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The real equilibrium South African rand/US dollar exchange rate: a comparison of alternative measures.

Abstract This article indicates how different measures of the real exchange rate, i.e., the exchange rate adapted for cost inflation, price inflation and labour costs, influence the equilibrium view and misalignment of the South African rand/US dollar exchange rate. The approach followed is based on the behavioural equilibrium exchange rate approach by Clark and MacDonald (1998), where the exchange rate is influenced by a number of fundamental and transitory factors. The real equilibrium exchange is estimated by using a single equation regression and a number of key explanatory variables. To determine the long-run relationship a Vector Error Correction Mechanism is used.

Keywords equilibrium exchange rate * South Africa


Since the fall of the Bretton Woods fixed exchange rate system, currencies worldwide have experienced increased velocity. This is also true for the South African rand (ZAR), which turned to various degrees of a floating exchange rate system after the abolishment of the Bretton Woods system. During the 1980s and 1990s, the South African rand exchange rate was determined according to a managed floating system. During much of this time (1985 to 1995), the dual exchange rate system, i.e., the commercial rand and the financial rand, was in use. In 1995 the financial rand was abolished and exchange controls on residents were gradually relaxed (van der Merwe, 2003). This left South Africa with one exchange rate, which proved to be increasingly volatile in a volatile global environment.

After a period of stability, the ZAR started to crack in February 1996 and between the end of March 1996 and April 1996, the effective exchange rate of the rand plummeted by approximately 8%. The prime rate reached 20.50% in May 1996 and in the first 6 months of 1996 the ZAR lost 15.7% to a basket of currencies. The introduction of GEAR (Growth, Employment and Redistribution Plan) saw a change in sentiment towards the ZAR and the ZAR kept its ground throughout the early days of the Asian crisis in 1997. But the first couple of months in 1998 saw the rand shedding approximately 8% of its value. The Russian crisis, coupled with the end of term of the Reserve Bank governor (often referred to as the Mboweni bump), sucked South Africa backed into the vortex with the ZAR shedding 23.2% of its value against the dollar from May to July 1998 (Steyn, 2004).

More emerging market crises (for example Brazil in 1999 and Argentina in 2001-02) led to greater world financial instability and affected the value of the ZAR and the nominal effective exchange rate of the ZAR decreased by 12 1/2% in 2000 and by another 34 1/2% in 2001. Steyn (2004) states that one lesson learned from all these crises is that it does not work to try and manage the value of the exchange rate if there is pressure on it to weaken. This led the Reserve Bank to implement a formal inflation targeting approach and a flexible exchange rate in February 2000.

It was generally expected that the ZAR would depreciate gradually against developed country currencies (such as the US dollar and the euro), but since the end of 2002 the ZAR has recovered strongly against both the US dollar and the euro with an increase in value of 26% in 2002 and 19% in the first quarter of 2003. Even though the ZAR has also depreciated under the managed floating exchange rate system during the 1990s, the recovery in 2002 was the first time in the past 30 years that such as sharp reversal in the exchange rate of the ZAR has occurred (van der Merwe, 2003). This has obviously led to various concerns regarding the level of the exchange rate and the competitiveness of South African exports. The Reserve Bank and government has been under pressure from, amongst others, labour unions and the mining houses, to intervene in the market and devalue the currency in order to stimulate export and job creation.

Yet, the policy-makers have stuck to their decision not to intervene and the ZAR has remained relative stable at its current stronger levels. Despite the doomed prophecies for the economy because of the stronger ZAR, the economy has performed reasonably well in the past two to three years. Economic growth has increased, unemployment levels are down, inflation is under control and the current account deficit is financed by positive capital inflows.

The question that remains to be answered is whether the South African rand is currently overvalued in real terms, since it obviously have an impact on the competitiveness of the country and the long-term stability of the currency? While this question may seem quite straightforward to answer at first, a closer examination reveals that it contains a number of controversies. Firstly it should be determined what is meant by the real exchange rate? And secondly, how will the equilibrium exchange rate level be determined in order to evaluate whether the currency is over or undervalued? These questions will be addressed in the next section, after which the method used will be discussed, followed by the results.

