On the Rand: A Note on the South African Exchange Rate.

1 st draft April 18, 2006 On the Rand: A Note on the South African Exchange Rate. Professor Jeffrey Frankel, Kennedy School of Government, Harvard University This work was done with the able research assistance of Melesse Tashu. It is part of the contribution of the Macroeconomics Group within the Harvard University Center for International Development s Project on South Africa: Performance and Prospects The rand has undergone large movements in recent years. What explains these swings? Important questions include: Is the rand a commodity currency, like the Australian and Canadian dollar are said to be (to pick two floaters)? That is, is it a currency that appreciates when prices of the mineral products that it produces are strong on world markets and depreciates when they are weak? In other respects, does the rand behave like currencies of industrialized countries, in light of its developed financial markets? (South Africa borrows in rand, for example, unlike most developing countries.) This does not necessarily mean fitting standard theories closely, as those theories don t work well in practice for major industrialized currencies either. But such variables as GDP and inflation should have an effect. Has there been an element of momentum or bandwagon to some recent movements? Our general equation is: Log Rand value t = α + β 1 Log Real P Minerals t + β 2 Log (SA GDP/foreign GDP) t + β 3 Log Rand value t-1 + β 4 Inflation Differential t + β 5 Real Interest Differential t + β 6 Country Risk Premium t + β 7 trend t + u t. We try various versions of this equation: with the value of the rand defined in nominal terms or real terms, and bilateral against the dollar, or trade weighted. Real P Minerals t is computed as a weighted average of the prices of the specific mineral products that South Africa produces and exports. It is intended to capture the terms of trade, and so is expressed in real form by deflating by the foreign (e.g., US) price level. (SA GDP/foreign GDP) t captures an important determinant of the demand for money (domestic relative to foreign). When the dependent variable is expressed in nominal terms, then the GDPs are expressed in nominal terms (which amounts to imposing the constraint that the elasticity of demand for money with respect to income is 1, as in the quantity theory of money). When the dependent variable is expressed in real terms, then the GDPs are also expressed in real terms. It is only

possible to include the GDP variable when we are working with quarterly data; we are forced to drop it when working with monthly data. Log Rand Value t-1 is entered experimentally to capture the idea of bandwagon or momentum elements. The remaining three variables capture rates of return. It is not enough simply to add interest rates as a rate of return, and hope for a positive coefficient, because nominal high interest rates in developing countries usually reflect expected inflation, default risk, and devaluation risk. o Inflation Differential (South African minus foreign) should have a negative effect on the expected rate of return to holding rand, and therefore on the demand for rand, and thence on the value of the rand. Here we use the oneyear lag in the inflation rate to capture the expected future inflation rate. o Real interest differential (nominal interest rate on rand government bonds, minus expected inflation, minus the same for abroad) should have a positive effect on the perceived rate of return to holding rand assets and therefore on the value of the rand. o A country risk premium is included to control for risk of default, or risk of future imposition of capital controls, when looking for a positive coefficient on the real interest differential. The preferred measure of the country risk premium would be the spread between the interest rate at which South Africa borrows when borrowing in dollars (not rand, because we want to separate out currency risk) and a foreign dollar interest rate of the same maturity. We have not been able to find any data on the interest rate at which South Africa borrows in dollars. So instead we use the spread between the corporate rand interest rate and the government rand rate, under the theory that when default risk raises the South African government interest rates, it raises the corporate interest rate proportionately more, so that this spread is a good proxy for country risk. Further Details on data sources and how these variables were computed are given in the appendix. The regression results for the nominal and real exchange rate are given below. The results are highly varied. But the real commodity price index does appear generally to have the hypothesized positive sign, as does real GDP when included. Sometimes the lagged rate of change in the exchange rate shows a positive effect, suggesting a bandwagon phenomenon. The results for the rate of return variables are somewhat more mixed. Perhaps the lack of data on the dollar interest rate for South Africa is the problem. 2

