading partners.2

An increase in the world price of the commodities that a country exports would also tend to appreciate the real exchange rate. Such an increase would induce higher wages and a higher price of nontradables (see Cashin, Céspedes, and Sahay, 2002). An increase in commodity prices could also induce—more generally—a positive wealth effect, which would raise domestic demand and hence the price of nontradables (see Díaz-Alejandro, 1982). In principle, these effects should be captured more comprehensively by the terms of trade, as their numerator encompasses all exports—as opposed to only commodity-based exports—and their denominator reflects the price of country-specific imports, as opposed to a generic industrial country export deflator. In practice, few studies find a significant effect of the terms of trade (see, however, Goldfajn and Valdés, 1999), but many researchers find commodity prices to be strongly cointegrated with the real exchange rate of commodity exporters (see Chen and Rogoff, 2002, MacDonald, 2002, and Cashin, Céspedes, and Sahay, 2002). One rationale for the findings is provided by the relative accuracy of the measurement of commodity prices, as opposed to the arbitrariness involved in the construction of country-specific export and import deflators. Another rationale relates to how frequently commodity price data are made available, which may allow financial markets to tailor their financial decisions about the currencies of commodity exporters to the prices of these commodities.

The real interest rate differential could represent several factors—aggregate demand, productivity, and persistent monetary policy—all pointing to a positive relationship with the real exchange rate. First, an increase in absorption relative to savings would put upward pressure on the real interest rate in an economy with less-than-perfect capital mobility. At the same time, the demand for both tradable and nontradable goods would increase, inducing an increase in the price of nontradables, which in turn would result in an appreciation of the real exchange rate. Second, real interest rate differentials may also reflect productivity differentials: to the extent that the measure employed to proxy for the Balassa-Samuelson effect is not perfect, the real interest rate differential may help capture this empirically; also, if the productivity of capital rises with respect to trading partners, capital will flow to the home country, thereby inducing an appreciation of the real exchange rate.3 Third, a tightening of monetary policy would raise real interest rates—an outcome that would need to be associated with an expectation of currency depreciation, given the interest parity condition. Hence, the nominal exchange rate would appreciate beyond its long-run value, so as to allow the expected depreciation to occur once the monetary policy shock had disappeared (the “overshooting” effect described in Dornbusch, 1976). In the presence of price rigidities, the real exchange rate could also be appreciated relative to its long-run value (see Obstfeld and Rogoff, 1996, for a formal derivation in the new open macroeconomic setup). This last effect could be persistent if the monetary shock—that is, the rise in real interest rates—is persistent: in this sense, the cointegration analysis would capture this effect as part of the “long-run” relation.4

An improvement in the fiscal balance will have an ambiguous effect on the real exchange rate. On the one hand, depreciation would tend to occur because the improved fiscal balance would normally induce a less-than-proportional reduction in private saving, so that total domestic demand would decrease while overall savings would increase.5 As part of the decline in spending falls on nontradable goods, their prices would drop, bringing about a depreciation of the real exchange rate. The effect is likely to be stronger if the fiscal improvement comes from a reduction in government consumption, as opposed to an increase in taxes, to the extent that government consumption falls more intensively on nontradable goods than private spending (in which case, the depreciation would be reinforced in the presence of imperfectly substitutable traded goods).6 In principle, the fiscal effect should simply be part of the main aggregate demand effect described previously; whether the interest rate fully captures both effects is an empirical question. On the other hand, a further effect would operate on the relative price of traded goods in a model that features stock-flow consistency (such as the portfolio balance model). In such a model the current account surplus generated by the initial real depreciation would have to be eliminated in the long run by a real appreciation that ensures a sufficient trade deficit to offset the positive net foreign assets.

A more-open trade regime is likely to be associated with a more-depreciated real exchange rate. Trade restrictions increase the domestic price of tradable goods, thereby raising the overall price level and the real exchange rate (see Goldfajn and Valdés, 1999). In the present study, openness is proxied by the ratio of exports plus imports to GDP. Such a measure is widely used, even though it is an imperfect substitute reflecting in addition a multiplicity of factors other than trade and exchange restrictions. In the context of the present chapter, these drawbacks are likely to have a limited impact. In fact, the endogeneity of the openness ratio to the real exchange rate is corrected for automatically by the econometric methodology employed. The ratio would also reflect the effect of trade sanctions during the apartheid period, which is likely to induce a similar effect on the domestic price of tradable goods and, hence, on the real exchange rate.

