This Selected Issues paper estimates an equilibrium path for South Africa’s real effective exchange rate. The paper briefly describes the dynamics of the real exchange rate and its determinants. It investigates the presence of a long-term relationship between the real exchange rate and certain explanatory variables, estimates the speed at which the real exchange rate converges toward its equilibrium level, and derives measures for the equilibrium real exchange rate. The paper also examines the real money demand, consumer prices, and the real exchange rate in South Africa.


This Selected Issues paper estimates an equilibrium path for South Africa’s real effective exchange rate. The paper briefly describes the dynamics of the real exchange rate and its determinants. It investigates the presence of a long-term relationship between the real exchange rate and certain explanatory variables, estimates the speed at which the real exchange rate converges toward its equilibrium level, and derives measures for the equilibrium real exchange rate. The paper also examines the real money demand, consumer prices, and the real exchange rate in South Africa.

IV. Potential Output and the Sources of Growth38

60. The policy outlook for a country depends importantly on both near- and long-term prospects for real output growth. Near-term prospects can be measured by potential output growth and the output gap (measured as the difference between actual and potential output), which, in conjunction with other indicators, provide an indication of the intensity of resource utilization and of inflationary pressures. Longer-term growth prospects are based on the full utilization of factors of production and the output gains that arise as these factors are more efficiently utilized, for example through structural reforms.

61. This section provides estimates of potential real GDP growth in South Africa based on alternative methodologies, including a production function approach that is standard in the literature.39 The estimates suggest that during 1994–2001, potential output growth has been around 2½–2¾ percent annually, and that in 2001 the output gap was around zero. The estimates of the output gap are reasonably closely correlated over time with inflation and capacity utilization, which are other indicators of the intensity of resource utilization.

62. To shed light on South Africa’s longer-term growth prospects, the section analyzes the sources of real GDP growth in the country building on previous work by the staff (see IMF, 1998). A striking fact is that the average annual growth rate of real GDP has increased significantly since 1994, rising from 1 percent in 1980–93 to 2.7 percent in 1994–2001.40 The increase can be attributed principally to total-factor-productivity (TFP) growth—or improvements in efficiency and technology—rather than to increases in the factors of production. If the TFP growth rates experienced since 1994 are sustained, and labor-market rigidities are eased sufficiently so that employment rises in step with future increases in the labor force, then the economy could achieve growth rates around 5 percent over the longer term.

A. Potential Output and the Output Gap

Potential output growth: alternative methodologies

63. A number of methodologies can be used to estimate potential output growth, ranging from purely statistical approaches to more structural methods such as the production function approach. Since each of these approaches has problems, it is useful to examine the results based on a variety of measures. The results suggest that the average annual growth rate of potential GDP in 1994–2001 was roughly 2½–2¾ percent (Table IV. 1).41 This represents a substantial pick-up from 1980–93, when potential growth was only around 1–1¼ percent.

Table IV. 1.

Estimates of Potential Output Growth

(in percent)

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Sources: Authors’ estimates and South African Reserve Bank.

1995–2001, because of a sustained increase in the estimated potential growth rate starting in 1995.

SARB (South African Reserve Bank).

64. A common technique used for detrending economic time series is the Hodrick-Prescott (HP) filter.42 In the context of the real GDP series, the HP filter derives a “trend” output such that it minimizes a weighted average of the gap between actual output and trend output and the rate of change in trend output. Trend output growth on this basis was 2½ percent during 1994–96. A disadvantage of the HP filter is that the end points of the filtered trend output series tend to be sensitive to the last few observations in the sample. However, estimates based on a Kalman filter, which is not susceptible to the end-point problem, were similar to the HP estimates.

65. The growth rate of potential output can also be estimated by a structural vector autoregression (VAR), such as the Blanchard-Quah bivariate decomposition in which output is divided into its trend and cyclical components. In addition to using the information contained in the real output series, as is done by the HP filter, the Blanchard-Quah decomposition incorporates information from cyclical variables such as inflation. The Blanchard-Quah approach allows the trend component of output to be stochastic, but does not restrict it to be a random walk, which is consistent with the belief that the permanent component of output is driven in part by supply shocks such as technological innovation. Based on the Blanchard-Quah decomposition, potential output growth was estimated to be 2¾ percent in 1994–2001.