Variable definitions Nominal Bilateral Exchange Rate (NER): the nominal exchange rate expressed in USD per South African Rand. The indexed variable name is NERI, expressed as index with base year 2000. Real Bilateral Exchange Rate Index (RERI): the nominal exchange rate multiplied by the ratio of South African consumer price index to US consumer price index. Commodity Prices: Nominal weighted mineral and metal price index (wmpi): the weighted price index of South African major mineral and metal export commodities. Real weighted mineral and metal price index (RwMPI): wmpi divided by the US CPI. Real multilateral weighted mineral and metal price index (RmwMPI): the wmpi divided by the trade weighted consumer price index of South Africa s major trade partners, with weights similar to that used for weighted foreign GDP. DNERI : One-year lagged rate of change of exchange rate. GDP Ratios: (i) Real GDP ratio between S. Africa and the US (RGDPbrat): used in the model of bilateral real exchange rate (ii) Nominal GDP ratio between S. Africa and the US (NGDPbrat): used in the model of bilateral nominal exchange rate (iii) Real GDP ratio between S. Africa and the trade-weighted real GDP of South African major trading partner countries (RGDPmrat). Rates of return: DEFRSA Default risk premium for S. Africa RGBRDIF Real Government Bond Rate Differential INFLDIF One year lag of inflation rate differential 3

Graphs and Regression Results for Bilateral Nominal Exchange Rates Monthly Results for Nominal Exchange Rate: Dependent Variable: LOG(NERI) Date: 04/18/06 Time: 02:18 Sample(adjusted): 1979:02 2005:11 Included observations: 322 after adjusting endpoints LOG(WMPI) 0.606336 0.051860 11.69167 0.0000 DNERI 0.378630 0.185935 2.036356 0.0426 DEFRSA -0.116796 0.021514-5.428824 0.0000 GBRDIF -0.026257 0.003386-7.754833 0.0000 INFDIFL -0.001347 0.002144-0.628544 0.5301 TREND -0.006844 9.69E-05-70.59374 0.0000 C 3.818298 0.260363 14.66528 0.0000 R-squared 0.976591 Mean dependent var 5.442362 Adjusted R-squared 0.976145 S.D. dependent var 0.736792 S.E. of regression 0.113797 Akaike info criterion -1.487295 Sum squared resid 4.079203 Schwarz criterion -1.405239 Log likelihood 246.4545 F-statistic 2190.243 Durbin-Watson stat 0.096262 Prob(F-statistic) 0.000000 7 6 0.4 0.2 0.0 5 4-0.2-0.4-0.6 80 82 84 86 88 90 92 94 96 98 00 02 04 Residual Actual Fitted 4

Fig Monthly Trends in Log of Nominal Exchange Rate Index vs Log of weighted Mineral Price Index 7.5000 7.0000 6.5000 6.0000 5.5000 5.0000 4.5000 4.0000 3.5000 3.0000 8.0000 7.0000 6.0000 5.0000 4.0000 3.0000 2.0000 1.0000 0.0000-1.0000 Q1 1979 Q4 1979 Q3 1980 Q2 1981 Q1 1982 Q4 1982 Q3 1983 Q2 1984 Q1 1985 Q4 1985 Q3 1986 lnneri lnwmpi Q2 1987 Q1 1988 Q4 1988 Q3 1989 Q2 1990 Q1 1991 Q4 1991 Q3 1992 Q2 1993 Q1 1994 Q4 1994 Q3 1995 Q2 1996 Q1 1997 Q4 1997 Q3 1998 Q2 1999 Q1 2000 Q4 2000 Q3 2001 Q2 2002 Q1 2003 Q4 2003 Q3 2004 Q2 2005 Fig Quarterly Trends in Log of Nominal Exchange Rate Index vs Log of Nominal GDP ratio lnneri lnngdpbrat Q1 1979 Q4 1979 Q3 1980 Q2 1981 Q1 1982 Q4 1982 Q3 1983 Q2 1984 Q1 1985 Q4 1985 Q3 1986 Q2 1987 Q1 1988 Q4 1988 Q3 1989 Q2 1990 Q1 1991 Q4 1991 Q3 1992 Q2 1993 Q1 1994 Q4 1994 Q3 1995 Q2 1996 Q1 1997 Q4 1997 Q3 1998 Q2 1999 Q1 2000 Q4 2000 Q3 2001 Q2 2002 Q1 2003 Q4 2003 Q3 2004 Q2 2005 5