The size of net foreign assets is likely to be associated with a more-appreciated exchange rate in the long run. Higher net foreign assets induce larger expenditure on domestic goods, thus raising the price of nontradables and appreciating the real exchange rate. An alternative mechanism is based on the absence of price equalization of tradables: a country that reaches a higher level of net foreign assets can afford to finance a worse current account balance and can therefore sustain any loss in competitiveness associated with a more-appreciated real exchange rate. For a theoretical discussion and empirical evidence, see Lane and Milesi-Ferretti (2004).7

In terms of previous work on South Africa, see Aron, Elbadawi, and Kahn (2000), which provides an estimation of the equilibrium real effective exchange rate for the country over the period 1970–1995. Aron and her colleagues use a single-equation approach to identify a long-run relation on the basis of the following explanatory variables: terms of trade, price of gold, tariffs, capital flows, official reserves, and government consumption. The paper also offers an interesting historical background. Very recently, Aron, Muellbauer, and Smit (2003) estimated the real exchange rate within the context of a six-equation macroeconometric model.

Data and Methodology

Figures 5.1 and 5.2 plot the real effective exchange rate and the main variables employed in the empirical analysis, respectively, over the 1970–2001 period.8 Some interesting patterns are worth highlighting, particularly for the recent period:

  • the significant real depreciation of the rand since 1995, which accelerated in 2001;
  • the increase in real interest rates in the 1990s, partly associated with tight monetary policy;
  • the persistent decline in real GDP per capita with respect to trading-partner countries, throughout the sample period;9
  • the steady decline in real prices for South Africa’s main commodity exports since the beginning of the 1980s;
  • the decline in openness during the 1980s—in part owing to trade sanctions—and the opening up of the economy since the end of apartheid;
  • the strengthening of fiscal performance, as measured by the fiscal balance, in the postapartheid period; and
  • the recent improvement in the net foreign asset position, owing in great part to the reduction of the forward book.

Figure 5.1.Real Effective Exchange Rate, 1970:Q1–2002:Q1

(Index, 1995 = 100)

The exchange rate regime has changed throughout the sample, from a fixed exchange rate regime to a dual exchange rate system and then to a floating exchange rate regime (for a detailed description of exchange rate policy over the past three decades, see Aron, Elbadawi, and Kahn, 2000).10

It is therefore possible that our model will not properly pick up some fluctuations in the real exchange rate. As we will show, when we add dummies to account for large outliers, the results remain virtually unaltered.

Our empirical work focuses on the following vector:

Xt =[LREERS, RIRR, LRGDPPCR, LPR2COMM5, OPENY, FBYA, NFAOPFY],

where variables are as defined in Appendix 5.1. To investigate the existence of a long-run cointegrating relationship among the variables in this vector, we use the maximum-likelihood estimator of Johansen (1995), which corrects for autocorrelation and endogeneity parametrically, using a vector error correction mechanism (VECM) specification.11 Since this methodology is now well known, we do not discuss it further here. One of the key advantages of the Johansen methodology in the current application is that the estimated coefficient—the beta vector—can be used to provide a measure of the equilibrium real exchange rate and therefore a quantification of the gap between the prevailing real exchange rate and its equilibrium level. The methodology also derives estimates of the speed at which the real exchange rates converges to the equilibrium level.

Figure 5.2.Determinants of Real Effective Exchange Rate, 1970–2002

(In percent)

Sources: South African Reserve Bank; Statistics South Africa; and IMF staff estimates.

Econometric Results and Their Robustness

The first column of Table 5.1 shows the estimation of the VECM specification employing the following variables: the real effective exchange rate in log terms (LREERS), real interest rate relative to trading partners (RIRR), the logarithm of the real GDP per capita relative to trading partners (LRGDPPCR), real commodity prices under various definitions (for example, LPR2COMM5, the most general one, based on five commodities and deflated by the industrial countries export deflator; see Appendix 5.1 for further explanation), openness (OPENY, that is, the average ratio to GDP of exports and imports), the ratio of the fiscal balance to GDP (FBYA), and the ratio to GDP of net foreign assets of the banking system (NFAOFPY).12 The specification includes four lags for the changes in each variable and centered seasonal dummies: such a structure is quite common when quarterly data are employed (as discussed subsequently, the lag structure is supported by appropriate tests).