Literature Review

The Real Exchange Rate

Standard international economics textbooks define the real exchange rate as the price adjusted nominal exchange rate. The real exchange rate (E) is thus the nominal exchange rate (e) times the ratio of the foreign price level (P*) to the local price level (P*). In other words:

E = e [P*/P]

It can thus be noted that the real exchange rate denotes the ratio of prices of foreign goods to prices of domestic goods, expressed in the home currency. An increase in the real exchange rate would thus indicate that the home country becomes more competitive (Chacholiades, 1990, p. 354).

Yet, the price indices that should be used remain a question. Balvers and Bergstrand (1997, p. 349) suggested the use of the consumer price indices (CPI* and CPI) of the foreign and domestic country. Baffes, Elbadawi, and O'Connell (1997, p. 2) indicates that the foreign price of traded goods ([P*.sub.T]) and the domestic price of non-traded goods ([P.sub.N]) could be used. Chou and Shih (1998, p. 167) applies the wholesale price index (or producer price index) of the foreign country (WPI*) as a proxy for the price of foreign tradables, and the domestic consumer price index (CPI) as a proxy for local non-tradables. This is normally also the approach used in determining the real effective exchange rate of the ZAR.

On the other hand, Lipschitz and McDonald (1991, p. 1) indicate that an indicator of competitiveness should have the critical property that a loss of competitiveness of one country should lead to an erosion of producers of traded goods in that country's share in both domestic and foreign markets. They suggest the use of unit labour cost in assessing the relative price differences between countries. It can thus be concluded that three different measures of the real exchange rate can be applied namely, one based on consumer prices (Eq. 1), the second on the relative prices of tradables and non-tradables (Eq. 2) and a third based on the relative labour cost indices (Eq. 3).

E = e [CPI*/CPI] (1)

E = e [[P*.sub.T]/[P.sub.N]] = e [WPI*/CPI] (2)

E = e [ULC*/ULC] (3)

The Equilibrium Exchange Rate

Standard macroeconomics and international economic textbooks normally define the equilibrium exchange rate in terms of purchasing power parity (PPP). This proposition is based on the idea that a change in a country's exchange rate is equal to difference in prices between countries (Ethier, 1995, p. 531). Yet, Balvers and Bergstrand (1997, pp. 345-346) indicate that real exchange rates have departed for great periods of time from its PPP level and to explain these variations, various models of equilibrium exchange rate determination have surfaced. MacDonald (2001, p. 1) indicates that these models are distinguished by a wide variety of acronyms such as FEER, BEER, PEER, DEER and NATREX. A brief review of the different models reveals distinct differences between them, including differences in estimating techniques and underlying assumptions. While the aim of this paper is not to present a thorough discussion of the differences, a brief summary thereof is necessary to eliminate ambiguity.

The fundamental equilibrium exchange rate (FEER) was made popular by John Williamson in 1994 and is a macro-economic equilibrium approach to the equilibrium exchange rate. The FEER is the exchange rate that is consistent with internal and external economic equilibrium (Williamson, 1994, pp. 179-180). The approach is often called a current account approach to the equilibrium exchange rate, since the balance of payments identity lies at the hart of this approach. Estimating the FEER normally requires the use of a complete macroeconomic model or a partial equilibrium model. Recent studies that made use of a complete macroeconomic model include the studies of Hallet and Richter (2004), Smidkova (1998), Wren-Lewis (2003) and Piscitelli and Westaway (2004). The partial equilibrium approach was engineered and used by Williamson (Piscitelli & Westaway, 2004) and Barrell and Wren-Lewis (1989).