Quarterly Results for Nominal Exchange Rate Dependent Variable: LOG(NERI) Date: 04/16/06 Time: 23:49 Sample(adjusted): 1979:2 2005:3 Included observations: 106 after adjusting endpoints LOG(NGDPBRAT) 0.861547 0.036008 23.92628 0.0000 LOG(WMPI) 0.044897 0.043790 1.025275 0.3077 DNERI 0.024776 0.067547 0.366797 0.7146 GBRDIF -0.014578 0.002046-7.124969 0.0000 DEFRSA 0.055154 0.016742 3.294282 0.0014 TREND -0.018347 0.000186-98.64251 0.0000 C 5.788016 0.203902 28.38623 0.0000 R-squared 0.996852 Mean dependent var 5.439803 Adjusted R-squared 0.996661 S.D. dependent var 0.733701 S.E. of regression 0.042394 Akaike info criterion -3.419840 Sum squared resid 0.177932 Schwarz criterion -3.243953 Log likelihood 188.2515 F-statistic 5225.021 Durbin-Watson stat 0.318659 Prob(F-statistic) 0.000000 Dependent Variable: D(LOG(NERI)) Date: 04/16/06 Time: 23:52 Sample(adjusted): 1979:2 2005:3 Included observations: 106 after adjusting endpoints D(LOG(NGDPBRAT)) 1.002999 0.028649 35.00936 0.0000 D(LOG(WMPI)) -0.148439 0.034610-4.288915 0.0000 D(GBRDIF) -0.001727 0.002228-0.774978 0.4402 D(DEFRSA) 0.006342 0.008965 0.707389 0.4810 C -0.017101 0.001656-10.32881 0.0000 R-squared 0.937979 Mean dependent var -0.019124 Adjusted R-squared 0.935522 S.D. dependent var 0.066405 S.E. of regression 0.016862 Akaike info criterion -5.281511 Sum squared resid 0.028716 Schwarz criterion -5.155877 Log likelihood 284.9201 F-statistic 381.8670 Durbin-Watson stat 1.589170 Prob(F-statistic) 0.000000 6

Bilateral Real Exchange Rates Fig Log RERI vs Log of real mineral commodity price index 6.000 5.000 4.000 3.000 2.000 1.000 0.000-1.000 M1 1979-2.000 6.0000 5.0000 M10 1979 M7 1980 M4 1981 M1 1982 M10 1982 M7 1983 M4 1984 M1 1985 M10 1985 M7 1986 M4 1987 M1 1988 M10 1988 M7 1989 M4 1990 M1 1991 M10 1991 M7 1992 M4 1993 M1 1994 M10 1994 M7 1995 M4 1996 M1 1997 M10 1997 M7 1998 M4 1999 M1 2000 M10 2000 M7 2001 M4 2002 M1 2003 M10 2003 M7 2004 M4 2005 Fig Quarterly Trends in Log of RER index vs Log of Real GDP ratio with respect to the US lnreri lnrwmpi 4.0000 3.0000 2.0000 lnreri lnrgdpbrat 1.0000 0.0000-1.0000 7

Monthly Results for Real Exchange Rate Dependent Variable: LOG(RERI) Date: 04/17/06 Time: 15:10 Sample(adjusted): 1979:02 2005:11 Included observations: 322 after adjusting endpoints LOG(RWMPI) 0.509604 0.062323 8.176862 0.0000 DNERI 0.530224 0.224073 2.366303 0.0186 DEFRSA -0.240114 0.024854-9.660910 0.0000 RGBRDIF 0.002830 0.004315 0.655897 0.5124 INFDIFL 0.003059 0.003842 0.796374 0.4264 TREND 1.37E-05 0.000196 0.070149 0.9441 C 4.699175 0.075214 62.47729 0.0000 R-squared 0.699872 Mean dependent var 4.902766 Adjusted R-squared 0.694155 S.D. dependent var 0.246429 S.E. of regression 0.136283 Akaike info criterion -1.126665 Sum squared resid 5.850523 Schwarz criterion -1.044610 Log likelihood 188.3931 F-statistic 122.4251 Durbin-Watson stat 0.099986 Prob(F-statistic) 0.000000 Dependent Variable: D(LOG(RERI)) Date: 04/17/06 Time: 15:09 Sample(adjusted): 1979:02 2005:11 Included observations: 322 after adjusting endpoints D(LOG(RWMPI)) 0.192155 0.059439 3.232826 0.0014 D(DEFRSA) 0.009538 0.015014 0.635298 0.5257 D(RGBRDIF) -0.016644 0.004006-4.154818 0.0000 D(INFDIFL) -0.013770 0.004836-2.847275 0.0047 C -0.000909 0.001932-0.470722 0.6382 R-squared 0.099950 Mean dependent var -0.001312 Adjusted R-squared 0.088593 S.D. dependent var 0.036282 S.E. of regression 0.034637 Akaike info criterion -3.872374 Sum squared resid 0.380315 Schwarz criterion -3.813763 Log likelihood 628.4523 F-statistic 8.800649 Durbin-Watson stat 1.431675 Prob(F-statistic) 0.000001 8