The second column of Table 5.1 presents results for the VECM specification estimated using the same variables as in the previous specification, with the addition of dummies that control for the presence of outliers, so as to eliminate the effect of those outliers on the estimates.13

Both specifications pass a number of tests. Cointegration tests indicate the presence of one cointegrating vector using a 1 percent significance level (see Table 5.1, columns (1) and (2)).14 We have used the 1 percent significance level, rather than the usual 5 percent level, to address potential small-sample bias in our estimates. The coefficients of the cointegrating vector are plausible, significant, and of the correct sign. All of the variables prove to be nonstationary when the Johansen test (seethe first and second columns of Table 5.2), which (unlike standard sta-tionarity tests) takes into account the cointegration space, is employed. Implicitly, this test indicates that the presence of cointegration is not driven by stationarity of any single variable. Hence the cointegration analysis is both appropriate (as variables are nonstationary) and meaningful (that is, not driven by stationarity of one variable). Furthermore, the exclusion test suggests that none of the variables—with the exception of LRGDPPCR—can be excluded from the long-run relationship (third and fourth columns of Table 5.2) at the 5 percent significance level. However, we retain LRGDPPCR in the econometric model, as the hypothesis of exclusion is not far from rejection in Table 5.2 and is often rejected in other experimental specifications.

Table 5.1.Selected Results of the VECM Specification
Regression number(1)(2)(3)(4)(5)(6)(7)
Estimates of the cointegrating relationship with the real exchange rate
LREERS(–1)1111111
RIRR(–1)–0.03

(–6.96)
–0.03

(–7.03)
–0.04

(–5.58)
–0.03

(–6.67)
–0.04

(–5.71)
–0.03

(–6.66)
–0.04

(–5.98)
LRGDPPCR(–1)–0.14

(–1.88)
–0.13

(–1.75)
0.05

(–0.43)
–0.09

(–1.16)
0.08

(–0.71)
–0.13

(–1.62)
0.01

(–0.06)
OPENY(–1)0.01

(–5.97)
0.01

(–5.87)
0.01

(–3.7)
0.01

(–5.67)
0.01

(–3.99)
0.01

(–5.90)
0.01

(–4.64)
FBYA(–1)0.02

(–4.31)
0.02

(–5.60)
0.01

(–1.95)
0.02

(–5.02)
0.01

(–1.45)
0.02

(4.90)
0.01

(1.64)
NFAOFPY(–1)–0.01

(–5.09)
–0.01

(–4.50)
–0.01

(–3.24)
–0.01

(–5.24)
–0.01

(–3.99)
–0.01

(–5.37)
–0.01

(–4.44)
LPR2COMM5(–1)–0.46

(–12.17)
–0.45

(–11.75)
LPRCOMM5(–1)–0.48

(–8.51)
LPR2COMM3(–1)–0.46

(–11.23)
LPRCOMM3(–1)–0.49

(–8.74)
LPR2GOLD(–1)–0.42

(–11.19)
LPRGOLD(–1)–0.43

(–9.28)
Constant–4.96

(–57.41)
–4.95

(–56.66)
–5.06

(–35.92)
–4.98

(–53.65)
–5.13

(–36.53)
–4.45

(–46.89)
–4.56

(–37.11)
Estimates of the short-term impact of net foreign assets on the real exchange rate
(DLREERS) D(NFAOFPY(–1))–0.01

(–2.62)
–0.01

(–2.35)
–0.01

(–2.64)
–0.01

(2.19)
–0.01

(–2.47)
–0.01

(–2.19)
–0.01

(–2.46)
Estimates of the speed of adjustment of the real exchange rate
CointEq1–0.08

(–0.91)
–0.07

(–0.92)
–0.1

(–1.92)
–0.05

(–0.61)
–0.09

(–1.66)
–0.04

(–0.58)
–0.09

(–1.61)
Half-life of the deviation from equilibrium exchange rate (in years)2.12.41.63.41.84.21.8
Note: t-statistics in parentheses. In all regressions, the number of cointegrating vectors (as identified by the trace statistic or the max eigenvalue statistic) is one, with the exception of regression (1) with the trace statistic at the 5 percent level of statistical significance, where the number of cointegrating vectors is two.
Note: t-statistics in parentheses. In all regressions, the number of cointegrating vectors (as identified by the trace statistic or the max eigenvalue statistic) is one, with the exception of regression (1) with the trace statistic at the 5 percent level of statistical significance, where the number of cointegrating vectors is two.