66. A key shortcoming of statistical detrending techniques is that they do not have an economic basis, in the sense that the estimated productive limits of the economy are not based on the available factors of production. In contrast, a production-function approach explicitly models output in terms of the factors of production (capital and labor) and TFP. This approach requires the assumption of a functional form for the aggregate production function and the construction of a series for potential labor and TFP. A standard assumption for the functional form is a Cobb-Douglas production function, with constant shares over time for labor and capital.43

67. The production-function approach to estimating potential output growth involves three key steps. First, TFP growth is derived as the difference between observed real GDP growth and the weighted sum of employment and capital growth.44 Second, the potential growth rates of TFP and employment are derived by assuming that TFP and employment were at their potential levels in 1981 and 1996, which appear to have been cyclical peaks, and assuming that the potential growth rates are equal to the trend (HP) growth rates between those peak years.45 Finally, potential GDP growth is estimated as potential TFP growth plus the weighted sum of the growth in potential employment and the capital stock.46 Based on the production-function approach, annual potential output growth was estimated to be 2¾ percent during 1994–2001.

68. While all of the methodologies used above result in potential GDP growth rates of 2½–2¾ percent during 1994–2001, it should be noted that since the estimations are based on historical data they build in the labor-market and other rigidities that existed in the past. Looking ahead, reforms that contribute to an easing of these rigidities could lead to an increase in potential output growth.

Output gap

69. The level of potential output can be determined by applying the estimated growth rate of potential, based on the production-function approach, to the level of actual output in a base year in which output is judged to have been close to potential based on other indicators of resource utilization.47 Real GDP appears to have been close to its potential level in 1999, as evidenced by low inflation and an absence of other indications of resource underutilization or overutilization as reflected in, for example, a capacity utilization rate that was very close to its long-run average. The output gap derived from this potential output series was around zero in 2001 (Figure IV. 1).

Figure IV.1.
Figure IV.1.

Actual Output, Potential Output, and Output Gap, 1981–2001

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A004

Correlation with other measures of resource utilization

70. The estimated output gap is positively correlated with changes in CPI inflation, with a lag of one year, and with deviations in manufacturing capacity utilization around a long-run average (Figure IV.2).48 This suggests that the output gap may be a useful indicator for gauging the intensity of resource utilization in the economy and the building of inflationary pressures.

Figure IV.2.
Figure IV.2.

Output Gap, Inflation, and Capacity Utilization, 1981–2001

Citation: IMF Staff Country Reports 2003, 018; 10.5089/9781451840995.002.A004

B. Sources of Growth

71. The analysis suggests that the significant increase in real GDP growth after 1994 relates principally to a substantial increase in TFP growth rather than to greater factor accumulation (Table IV.2).49 The significance of the prominent role of TFP in South Africa’s recent growth performance is that GDP growth can generally be sustained over longer periods of time when it is based on improvements in technology and efficiency—which are embodied in TFP—rather than on factor accumulation, which is subject to inherent limits based on demographics and diminishing returns.

Table IV.2.

Contributions to Growth, 1980–2001

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Sources: Statistics South Africa; and authors’ estimates.

72. The decline in the contributions to growth of capital and labor during 1994–2001 relative to the previous period reflects a continuation of the slowing in factor accumulation that started in the 1980s. Average annual growth in the capital stock declined from just over 2 percent during 1980–93 to 1.3 percent during 1994–2001. Employment actually shrank during 1994–2001, as the positive annual average growth of 0.2 percent during 1980–93 was replaced by negative growth of 1.6 percent.50 As a result, the contribution to GDP growth of capital and labor together fell from 1 percentage point annually during 1980–93 to negative0.3 percentage points during 1994–2001.

