Unless otherwise indicated, the data series are from the South African Reserve Bank (SARB), Quarterly Bulletin.
p: Underlying consumer price index. This index was provided by the SARB for 1975-98, and equals headline consumer price index excluding “food and non-alcoholic beverages,” “home owner’s cost” and “value-added tax.” For 1970-75, the series was defined as the headline consumer price index net of food prices.
nc: Notes and coins outside the banking system.
m3: nc plus checking deposits, and short-, medium-, and long-term deposits.
i-short: Interest rate on three-month T-bills. Source: International Financial Statistics (IFS), IMF.
i-long: Interest rate on ten-year government bonds. Source: IFS, IMF.
e: Nominal effective exchange rate including (weights in brackets) U.S. dollar (51.7), pound sterling (20.2), deutsche mark (17.2), and Japanese yen (10.9).
q: Effective consumer price index in foreign countries, including the same four countries and weights as when calculating e. Source: IFS, IMF.
y: Gross domestic product, 1990 prices, seasonally adjusted.
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Gunnar Jonsson is a Senior Economist at the International Monetary Fund. He wishes to thank Trevor Alleyne, Torbjorn Becker, David Coe, Neil Ericsson, Jose Fajgenbaum, Zenon Kontolemis, Michael Nowak, Jean-Claude Nachega, Eric Schalling, Arvind Subramanian, Yougesh Khatri, Krishna Srinivasan, Carl Walsh, Tarik Yousef, and seminar participants at IMF’s African Department and the University of Cape Town for discussions and comments. The usual disclaimer applies.
It should be noted that South Africa remained a fairly open economy during the 1970s and 1980s, notwithstanding long periods of international trade and financial sanctions. For example, the sum of merchandise exports and imports remained at about 35 percent of GDP during the sanctions period 1985-95, although the financial sanctions forced South Africa to shift from running external current account deficits in the early 1980s to current account surpluses from 1985 to the early 1990s; see, for example, Jonsson and Subramanian (2000) and Lipton (1998) for discussions.
From a policy perspective, it would be important to also examine how several other variables—such as wages, fiscal variables, and capacity utilization—are related to inflation developments in South Africa. This is, however, beyond the scope of the current paper.
Johansen and Juselius (1990), Hendry and Ericsson (1991), and Ericsson (1998) are examples of useful studies that discuss a range of econometric and time-series issues that arises in studies of money demand. MacDonald (1995), Rogoff (1996), and Habermeier and Mesquita (1999) are examples of studies that survey the PPP literature and provide some new results using cointegration methods.
Hurn and Muscatelli (1992) point out that a number of the earlier empirical studies on money demand in South Africa did not estimate the long-run elasticites in an econometrically satisfactory way.
A variant of the simplest PPP hypothesis suggests that expression (1) should only hold for tradeable goods, while prices for nontradables in part depends on relative productivity levels. The current study does not make a distinction between prices of tradables and nontradables.
More precisely, economic theory suggests that demand for money depends on the opportunity cost of holding money. Although the opportunity cost for holding cash is larger when the nominal interest rate is higher, it is ambiguous whether broader definitions of money are positively or negatively related to the nominal interest rate, as broad money typically is interest bearing. See the first part of Section II for further discussion.
Visual inspection suggests that a time trend arguably should be included in the first difference test for q. Allowing for such a trend also indicates that this series is integrated of order 1. Moreover, the foreign price series adjusted for the effective exchange rate is clearly integrated of order 1.
Foreign prices could arguably be treated as an exogenous variable. Indeed, as shown below, the empirical results reveal that foreign prices do not respond to deviations from the estimated long-run relationships.
The number of cointegrating vectors was estimated using both the maximum eigenvalue statistic and the trace statistic (allowing for unrestricted intercepts but no trends), with the significance level set to 5 percent.
A time dummy for the period 1994:1-1998:2 and seasonal dummies were included in the model as well. The time dummy was included without restricting it to the cointegrating vector, implying that the average growth rates of the variables can change at the time of the structural change, while the cointegrating vectors remain unchanged.
By not constraining the coefficients on q and e, the test allows for various fixed costs, such as transportation and menu costs, to vary over time and across countries. The interpretation of this test is simply that the series p, e, and q do not drift too far away from each other. A stricter test of PPP imposes the homogeneity and symmetry restrictions that the coefficients on both q and e equal 1 (in absolute values), see MacDonald (1995).
The reported parameters in Table 2 are estimated under the assumption of two cointegrating vectors, with exclusion restrictions placed on the β-matrix as discussed in the previous section.
The short-term interest rate refers to the three-month T-bill rate. Although a preferable measure of the own rate of return would be the actual bank deposit rate, such a series exists only since 1978. Nevertheless, the T-bill rate seems to be a good proxy for the own rate of return, as it is highly correlated with the deposit rate; indeed, the correlation coefficient between the two interest rate series is 0.95 for the period 1978-98.
In fact, Podivinsky (1998) shows that it is preferable to overspecify the number of variables in the model and later add exclusion restrictions, rather than underspecifying the model, as the latter has low power in detecting the true number of cointegrating vectors.
The restricted cointegrated vectors in Figure 2 are given by the fourth specification in the lower part of Table 4, that is, CVPPP = [p + 0.88*e - 1.28*prow] and CVmd = [p - m3 + 1.22*y - 0.04*i-long + 0.02*ishort].
The recursive estimations occasionally failed to converge due to the sharp reductions in the number of observations. Hence, these estimations were done under the assumption of two (rather than three) cointegrating relationships, and without constraining the coefficient on m3 to - 1. Nevertheless, the estimated coefficient on m3 was always relatively close to - 1; the fact that it was not constrained to this value implies that the recursively estimated coefficient on y is a somewhat (upward) biased estimate of the income elasticity.
As discussed in the first section, the coefficients in the α-matrix capture the speed of adjustment of a particular variable to a deviation from the long-run equilibria; thus, a zero restriction on any coefficient in this matrix correspond to the null hypothesis that the particular variable does not adjust to restore the long-run equilibrium, and therefore can be treated as weakly exogenous.
As a comparison, MacDonald (1995) finds that the average speed of the nominal exchange rate adjustment following a deviation from PPP is about 2 percent per month for a set of bilateral U.S. dollar exchange rates, implying a half-life of a shock to PPP of about 36 months.
The main monetary policy instrument in South Africa is the overnight interest rate rather than i-short (the T-bill rate). In practice, however, the T-bill rate closely tracks fluctuations in the overnight rate (the correlation coefficient between the two interest rate series is 0.99 between 1970-98), and could therefore be regarded as controlled by the Reserve Bank.
The practical significance of the ordering is that a shock to a variable is allowed to have contemporaneous effects only on the variable itself and the succeeding variables in the ordering. Thus, the assumed ordering implies that a shock to, for example, real output may have a contemporaneous effect on the nominal variables m3, p, e, and i, while a shock to any of these nominal variables can only affect real output with (at least) a one quarter lag. In the current study, the reported results are quite robust to alternative orderings of the variables.