In Table 5.3 we present normality tests for the specifications listed in columns (1) and (2) of Table 5.1, which indicate that the hypothesis that the residuals have a normal distribution (panel (a)) is rejected because of excessive kurtosis. Paruolo (1997) has demonstrated that in instances where normality is rejected for this reason, rather than skewness, the Johansen results are not affected.15Table 5.3 also indicates that all four lags are necessary in our VECM specification (the test results in the first column of panel (b) enable us to reject the hypothesis that each of the four lags is jointly insignificant across equations). The lag structure appears to be correct: if a fifth lag is introduced, the test accepts the hypothesis that the additional lag is jointly insignificant across equations (Table 5.3, panel (b), second column). The results of the diagnostic tests presented in Tables 5.2 and 5.3 generally carry through all specifications in Table 5.1. To assess the robustness of the results, several exercises have been performed. First, the main specification is also run with different measures of commodity prices, as this variable is found to be the most important variable explaining the long-run behavior of the real exchange rate both in this study and in other studies related to countries similar to South Africa.16 As shown in Table 5.1 (columns (3)–(7)) the results are broadly similar. Second, variables are dropped sequentially, which is determined not to have major impacts on the other coefficients, apart from the case of variables that are already weak (such as LRGDPPCR). Third, labor productivity in the manufacturing sector (as a ratio of trading partners’ labor productivity) is substituted for relative real GDP per capita as a proxy for the Balassa-Samuelson effect and is found not to perform as well. In fact, if labor productivity is entered instead of LRGDPPCR, its coefficient is insignificant. This could be due to the large fluctuations in employment in South Africa, which alter the link between labor productivity and total factor productivity.

Table 5.2.Johansen Test for Stationarity and Exclusion Test(Chi-square test statistics)
Johansen Test for StationarityExclusion Test
Regression (1)Regression (2)Regression (1)Regression (2)
CHISQ14.0714.073.843.84
LREERS47.1058.1029.6531.47
RIRR52.4963.1328.1834.40
LRGDPPCR38.8747.213.183.15
LPR2COMM557.7171.3631.7938.29
OPENY48.0558.4313.9115.74
FBYA44.4255.2312.2021.04
NFAOFPY49.9457.929.908.55
Constant27.7529.16
Note: The significance level employed is 5 percent. For the Johansen test, H0: variable is stationary (if corresponding statistic is smaller than CHISQ). For the exclusion test, H0: variable can be excluded (if corresponding statistic is smaller than CHISQ).
Note: The significance level employed is 5 percent. For the Johansen test, H0: variable is stationary (if corresponding statistic is smaller than CHISQ). For the exclusion test, H0: variable can be excluded (if corresponding statistic is smaller than CHISQ).

The Long-Run Relationship

Table 5.1 shows evidence of cointegration between the real exchange rate and the explanatory variables. Accordingly, the long-run relationship between the real exchange rate and these variables can be identified as follows:

  • An increase in the real interest rate relative to that of trading-partner countries of 1 percentage point is associated with an appreciation of the real effective exchange rate of around 3 percent.
  • An increase in real GDP per capita relative to trading-partner countries of 1 percent is associated with an appreciation of the real effective exchange rate of 0.1–0.2 percent.17
Table 5.3.Vector Error Correction Tests(Chi-square test statistics)
a. Vector error correction test for skewness, kurtosis, and normality of residuals
Degrees of freedomRegression (1) ProbabilityRegression (2) Probability
Skewness70.140.52
Kurtosis70.000.00
Normality140.000.00
b. Vector error correction lag exclusion Wald test
Regression (1) JointRegression (1) JointRegression (2) JointRegression (2) Joint
DLag1137.20