73. The decline in the contribution from factor accumulation was more than offset by a substantial increase in TFP growth.51 The turnaround in TFP performance in the recent period reflects in part the policy and institutional changes during the period (see IMF, 1998). International trade and investment offer important vehicles for technological spillover effects, and greater private sector participation in the economy increases the scope for technological innovation. In South Africa, the scope for such effects has increased with the increasing openness of the economy; a rising share of equipment and machinery in total investment; and a greater share of investment, including in equipment and machinery, being accounted for by the private sector (Table IV.3).

Table IV.3.

Selected Factors Affecting TFP Growth, 1980–2001

(in percent)

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Sources: South African Reserve Bank; and authors’ estimates.

74. The growth accounting exercise can be extended to estimate the economy’s long-run growth prospects. In the neoclassical growth model, the steady state capital-labor ratio is constant and the growth rate of output is equal to the rate of TFP growth plus employment growth.52 If the recent rates of TFP growth (3 percent) are maintained and if, with labor-market reforms and other institutional changes, the prospective annual labor-force growth of 2 percent is fully absorbed into employment, then the long-run real GDP growth rate could be 5 percent (Table IV.4).53 If the labor-market changes are sufficient to absorb only half of the increase in the labor force, then growth could be 4 percent. However, if the labor-market changes are sufficient only to stop the contraction in employment—which would still represent a substantial improvement over the recent experience—then GDP growth would remain at 3 percent.

Table IV.4.

Long-Run Growth Prospects

(Annual GDP growth rate, in percent)1

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Authors’ calculations. All scenarios assume annual TFP growth of 3 percent. Baseline and depressed labor-force growth rates are assumed to be 2 percent and 1 percent, respectively.

75. In addition, it is possible that labor-force growth may be lower than currently projected, for example on account of the HIV/AIDS pandemic (see, for example, United Nations, 2002). If the labor force grows only half as fast as currently projected, then GDP growth could fall in the 3–4 percent range based on alternative assumptions about labor-market conditions.54

76. These estimates suggest a wide range of possibilities for long-run output growth. However, the estimates all suggest that there is scope for output growth to increase to substantially higher levels provided that a strong effort is made to improve labor market conditions. In addition, the outlook depends crucially on maintaining high rates of TFP growth, which in turn depends on the extent of market-related activity, private-sector participation, skills development, and innovation.


  • Chadha, B., 1995, “Disequilibrium in the Labor Market in South Africa,IMF Staff Papers, Vol. 42, No. 3, pp. 642669.

  • De Masi, P., J. Chan-Lau, and A. Keenan, 1999, “Measures of Potential Output, NAIRU, and Capacity Utilization,” in United States—Selected Issues, IMF Staff Country Report No. 99/101.

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  • Hodrick, R., and E. Prescott, 1997, “Postwar U.S. Business Cycles: An Empirical Investigation,Journal of Money, Credit, and Banking, Vol. 29, pp. 116.

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  • International Monetary Fund, 1998, South Africa—Selected Issues, Section II, “Growth Accounting,” pp. 3848.

  • Lewis, J., 2001, “Policies to Promote Growth and Employment in South Africa,Informal Discussion Paper on Aspects of the Economy of South Africa, No. 16, The World Bank.

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  • Sarel, M., 1997, “Growth and Productivity in ASEAN Countries,IMF Working Paper, WP/97/97.

  • United Nations, 2002, World Urbanization Prospects: The 2001 Revision, (New York: The United Nations).

  • U.S. Congressional Budget Office, 2001, “CBO’s Method for Estimating Potential Output: An Update,” (Washington, D.C.: CBO).


Prepared by Vivek Arora, Ashok Bhundia, and Gustavo Bagattini.


See U.S. Congressional Budget Office (2001) and DeMasi, Chan Lau, and Keenan (1999) for a description of the production-function approach and estimates based on alternative methodologies for the United States, respectively.