The behavioural equilibrium exchange rate (BEER) splits the normative aspects of exchange rate modelling from the behavioural aspects. Normally this entails a two-stage procedure, where the first stage entails the estimation of the behavioural exchange rate relationship and the second stage entails the construction of an assessment of whether the exchange rate is overvalued or not (MacDonald, 2001, p. 1). This misalignment depends on short-term transitory factors and the departure of the fundamentals from their long-term value. The total misalignment can thus be split into a permanent and transitory component and therefore the permanent equilibrium exchange rate acronym (PEER) (Egbert, 2002, p. 6). Methodology-wise, this model normally makes use of single equation regressions and is often said to be an a-theoretical approach to equilibrium exchange rate modelling. Landmark studies in this regard are those of Clark and MacDonald (2000), MacDonald (2001) and Baffes et al. (1997).

The desired equilibrium exchange rate (DEER) refers to the equilibrium real exchange rate consistent with macroeconomic balance, based upon a set of desired macroeconomic objectives. The exchange rate is therefore not the actual exchange rate, but an estimate of what the exchange rate should be at the desired internal and external macroeconomic balance. It is mostly a static view of the exchange rate in the medium term, whereas the FEER approach is a long-term analysis with all economic forces returning to long-run equilibrium levels (Bayoumi, Clark, Symansky, & Taylor, 1994, pp. 20-21). The DEER framework uses partial equilibrium methodology and important studies utilising this approach to exchange rate modelling include that of Bayoumi et al. (1994) and Church (1992). The Multimod macroeconomic model of the IMF is often used in these estimates of the equilibrium real exchange rate.

NATREX is the acronym for natural real exchange rate, which refers to the medium-run, intercyclical equilibrium exchange rate as determined by real, fundamental factors. It is a moving equilibrium real exchange rate that responds to continual changes in exogenous and endogenous real fundamentals. This methodology is again based on fundamentals and is narrowly associated with the current account approach, but focuses more closely on the particular characteristics of the countries involved. It also endogenises changes in capital, wealth and net debt of foreigners, but excludes speculative capital flows and movements in international reserves (Allen, 1995, pp. 1-6). Martinez (2003, p. 25) indicates that the NATREX equilibrium is a sequence of medium run equilibriums that evolve into a long run reference rate. Studies on NATREX normally utilises complete to partial equilibrium models, such as those conducted by Martinez (2003), Stein (1995) and Crouhy-Veyrac and Saint Marc (1995).

It can thus be concluded that the FEER, DEER and NATREX are strongly based on macroeconomic equilibrium principles and the resulting equilibrium exchange rate is consistent with medium- or long-run macroeconomic equilibrium. The BEER approach, on the other hand, is a more a-theoretical way of looking at the equilibrium exchange rate and identifies factors (called fundamentals) that are driving the current exchange rate.

Materials and Methods

The basic underlying model used in this paper is the behavioural exchange rate (BEER) model. The appeal of this model lies in the fact that the equilibrium exchange rate is determined by an appropriate set of explanatory variables and is not derived from macroeconomic balance. The real exchange rate is calculated using the fundamental determinants of the actual real exchange rate and not the exchange rate that is consistent with internal and external balance. Therefore, the actual real exchange rate is in equilibrium in a behavioural sense when its movements reflect changes in these fundamentals (Zhang, 2001, p. 83). It is also an approach that lends itself to the assessment of the degree of over- or under-evaluation, utilising a single equation regression approach. The method followed is similar to that employed by MacDonald (2001), MacDonald and Ricci (2003) and Baffes et al. (1997) and the discussion of the method is therefore based on their discussion.

The relationship between the actual values of the real exchange rate and its fundamental determinants can be presented as follows:

ln [E.sub.t] = [beta]'[F.sub.t] + [[epsilon].sub.t] (4)

where [E.sub.t] is the real exchange rate, [F.sub.t] is the vector of fundamentals and [[epsilon].sub.t] is the white noise variable with a zero mean and constant variance.