(0.00)
128.80

(0.00)
131.90

(0.00)
120.10

(0.00)
DLag270.90

(0.02)
67.60

(0.04)
71.90

(0.02)
66.10

(0.05)
DLag3122.20

(0.00)
122.30

(0.00)
113.30

(0.00)
114.70

(0.00)
DLag482.40

(0.00)
87.70

(0.00)
80.90

(0.00)
80.50

(0.00)
DLag547.60

(0.53)
49.80

(0.44)
Note: In panel (a), H0: Residuals have no skewness and no kurtosis and are normal, respectively, if probability value for each, respectively, is larger than the chosen significance level. Skewness and kurtosis are based on the joint chi-square test; normality is based on joint Jarque-Bera test; and orthogonalization is based on Cholesky (Lutkepohl). In panel (b), numbers in parentheses are probability values. H0: Lag’s coefficients are jointly nonsignificantly different from zero (that is, can be excluded) if probability value is larger than chosen significance level. Degrees of freedom are 49 for all four regressions in panel (b).
Note: In panel (a), H0: Residuals have no skewness and no kurtosis and are normal, respectively, if probability value for each, respectively, is larger than the chosen significance level. Skewness and kurtosis are based on the joint chi-square test; normality is based on joint Jarque-Bera test; and orthogonalization is based on Cholesky (Lutkepohl). In panel (b), numbers in parentheses are probability values. H0: Lag’s coefficients are jointly nonsignificantly different from zero (that is, can be excluded) if probability value is larger than chosen significance level. Degrees of freedom are 49 for all four regressions in panel (b).
  • An increase in real commodity prices of 1 percent is associated with an appreciation of the real effective exchange rate of around 0.5 percent.
  • An increase in openness of 1 percentage point of GDP is associated with a depreciation of the real effective exchange rate of about 1 percent.
  • An improvement in the fiscal balance of 1 percentage point of GDP is associated with a depreciation of the real effective exchange rate of around 2 percent.
  • An increase in net foreign assets of 1 percentage point of GDP is associated with an appreciation of the real effective exchange rate of around 1 percent.

The Short-Run Relationship

Short-run effects are generally found to be insignificant across the various specifications (and therefore are not reported here), with the exception of one. As shown in Table 5.1 by the coefficient of D(NFAOFPY(—1)), an increase in net foreign assets of the banking system is likely to depreciate the real exchange rate in the short run (that is, one quarter). This effect is likely to be due to the temporary impact of changes in reserves on the nominal exchange rate. Hence, an improvement in the net foreign asset position (like that arising from the reduction of the forward book in recent years) is likely to induce a temporary depreciation of the exchange rate, but in the long run it is likely to be associated with an appreciation of the equilibrium real exchange rate.

Equilibrium Real Exchange Rate

The long-run relationship summarized in the previous section permits the calculation of an estimate of the equilibrium real exchange rate. Ideally, this measure can be defined as the level of the real exchange rate that is consistent in the long run with the equilibrium values of the explanatory variables. It can therefore be obtained by evaluating the cointegrating relationship at these equilibrium levels.

As is evident from Figure 5.2, however, the explanatory variables can exhibit a substantial degree of noise or fluctuations. One way of neutralizing the impact of the temporary fluctuations in these variables on the evaluation of the equilibrium real exchange rate is the application of smoothing techniques to eliminate short-run fluctuations in explanatory variables, so as to derive a proxy for the long-run equilibrium values of these variables. Panel (a) of Figure 5.3 shows an example of the equilibrium real exchange rate derived in this manner and compares the outcome with the actual real effective exchange rate.18

According to panel (a) of Figure 5.3, the actual rate appears to have been close to its estimated equilibrium level in the first half of the 1990s, but it subsequently depreciated by much more than the equilibrium rate, that is, by about 44 percent versus 28 percent, respectively. The decline of the equilibrium level over this period arose from conflicting factors. On the one hand, the decline in commodity prices, the increase in openness, the improvement in the fiscal balance, and the slower productivity growth relative to trading partners accounted for depreciations of the equilibrium real exchange rate on the order of 13 percent, 15 percent, 12 percent, and 1 percent, respectively. On the other hand, the increase in net foreign assets and in the real interest rate differential partly offset these forces by contributing to appreciations on the order of 7 and 5 percent, respectively.