Statistical tests for a structural break in the real GDP series indicated a break in 1993. The recent data also reflect a statistical revision in June 1999, which implemented the 1993 System of National Accounts and resulted in an upward revision in measured annual real GDP growth during 1994–98 from 2.2 percent to 2.7 percent.


Due to data availability, the analysis in this section is based on annual data for 1980–2001.


See IMF (1998) for an analysis of GDP growth in South Africa based on a Cobb-Douglas production function, and U.S. Congressional Budget Office (2001) and DeMasi, Chan Lau, and Keenan (1999) for an analysis for the United States. The shares of labor and capital in the production function were based on their shares in national income—55 percent and 45 percent, respectively. The use of national-income shares has been criticized by Sarel (1997), as discussed below, but the results do not vary significantly with alternative assumptions regarding the labor and capital shares.


The weights are equal to the labor and capital shares in the production function. Employment is used as the labor variable in the production function because it is employment, rather than the total labor force, that has contributed to past production.


It would have been preferable to estimate potential employment based on its economic determinants rather than on statistical time trend techniques such as HP filters. However, such estimation was impeded by data limitations, in particular breaks in the employment series in the mid-1990s. These also hindered estimation of a NAIRU for South Africa, as tests for a Phillips-curve relationship failed to find any robust inflation-unemployment relationship after controlling for other factors. For the period through 1991, Chadha (1995) found that the high unemployment in South Africa was largely structural rather than cyclical in nature.


The capital stock is used in its actual rather than smoothed form because it is assumed to be fully utilized. Also, it is lagged one period. These are standard assumptions (e.g., see CBO, 2001).


The production-function method is used because it has the strongest economic basis. However, as noted, the results are not significantly different than those based on the other approaches.


The correlation coefficients are 0.41 and 0.64, respectively.


This reinforces the conclusion of the previous staff study on the subject of growth accounting which found that TFP growth turned around during the early 1990s and bolstered a flagging growth performance (see IMF, 1998). The data for the subsequent period indicate that the increase in TFP growth has been sustained and has contributed to a substantial increase in real GDP growth.


See Lewis (2001) for a discussion of some of the factors behind the employment decline.


This general conclusion is robust to alternative assumptions regarding the shares of capital and labor in output. The use of national-income-based shares is sometimes criticized in part because it assumes that capital and labor markets are perfectly competitive. In South Africa, with large imperfections in labor market, the assumption may be unrealistic. However, an alternative estimate of the labor share based on Sarel (1997), which uses a disaggregated approach and adjusts for market imperfections, is 0.68 instead of 0.55. Under this alternative assumption, it is still true that the turnaround in GDP growth in the recent period owed to TFP growth, whose annual contribution increased from0.2 percentage points in 1980–93 to 3.4 percentage points in 1994–2001.


The production function is Y = A.KαLI–α, where Y represents real GDP; A, K, and L represent TFP, capital, and employment, respectively; and a and (1 -α) represent the shares of capital and labor in output. The growth rate of output is thus: ΔY/Y=ΔA/A+ α.ΔK/K + (1-α).ΔL/L. In the steady state, if the capital-labor ratio is constant (as it is in the neoclassical growth model), then ΔY/ΔY = ΔA/A + AL/L.


In this scenario, growth rates could be even higher than 5 percent if labor-market and other reforms are substantial enough to generate employment growth that absorbs not only increases in the labor force, but also the currently unemployed, resulting in a decline in the unemployment rate.


All of these conclusions are based on a neoclassical growth model. In an endogenous growth model, the steady state is characterized by a constant capital-output ratio and output growth is given by ΔY/Y = [(ΔA/A)/ (1-α)] + ΔL/L. There are no diminishing returns to capital and long-run growth is thus higher. Under the same assumptions as above on labor-force growth and labor-market reforms, this model would suggest that long-run GDP growth rates could be in the 5½–7½ percent range. However, such high growth rates should be considered only a theoretical possibility at this stage, given that they have not been observed over sustained periods in South Africa in the past and the many assumptions that are involved.

South Africa: Selected Issues
Author: International Monetary Fund