To decide on the variables that need to be included in the "Fundamental" term, previous research on South African exchange rates were consulted. These studies include those of Aron, Elbadawi and Kahn (1997) and MacDonald and Ricci (2003). Both these studies used the real effective exchange rate as the dependent variable, while this paper uses various measures of the real rand/dollar exchange rate. The variables included in their analyses are indicated in Table 1. The data used is quarterly data, spanning from 1978 to the second quarter of 2005.

While there are definitely some similarities between the variables used, there are also clear differences. Based on the above, the variables tested for inclusion in this paper are the following: The log of the nominal South African rand/US dollar exchange rate (denominated as dollars for rand) adapted for price differences according to Eqs. 1 to 3, respectively, the real GDP per capita of South Africa relative to the USA, the real interest rate differential between South Africa and the USA, the South African terms of trade, net foreign assets of the South African monetary sector as a percentage of GDP, the log of the real gold price, the openness of the South African economy, the ratio of fiscal balance to GDP, the log of government expenditure as a percentage of GDP, the log of a commodity index and the log of gross reserves of the South African Reserve Bank as a percentage of GDP. Table 2 indicates the variable description as well as the data sources.

What can be expected from these variables?

* The real interest rate differential represents aggregate demand, productivity, and persistent monetary policy (MacDonald & Ricci, 2003). All of these factors have a positive relationship with the real exchange rate and it is thus expected that an increase in the interest rate will lead to an appreciation of the currency.

* When the price of exported commodities increases, the real exchange rate will be likely to appreciate (Cashin, Cespedes, & Sahay, 2002), indicating a positive relationship between commodity prices and the exchange rate.

* According to Goldfajn and Valdes (1999), a more open trade regime is associated with a more depreciated real exchange rate and a negative relationship between openness and the exchange rate is thus expected.

* Theoretically, the stock of foreign exchange reserves is expected to have a positive effect on the real exchange rate. This is consistent with the role of the foreign exchange reserves as a relatively liquid indicator of the stock of national wealth (Aron et al., 1997), and a positive relationship can thus be expected.

* The magnitude of net foreign assets is associated with a more appreciated exchange rate in the long term. A country that has reached a higher level of net foreign assets is in a position to finance a worse current account balance and can thus maintain a loss in competitiveness associated with a more appreciated real exchange rate (MacDonald & Ricci, 2003).

* An improvement in the fiscal balance will have an ambiguous effect on the real exchange rate. Depreciation might occur because the improved fiscal balance would normally induce a less-than-proportional reduction in private saving (MacDonald & Ricci, 2003).

* If there is an increase in the price of exported goods, implying an improvement in the terms of trade, there will be an increase in wages, which tends to increase the prices of non-tradable goods (the Balassa-Sameulson effect). Furthermore, when domestic income increases, an improvement in the terms of trade will increase the demand for non-tradable goods, leaving a further increase in the prices to re-establish market equilibrium (Guillaumont Jeanneney & Hua, 2002). A positive relationship can thus be expected.

Zhang (2001, p. 84) points out that, in essence, co-integration analysis tests for the existence of a systematic equilibrium relationship between the real exchange rate and its determinants. It thus captures a steady-state relationship between the actual values of the real exchange rate and economic fundamentals. The difference between the actual exchange rate and the BEER and the PEER gives an indication of the current misalignment (if any) between the two currencies.

The Johansen co-integration test is used to investigate the existence of a long-run relationship between the real exchange rate and the variables defined in Table 2. A vector (x) is defined on which the estimations are based. In this case the vector is:

[x.sub.t] = [lusdza[r.sub.t], irat[e.sub.t], lgdpp[c.sub.t], fi[s.sub.t], to[t.sub.t], ope[n.sub.t], lrgol[d.sub.t], nf[a.sub.t], lgre[s.sub.t], lkom[m.sub.t], lgove[x.sub.t]] (5)

It is assumed that the vector has an autoregressive representation of the form:

[x.sub.t] = [eta] + [p.summation over (i=1)] [[PI].sub.t][x.sub.t] + [[epsilon].sub.t] (6)

where [eta] is a vector of deterministic terms, p is the lag length and [epsilon] is a vector of white noise disturbances. Equation 6 can be redefined in the VECM form as:

[DELTA][x.sub.t] = [eta] + [p-1.summation over (i=1)] [[PHI].sub.i][DELTA][x.sub.t-i] + [PI][x.sub.t-1] + [[epsilon].sub.t] (7)

where [DELTA] is the differencing operator; [PI]=[alpha][beta]', where [alpha] and [beta] are k x r matrices, whose rank determines the number of co-integrating vectors; [alpha] represents the speed of adjustment to equilibrium and [beta] is a matrix of long-run coefficients; [PHI] is a k x r coefficient matrix. If [PI]=k (full rank) or if [PI]=0 (zero rank), there will be no co-integration amongst the elements in the long run relationship. MacDonald (2001) indicates that the model then has to be estimated in levels or first differences. But if [PI] is of reduced rank (r<k) a VECM model can be estimated.


The above-mentioned method is applied to the various real exchange rate estimates in order to determine the extent of misalignment of the currency according to the various measures of the real exchange rate. The software package Eviews 5.1 was used in all the estimations. Figure 1 indicates the US dollar/Rand real exchange rates according to the various measures.


Note that the denomination of the exchange rates is dollars for rand. The first real exchange rate (USDZAR1) is the exchange rate deflated by the relative CPI's, the second (USDZAR2) is the exchange rate deflated by the relative prices of tradables versus non-tradables, and the third (USDZAR3) is the exchange rate deflated by the relative unit labour cost indices. It is evident that the appreciation in the rand is more significant when the exchange rate is deflated by the relative labour cost indices.

The first step in the above analysis is to test for stationarity. Table 3 indicates the results of the Adapted Dickey-Fuller unit root test. It is evident that all the variables are non-stationary in levels, except the terms of trade and gross reserves, but that the lagged polynomials of all the other variables are stationary. The variables are therefore I(1), except the terms of trade and gross reserves that are I(0). The Johansen co-integration test is not affected if the variables are a combination of I(0) and I(1), but is affected when some of the variables are stationary in second differences.

In the estimate centred seasonal dummies are included--a common structure employed in seasonal data--as well as a structural dummy for the political unrest and subsequent debt standstill from 1984's second quarter to the end of 1985, the second to fourth quarters of 1998, during the Asian currency crisis, and the first three quarters of 2001, during the Zimbabwe crisis and Argentine currency crisis.

Testing the variables via Granger causality indicated that some of the variables will cause substantial multi-colinearity between variables, and therefore net foreign asset, real gold and openness were disregarded in the start of the analysis. Various combinations of the remaining variables were tested and the best results were found when the following variables are included: the relative GDP's per capita, gross reserves, the commodity index, fiscal balance as a percentage of GDP, the interest rate differential and the terms of trade.

Previous research, such as those conducted by MacDonald and Ricci (2003) and Aron et al. (1997) indicated that between 4 to 6 lags are found to be significant in the analysis. The LM test results confirmed that at least 4 lags should be considered in each case. The results of the Johansen co-integration test are indicated in Table 4 and in each case 4 lags were considered.

It can be seen that in all the cases there is at least one co-integrating vector at a 0.01 confidence level. In some cases, two co-integrating vectors are identified, especially according to the Trace test statistics. The maximum eigenvalue indicates only one case where two co-integrating vectors exist. Using the results from the Johansen test, the VECM is estimated with 4 lags and co-integration assuming a linear trend in the data, where an intercept is accepted in the VECM, but not a trend (option 3 in Table 4). The results of the various VECMs are indicated in Table 5. In these estimates, the x-vector thus consists of:


[x.sub.t] = (lusdza[r.sub.t], lkom[m.sub.t], lgre[s.sub.t], lgdpp[c.sub.t], to[t.sub.t], irat[e.sub.t], fi[s.sub.t])

All the signs of the variables in the long run relationship are as expected, except for the negative sign of the terms of trade. The long run relationship is, in total, also significant for all the real exchange rate proxies. However, the data seems to fit the exchange rate deflated by the price of tradables versus non-tradables (exchange rate 2), better. This is evident from the better R-square value, as well as the fact that all the variables in the co-integrating relationship are significant. Short-run fluctuations in this real exchange rate are also better captured by the data.