Figure 5.3.Real Effective Exchange Rate

The Gap Between the Real Exchange Rate and Its Equilibrium Level

At any point in time, the real exchange rate is likely to differ from the equilibrium level, either because a change in the explanatory variables alters the equilibrium level or because temporary factors (such as financial market pressure on the rand) move the real exchange rate away from it. One of the aims of the study presented in this chapter is to quantify this gap in the first quarter of 2002, when the rand was recovering from the large depreciation that occurred in late 2001. When the equilibrium values of the explanatory variables are smoothed, as in panel (a) of Figure 5.3, the gap is found to be on the order of 26 percent (see panel (b) of Figure 5.3).

Alternatively, one can evaluate the deviation of the real effective exchange rate from a notional equilibrium level, based on a set of economic priors for the equilibrium values of the explanatory variables. Interestingly, a gap of a similar magnitude (about 24 percent) would result from the following plausible values for the exogenous variables:

  • a real interest rate differential of about 250 basis points, that is, roughly the level of the yield spreads in 2001;
  • a relative real GDP per capita equal to the actual level in the first quarter of 2002 (given that the variable exhibits a clear and relatively smooth trend, its actual value can be considered a good proxy for its equilibrium value at each point in time);
  • a level of real commodity prices equal to the average for the period 1995—2001 (such a choice appears appropriate in light of the quick rebound of commodity prices in 2002);
  • a degree of openness equal to the average for the period 1995—2001 (close to 50 percent of GDP);
  • a fiscal deficit of about 2 percent of GDP, which corresponds roughly both to the average level since 1998 and to the authorities’ target; and
  • a net foreign assets position relative to GDP equal to the actual level in the first quarter of 2002.

As the large fluctuations in commodity prices (evident from Figure 5.2) are found to contribute heavily to movements in the real exchange rate, it is interesting to evaluate the gap for the first quarter of 2002 at the levels of commodity prices prevailing in 1995 or at the beginning of 2002, keeping the other variables unchanged at the values indicated previously. In the former case, the gap would amount to 28 percent, whereas in the latter case, the gap would correspond to only 19 percent.

Speed of Adjustment

When a gap between the real exchange rate and its equilibrium level arises, the real exchange rate will tend to converge to its equilibrium level. Depending on the cause of the gap, the adjustment requires that the real exchange rate either move progressively toward a new equilibrium level or return from its temporary deviation to the original equilibrium value. The estimates derived in this study (see Table 5.1) suggest that, on average, about 8 percent of the gap is eliminated every quarter, implying that in the absence of further shocks about half of the gap would be closed within two and one-half years. However, large deviations, such as those experienced in 2001 and 2002, could take less time to absorb, as suggested by the recent literature on nonlinear exchange rate models (see Sarno and Taylor, 2002). Of course in a joint system of this type, other variables can also possibly adjust to the equilibrium error, and this is indeed the case in the current application. However, these separate adjustments do not affect the speed of adjustment reported here for the exchange rate equation.

Conclusions

Drawing on existing literature, this chapter estimates a long-run equilibrium real exchange rate path for South Africa. The main explanatory variables are found to be commodity price movements, productivity and real interest rates differentials vis-à-vis trading-partner countries, measures of openness, the size of the fiscal balance, and the net foreign assets position. The analysis suggests that in the first half of the 1990s the real exchange rate was close to its equilibrium level and that about two-thirds of its subsequent depreciation until early 2002 can be accounted for by movements in the explanatory variables. In the first quarter of 2002, the average value of the rand (R11.5 per U.S. dollar) appeared to be about 25 percent more depreciated than the level (R8.8 per U.S. dollar) for the first quarter of 2002, consistent with the estimated equilibrium of the real exchange rate. Different ways of distinguishing between permanent and temporary movements in the explanatory variables provide similar results.

These calculations may, however, overestimate the equilibrium exchange rate to the extent that they do not account for structural factors, such as high unemployment and the HIV/AIDS pandemic; taking these into account could generate a smaller gap than that estimated.