Quarterly Results for Real Exchange Rate Dependent Variable: LOG(RERI) Date: 04/17/06 Time: 15:02 Sample(adjusted): 1979:2 2005:3 Included observations: 106 after adjusting endpoints LOG(RGDPBRAT) 0.980105 0.069396 14.12341 0.0000 LOG(RWMPI) -0.156130 0.079308-1.968665 0.0518 DEFRSA -0.119557 0.027614-4.329614 0.0000 INFDIFL 0.032524 0.004509 7.213247 0.0000 RGBRDIF 0.033085 0.004872 6.790378 0.0000 DNERI 0.237387 0.123581 1.920904 0.0577 TREND 0.017362 0.001392 12.46858 0.0000 C 2.622720 0.170706 15.36395 0.0000 R-squared 0.910659 Mean dependent var 4.902076 Adjusted R-squared 0.904278 S.D. dependent var 0.245627 S.E. of regression 0.075995 Akaike info criterion -2.243833 Sum squared resid 0.565970 Schwarz criterion -2.042818 Log likelihood 126.9231 F-statistic 142.7031 Durbin-Watson stat 0.287986 Prob(F-statistic) 0.000000 9

Dependent Variable: D(LOG(RERI)) Date: 04/17/06 Time: 15:04 Sample(adjusted): 1979:2 2005:3 Included observations: 106 after adjusting endpoints D(LOG(RGDPBRAT)) 0.976972 0.030181 32.37081 0.0000 D(LOG(RWMPI)) -0.049901 0.038044-1.311665 0.1926 D(DEFRSA) 0.013640 0.009874 1.381453 0.1702 D(INFDIFL) 0.007009 0.002803 2.500662 0.0140 D(RGBRDIF) 0.004116 0.002454 1.676948 0.0967 C 0.016312 0.001893 8.618389 0.0000 R-squared 0.926797 Mean dependent var -0.003883 Adjusted R-squared 0.923137 S.D. dependent var 0.066910 S.E. of regression 0.018550 Akaike info criterion -5.081722 Sum squared resid 0.034411 Schwarz criterion -4.930961 Log likelihood 275.3313 F-statistic 253.2118 Durbin-Watson stat 1.152732 Prob(F-statistic) 0.000000 1.1. Nominal Effective Exchange Rates Fig Monthly Trends in Log of NEER vs Log of weighted mineral commodity price index 7.000 6.000 5.000 4.000 3.000 M1 1979 M10 1979 M7 1980 M4 1981 M1 1982 M10 1982 M7 1983 M4 1984 M1 1985 M10 1985 M7 1986 M4 1987 M1 1988 M10 1988 M7 1989 M4 1990 M1 1991 M10 1991 M7 1992 M4 1993 M1 1994 M10 1994 M7 1995 M4 1996 M1 1997 M10 1997 M7 1998 M4 1999 M1 2000 M10 2000 M7 2001 M4 2002 M1 2003 M10 2003 M7 2004 M4 2005 10 lnneer lnwmpi

Fig Quarterly Trends in Log of NEER vs Log of Nominal GDP ratio with respect to trading partner countries 7.0000 6.0000 5.0000 4.0000 3.0000 lnneer lnngdpmrat 2.0000 1.0000 0.0000 [Regression results for Nominal and Real Effective Rand Exchange Rates Omitted.] [Regression results for Australian and Canadian Dollars Omitted.] 11