Interpreting the results of the VECMs, the co-integrating equation indicates the long run relationship. Accordingly, the long-run relationship between the real rand/dollar exchange rate and these variables can be described as follows:

* A 1% increase in the price of commodities, noteworthy platinum, gold, coal, iron, nickel palladium, manganese, leads to an appreciation of the exchange rate of between 1.5 to 2.5%.

* A 1% improvement of South Africa's gross reserves as a percentage of GDP, leads to an appreciation of the exchange rate of approximately 1 to 1.6%.

* If South Africa's GDP per capita improves by 1% against the American GDP per capita, the rand/dollar exchange rate appreciates by between 1.7 and 7.4%.


* A 1% increase in export prices relative to import prices depreciates South Africa's exchange rate by approximately 0.04-0.06%.

* If South Africa's real interest rate increases by 1% against US long-term interest rate, the value of the rand appreciates by 0.2-0.5%.

* An increase in the budget deficit of the fiscal government leads to a depreciation of the value of the Rand against the dollar.

The VEC residuals normality tests indicate that the hypothesis stating that the residuals--the difference between the observed value and the fitted value--are normally distributed is rejected due to excess kurtosis. According to Paruolo (1996), the Johansen test is not affected when normality is rejected due to excess kurtosis rather than skewness. The data distribution is therefore flat--platykurtic--relative to the normal.

The actual values of the variables are substituted in the estimated long-run relationship in order to determine the behavioural equilibrium exchange rate (BEER). These long-run relationships are indicated in the following graph:

From Fig. 2, it is evident that the different BEERs follow the same pattern, but that the level of the BEER differs according to the real exchange rate specified. The BEER for the real exchange rate based on CPI's lies much higher, indicating a stronger Rand equilibrium exchange rate. The estimates for the behavioural real exchange rate based on the relative price of tradables versus non-tradables (BEER2) and on labour cost (BEER 3) are closer matched.

The difference between these behavioural equilibrium exchange rates become more pronounced when the degree of currency misalignment is determined. Figures 3, 4, 5 indicate the degree of currency misalignment according to the different BEERs. According to the relative CPI real exchange rate and behaviour equilibrium exchange rate, the Rand was still undervalued during 2005 relative to the dollar. This is, however, not true in both the other scenarios.

The real exchange rate and behavioural equilibrium exchange rate based on the prices of tradables and non-tradables, as well as the real exchange rate and behavioural equilibrium exchange rate based on labour cost indicate that the rand is overvalued in 2005. A slight overvaluation, which might be seen as roughly similar to its equilibrium value, is evident in Fig. 4. Yet, according to labour cost estimations of the real exchange rate, the current exchange rate is grossly overvalued.


This article focussed on the degree of misalignment of the South Africa Rand. Three measures of the real exchange rate were constructed, namely on based on relative consumer prices, the second on the relative price of tradables to non-tradables and the third according to relative labour costs. A behavioural equilibrium exchange rate model was constructed along the lines of that of MacDonald (2001) and MacDonald and Ricci (2003).



The results show that the equilibrium exchange rate estimated follow similar patterns in all the cases, but that the real exchange rate based on relative consumer prices overestimates the equilibrium value. The degree of misalignment of the currency is also very dependent on the type of deflator used to determine the real exchange rate. Relative consumer price indices indicate an undervalued currency, while relative labour unit cost indicates a grossly overvalued currency.

Three important conclusions can be derived from this analysis. Firstly, when the real exchange rate is deflated by relative consumer prices, the competitiveness of the home country is not correctly adjusted for. More effort should be taken to include variables such as productivity differences and other labour-related indicators to adjust the level of the equilibrium exchange rate.