If the real exchange rate deviates from its equilibrium level owing to temporary factors, it can be expected to revert to equilibrium fairly quickly, in the absence of further shocks. The study suggests that about half of the gap is normally eliminated within two-and-one-half years. However, large deviations are likely to be absorbed at a faster pace.19

The chapter also shows that the rapid reduction of the forward book in recent years may have exerted only a temporary negative pressure on the exchange rate. In the long run, such an improvement in the net foreign asset position is likely to be associated with an appreciation of the equilibrium real exchange rate.

Appendix 5.1 Variables: Definitions and Sources

The data set for the study presented in this chapter consists of quarterly data from 1970 to the first quarter of 2002 for South Africa and four major trading partners. The variables employed in the regressions are as follows:

  • LREERS: Real effective exchange rate (in logarithmic terms). Source: South African Reserve Bank (SARB).
  • RIRR: Real interest rate relative to trading partners. Nominal interest rate on 10-year bond, minus inflation in past four quarters. Foreign variable calculated as the weighted average of four major trading partners, based on the SARB weights for the real effective exchange rate with those partners: Germany (proxy for European Union, 47 percent), United States (20 percent), United Kingdom (20 percent), and Japan (13 percent). Sources: SARB and International Monetary Fund, International Financial Statistics (IFS).
  • LRGDPPCR: Real GDP per capita relative to trading partners (in logarithmic terms). Normalized for each country to 1 in 2000. Foreign variable calculated as previously. Sources: SARB, IFS, and World Bank.
  • LPR2COMM5 and other indicators: Real commodity prices (in logarithmic terms). Six different indicators of commodity prices were constructed, based on three choices of aggregating the main commodities exported by South Africa and two ways of deflating them. The former encompassed weighted averages of the five, three, or single most-exported commodity(ies)—excluding diamonds, for which a price series is not available (see Table 5.A.1). The latter relate to the price deflator for developed countries’ exports (variables starting with LPR) or to the U.S. CPI level (variables starting with LPR2). The combination generates, respectively, LPR2COMM5, LPR2COMM3, LPR2GOLD, LPRCOMM5, LPRCOMM3, and LPRGOLD. Sources: Cashin, Céspedes, and Sahay (2002), Data Stream, and IFS.
  • OPENY: Openness. Ratio of exports and imports to GDP. Sources: SARB and IFS.
  • FBYA: Fiscal balance. Ratio of the annualized fiscal balance to GDP. Sources: SARB and IFS.
  • NFAOFPY: Net foreign assets including the forward book. Ratio of the end-of-period net foreign assets of the banking system (monetary authorities and commercial banks) to GDP. Numerator includes open forward position, as a liability, from the first quarter of 1984 onward, when data become available. Sources: IFS, SARB, and authors’ calculations.
Table 5.A.1.Main Commodities Exported and Relative Weights
CommodityWeight

1990–1999
Weight (5)

Normalized
Weight (3)

Normalized
(Gold)

Normalized
Gold0.6040.7100.9031
Coal0.1510.17700
Iron0.0330.0390.0490
Copper0.0320.0380.0480
Platinum0.0310.03600
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The authors are grateful to Michael Nowak, José Fajgenbaum, Vivek Arora, Paul Cashin, and other colleagues at the IMF, as well as colleagues at the South African Reserve Bank and National Treasury, and participants in the Bureau of Economic Research 2002 conference (Cape Town, November) and in the European Economic Association 2003 meetings (Stockholm, August) for useful discussions and comments. Gustavo Bagattini and Winifred Ellis have provided invaluable research and editorial assistance.

1

Other variables often include the investment-to-GDP ratio and the net capital inflows—to—GDP ratio.

2

For recent empirical evidence on the Balassa-Samuelson effect, see MacDonald and Ricci (2001, 2002).

3

However, the repayment of the net foreign liabilities accumulated would eventually require a depreciation of the real exchange rate to achieve current account surpluses.

4

This does not contradict the fact that in the steady state of the economy (the long run, as commonly conceived), the Dornbusch model would not predict an effect of monetary policy on the real exchange rate simply because, by definition, the monetary shock would have vanished in the steady state.

5

Assuming that Ricardian equivalence does not hold, for example, because of uncertainty about the duration of the improvement in the fiscal balance.