Appendix: Data Notes Exchange Rates: Nominal Bilateral Exchange Rate (NER): is the nominal exchange rate of South Africa expressed in USD per South African Rand. In the regression we have used it as an index, with base year 200, as all of the explanatory variables are indices with the same base year. So the indexed variable name is NERI. Real Bilateral Exchange Rate Index (RERI): is the nominal exchange rate multiplied by the ratio of South African consumer price index to US consumer price index, expressed as index with base year 2000. Effective exchange rate indices: Here we have the nominal effective exchange rate index (NEERI) and the real effective exchange rate index (REERI). These data are collected form the International Financial Statistics Database. The note taken from the IFS indicates that: Weights are derived from trade in manufactured goods among industrial countries over the period 1989-91. Weights reflect both relative importance of a country s trading partners in its direct bilateral trade relations and that resulting from competition in third markets. For REER index data are compiled from the NEER index and from a cost of indicators of relative normalized unit labor costs in manufacturing Weighted Mineral and Metal Prices Nominal weighted mineral and metal price index (wmpi): is the weighted price index of South African major mineral and metal export commodities. Weights are derived from the commodity s export share in the value of total exports of South Africa. While efforts are made to include the major commodities as possible, there are some major commodities that are not included because we are not able to find international price index for them, for example diamond. Here are the commodities that are included, with their respective weights: Table: South African Major Export Commodities Commodity Group Actual % share Adjusted % share Gold and platinum 17.54 56.22 Iron ores 2.78 8.90 Coal 5.69 18.23 Petroleum Oil 2.81 9.01 Aluminum 2.38 7.64 Total 31.19 100.00 Source: Compiled from data from South African Trade and Industry Department Real weighted mineral and metal price index (RwMPI): This is the wmpi divided by the consumer price index of the US. Real multilateral weighted mineral and metal price index (RmwMPI): This is the wmpi divided by the trade weighted consumer price index of South Africa s major trade partners, with weights similar to that used for weighted foreign GDP. Interest Rates: The different rates used in the regression are defined as follows 12

Variable name Definition A CBRSA 20 years Corporate Bond Rate of S. Africa B GBRSA 20 years Government Bond Rate of S. Africa C GBRUSA 20 years Government Bond Rate of USA D INFSAL One year lag of inflation of S. Africa E INFUSL One year lag of inflation of USA F=A-B DEFRSA Default risk of S. Africa G=B-D RGBRSA Real Government Bond Rate of S. Africa H=C-E RGBRUSA Real Government Bond Rate of USA I=G-H RGBRDIF Real Government Bond Rate Differential J=D-E INFDIFL One year lag of inflation rate differential K=B-C GBRDIF Nominal government bond rate differential GDP Ratios: Real and nominal GDPs are collected for South Africa and its trading partner countries. All figures are converted in to Dollar units. After that we calculated: (iv) Real GDP ratio between S. Africa and the US (RGDPbrat): used in the model of bilateral real exchange rate (v) Nominal GDP ratio between S. Africa and the US (NGDPbrat): used in the model of bilateral nominal exchange rate (vi) Real GDP ratio between S. Africa and the weighted real GDP of South African major trading partner countries (RGDPmrat): Average trade weights for the years 2002-05 (selected based on availability of data) are used. Based on a 2% cutoff 11 countries which cover about 57.5% of South African total trade were initially selected. But of the countries; China (4.6%), Saudi Arabia (2.9%), and Belgium (2%) are dropped because they don t have quarterly GDP data that covers our sample period. The remaining countries which cover 48% of South African total trade are included. Table: South African Major Trade Partners Country Average Share (2002-2005) Adjusted Share GERMANY 10.66900 0.22263 UNITED STATES 9.27153 0.19347 UNITED KINGDOM 8.39672 0.17521 JAPAN 7.92043 0.16528 FRANCE 3.55127 0.07410 NETHERLANDS 2.92757 0.06109 ITALY 2.85566 0.05959 AUSTRALIA 2.33022 0.04862 TOTAL 47.92240 1.00000 Source: Compiled from data from South African Trade and Industry Department (vii) Nominal GDP ratio between S. Africa and the weighted nominal GDP of South African major trading partner countries (NGDPmrat): The same methodology used as the real one. This one is used for the nominal effective exchange rate model. 13