Secondly, the real equilibrium exchange rate as determined via relative prices of tradables versus non-tradables, as well as via labour unit cost produces comparable results and might be viewed as closer proxies for the real exchange rate.

Thirdly, care should be taken when the equilibrium real exchange rate is estimated via a single-equation approach, since the outcome is dependent on the definition of the real exchange rate and variables not controlled for can cause major distortions in the estimations. The macro-economic equilibrium approach should produce more reliable results in this regard.

Acknowledgements The author would like to thank Paul Styger who provided the inspiration for the research and the attendees of the Exchange Rate session at the 61st International Atlantic Economic Conference in Berlin, March 15-19, 2006 for their valuable comments. All errors and omissions remain that of the author.


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Published online: 6 January 2007

[c] International Atlantic Economic Society 2007

A. Saayman ([mailing address])

School of Economics, North-West University, Potchefstroom Campus, Private Bag X6001, Potchefstroom, South Africa, 2521

Table 1 South African exchange rate variables

MacDonald and Ricci    Aron, Elbadawi and Kahn

Real interest rate     Terms of trade
Real GDP per capita    Real dollar gold price
Real commodity prices  Custom receipts to imports
Openness               Openness
Fiscal balance         Long run capital flows
Net foreign assets     Total capital flows
                       Gross reserves of the SARB
                       Government expenditure
                       Total domestic credit extension
                       Short run capital flows

Table 2 Data description and sources

Variable  Description                                 Source

Lusdzar   Log of the rand dollar exchange rate, in    SARB and IFS
            real terms
Lgdppc    Log of the relative GDP per capita of       IFS
            South Africa versus USA
irate     Real interest rate differential between     OECD; INTL, IFS
            South Africa and USA                        and SARB
tot       The South African terms of trade            SARB
            (excluding gold) (2000=100)
nfa       Net foreign assets of the South African     IFS
            monetary sector as a % of GDP
lrgold    Log of the real gold price. Gold price was  SARB, INTL and IFS
            deflated by the USA CPI.
open      The openness of the South African economy,  SARB
            as measured by (X + M) as % of GDP
fis       Ratio of the fiscal balance to GDP          SARB
lgovex    Log of government expenditure as a % of     IFS
lgres     Log of gross reserves of the SARB           IFS
            (excluding gold) in $ terms as a % of
lkomm     Log of commodity index (2000=100)           ABSA

Table 3 Results of the Dickey Fuller unit root test

Series    Prob.   Series       Prob.

LUSDZAR1  0.1825  D(LUSDZAR1)  0.0000
LUSDZAR2  0.0660  D(LUSDZAR2)  0.0000
LUSDZAR3  0.2266  D(LUSDZAR3)  0.0000
LGDPPC    0.6068  D(LGDPPC)    0.0000
LGOVEXP   0.3440  D(LGOVEXP)   0.0000
LGRES     0.0432  D(LGRES)     0.0000
LKOMM     0.3991  D(LKOMM)     0.0000
LRGOLD    0.6242  D(LRGOLD)    0.0000
FIS       0.2339  D(FIS)       0.0000
IRATE     0.5509  D(IRATE)     0.0000
NFA       0.8199  D(NFA)       0.0000
OPEN      0.3123  D(OPEN)      0.0000
TOT       0.0264  D(TOT)       0.0000

Table 4 Results of the Johansen co-integration test

Exogenous series: S1 S2 S3 SDUM
Lags interval: 1 to 4
Selected (0.01 level*) Number of Co-integrating Relations by Model

Data Trend:  None          None       Linear     Linear     Quadratic
Test Type    No Intercept  Intercept  Intercept  Intercept  Intercept
             No Trend      No Trend   No Trend   Trend      Trend
Trace        2             2          1          1          1
Max-Eig      2             1          1          1          1