6

See De Gregorio, Giovannini, and Wolf (1994) for a theoretical and empirical analysis of the impact of government spending on the real exchange rate. The effect of a reduction in government spending, as opposed to the effect of an increase in taxes, may also be stronger if the larger multiplier effect of the former is not neutralized by consumers’ optimal saving choices.

7

The rapid reduction of the central bank’s forward book since 1998 has often been indicated as contributing to the depreciation of the rand. As the reduction is associated with an improvement in the net foreign asset position, such a claim could appear incompatible with the theoretical prior outlined in this section. However, as shown in the last subsection of “Econometric Results and Their Robustness,” the negative pressure on the exchange rate from an increase in the net foreign asset position is likely to be temporary, and the long-run effect is likely to be positive, as theoretically predicted.

8

Definitions and sources for the variables are presented in Appendix 5.1. Note that the variables represented in Figures 5.1 and 5.2 are not in logarithmic terms.

9

As is often done in estimation of equilibrium exchange rates, we employ real GDP per capita with respect to trading-partner countries as a proxy for the Balassa-Samuelson effect. The very peculiar nature of labor market dynamics in South Africa before and after the end of apartheid prevents a meaningful use of labor productivity data.

10

The dual exchange rate system may pose an issue in terms of which exchange rate is appropriate for the calculation of the real effective exchange rate. We avoid imposing arbitrary choices by employing the series constructed by the South African Reserve Bank.

11

There are alternative ways of addressing serial correlation and endogeneity in a cointegrating framework, such as that in Phillips and Hansen (1990).

12

The role of different commodity prices and other variables is also investigated. The net foreign asset variable relates to commercial banks as well to the monetary authorities and includes the forward book of the latter. Note that whether the net foreign assets of the banking system are able to capture the long-run behavior of the economy’s net foreign assets is an empirical issue (quarterly data were not available for the variable at the economy-wide level).

13

The four dummies introduced take the value of one for 1984:Q1, 1985:Q4, 1986:Q1, and 1994:Q1, respectively. In these cases, residuals from the VECM specification estimated in column (1) had a size in excess of three times the standard deviation.

14

The trace-statistic test suggests there may be two cointegrating vectors at the 5 percent significance level for the first regression.

15

In some of the specifications that we run the hypothesis of normality is not rejected.

16

The commodity price variable is the variable that has the most stable and robust coefficient when alternative specifications are tried: even in a VECM specification with just the real exchange rate and commodity prices, the coefficient of the latter is—0.67, very close to the one presented in Table 5.1.

17

The coefficient of the proxy for the Balassa-Samuelson effect appears rather low. However, this coefficient is biased downward by the high correlation between the proxy and the net foreign asset variable. In a specification without NFAOFPY, most coefficients remain unchanged, but the coefficient of LRGDPPCR rises—in absolute value—to about 0.4, which is closer to the theoretical prediction for the Balassa-Samuelson effect (that is, the share of nontradables in GDP).

18

Choosing the degree of smoothing is admittedly arbitrary. The equilibrium real exchange rate in Figure 5.2 is derived by applying to the explanatory variables a Hodrick-Prescott filter with a smoothing factor of 1,600, which is what Hodrick and Prescott suggest for quarterly data. A larger (smaller) factor would generate a smoother (less smooth) equilibrium real exchange rate path. It should be noted that one unfortunate feature of the Hodrick-Prescott filter is that it tends in general to perform poorly at both ends of a series.

19

After overshooting at the end of 2001, the real exchange rate rebounded during the course of 2002 and the first quarter of 2003. From the first quarter of 2002 to the beginning of March 2003, the real exchange rate appreciated by nearly 40 percent, reflecting a nominal effective appreciation of about 28 percent and an inflation differential vis-a-vis trading partners of about 10 percent. This large appreciation of the real exchange rate was more than enough to close the gap that prevailed in the first quarter of 2002. At the same time, however, the strengthening of commodity prices may have induced an appreciation of the equilibrium real exchange rate. Assuming that commodity prices were to persist at the high levels prevailing at the beginning of March 2003 (say, US$350 per ounce for gold, US$650 per ounce for platinum, and US$26 per ton for coal), the dollar value of the rand consistent with the estimated equilibrium real exchange rate (and therefore with a zero gap) would be calculated at R7.8 per U.S. dollar for early March 2003.

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