Exogenous series: S1 S2 S3 SDUM
Warning: Rank Test critical values derived assuming no exogenous series
Lags interval: 1 to 4
Selected (0.01 level*) Number of Co-integrating Relations by Model

Data Trend:  None          None       Linear     Linear     Quadratic
Test Type    No Intercept  Intercept  Intercept  Intercept  Intercept
             No Trend      No Trend   No Trend   Trend      Trend
Trace        2             2          1          1          1
Max-Eig      1             1          1          1          1

Exogenous series: S1 S2 S3 SDUM
Warning: Rank Test critical values derived assuming no exogenous series
Lags interval: 1 to 4
Selected (0.01 level*) Number of Co-integrating Relations by Model

Data Trend:  None          None       Linear     Linear     Quadratic
Test Type    No Intercept  Intercept  Intercept  Intercept  Intercept
             No Trend      No Trend   No Trend   Trend      Trend
Trace        1             1          1          1          1
Max-Eig      1             1          1          1          1

Table 5 Results of the vector error correction mechanism estimations

Cointegrating Eq:

LUSDZAR1(-1)         1.000000
LKOMM(-1)            1.579773
LGRES(-1)            0.903873
LGDPPC(-1)           1.721337
TOT(-1)             -0.020812
FIS(-1)             -0.075043
IRATE(-1)            0.200318
C                   -1.927607
CointEq1            -0.067151
D(LGRES(-1))         0.083796
D(LGRES(-3))         0.050920
D(LGDPPC(-2))        1.625308
D(TOT(-1))          -0.004919
D(FIS(-1))          -0.008191
D(IRATE(-1))         0.022580
D(IRATE(-2))         0.017182
D(IRATE(-3))         0.019529
R-squared            0.598493
Sum sq. resids       0.183585
S.E. equation        0.053982
F-statistic          2.845724
Log likelihood     166.4477
Akaike AIC          -2.730881
Schwarz SC          -1.828405
S.D. dependent       0.069014

LUSDZAR2(-1)         1.000000
LKOMM(-1)            2.100058
LGRES(-1)            1.130348
LGDPPC(-1)           3.326571
TOT(-1)             -0.041107
FIS(-1)             -0.121529
IRATE(-1)            0.275566
C                    0.704204
CointEq1            -0.059444
D(LUSDZAR2(-3))      0.250289
D(LKOMM(-2))         0.331774
D(IRATE(-1))         0.023306
D(IRATE(-2))         0.019050
D(IRATE(-3))         0.021468
D(LGDPPC(-2))        1.500981
D(LGRES(-1))         0.091798
D(LGRES(-3))         0.046852
D(FIS(-1))          -0.010758
D(FIS(-3))          -0.007829
D(TOT(-1))          -0.005767
D(TOT(-3))          -0.005084
R-squared            0.612749
Sum sq. resids       0.166835
S.E. equation        0.051460
F-statistic          3.020764
Log likelihood     171.0879
Akaike AIC          -2.826555
Schwarz SC          -1.924079
S.D. dependent       0.066990

LUSDZAR3(-1)         1.000000
LKOMM(-1)            2.525082
LGRES(-1)            1.603634
LGDPPC(-1)           7.472514
TOT(-1)             -0.068060
FIS(-1)             -0.132182
IRATE(-1)            0.539402
C                    8.925017
CointEq1            -0.041696
D(LGRES(-1))         0.073169
D(LGRES(-3))         0.053277
D(TOT(-1))          -0.007088
D(IRATE(-1))         0.026385
D(IRATE(-2))         0.026559
D(IRATE(-3))         0.020302
SDUM                -0.056879
R-squared            0.487771
Sum sq. resids       0.309402
S.E. equation        0.070080
F-statistic          1.817935
Log likelihood     141.1324
Akaike AIC          -2.208916
Schwarz SC          -1.306440
S.D. dependent       0.079322

S.E. in () and t-statistic in []
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Author:Saayman, Andrea
Publication:International Advances in Economic Research
Geographic Code:6SOUT
Date:May 1, 2007
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