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Real interest rate persistence in South Africa: evidence and implications

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Abstract

The real interest rate is a very important variable in the transmission of monetary policy. It features in vast majority of financial and macroeconomic models. Though the theoretical importance of the real interest rate has generated a sizable literature that examines its long-run properties, surprisingly, there does not exist any study that delves into this issue for South Africa. Given this, using quarterly data (1960:Q2-2010:Q4) for South Africa, our paper endeavors to analyze the long-run properties of the ex post real rate by using tests of unit root, cointegration, fractional integration and structural breaks. In addition, we also analyze whether monetary shocks contribute to fluctuations in the real interest rate based on test of structural breaks of the rate of inflation, as well as, Bayesian change point analysis. Based on the tests conducted, we conclude that the South African EPPR can be best viewed as a very persistent but ultimately mean-reverting process. Also, the persistence in the real interest rate can be tentatively considered as a monetary phenomenon.

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Notes

  1. See Neely and Rapach (2008) for a detailed literature review.

  2. Studies that exists for South Africa only deals with the uncovered interest rate parity condition, or in other words, the interest rate behavior of South Africa relative to other developed or emerging economies. See for example Kahn and Farrell (2002), Kryshko (2006), Lacerda et al. (2010) and de Bruyn et al. (2011).

  3. In February of 2000, the Minister of Finance announced that inflation targeting would be the sole objective of the South African Reserve Bank. Currently, the Reserve Bank’s main monetary policy objective is to maintain CPI inflation between a target-band of 3–6 %, using discretionary changes in the repo rate as its main policy instrument.

  4. See Erdman and Emerson (2007) for a detailed literature review in this regard.

  5. See Sect. 3 for further details.

  6. The steady state real interest rate could also be affected by changes in distortionary tax rates (See Blanchard and Fischer 1989, pp. 56–59).

  7. Although much of the empirical literature analyzes EPRR in this manner, the time-series properties of EPRR can differ from those of the EARR, mainly because of two reasons: First, at short-horizons, the behavior of EPRR could differ from that of the EARR, and; second, some estimation techniques can generate different persistence properties between the EARR and EPRR. The reader is referred to Neely and Rapach (2008) for further details.

  8. This can be found in Neely and Rapach (2008).

  9. The annual population figures are interpolated to quarterly values.

  10. Specifically as far as the data is concerned, the 3-month Treasury constant maturity rate monthly data are converted to quarterly frequency by averaging over the three months comprising a quarter. The annualized CPI inflation rate is based on the seasonally adjusted (at an annual rate) CPI with the base year of 2005. Ex post real interest rate is defined as the three-month Treasury bill rate minus the realized inflation rate in the subsequent quarter. Finally, the annualized consumption growth rate is based on real personal consumption expenditures (base year of 2005) adjusted seasonally at an annual rate. Annualized inflation and consumption growth rates are computed by taking 400 times the first differences of the natural logs of the CPI deflator and consumption.

  11. Given this, we also conducted the Phillips and Perron (1988) [PP], Elliot et al. (1996) [ERS] point-optimal test and the Kwiatkowski et al. (1992) [KPSS] unit root tests on the treasury bill rate. The PP test could not reject the null of unit root even at the 10 % level, while the KPSS test rejected the null of stationarity at 1 % level of significance. However, the ERS point-optimal test rejected the null of unit root even at 1 % level. In addition, we also tested the EPRR based on the PP, ERS point-optimal test and KPSS test. The null of unit root was rejected even at 1 % based on the PP test, while the null of stationarity could not be rejected at 5 % based on the KPSS, but the ERS could not reject the null of unit root at even 10 %. Further, nonlinear unit root test proposed by Kapetanios et al. (2003) [KSS] and the Bayesian unit root test developed by Sims (1988) was also used. Both the KSS and the Bayesian tests rejected the null of unit root. These results are available upon request from the authors.

  12. Following Gregory and Hansen (1996), we also tested for cointegration using residual based tests that allows for regime shifts, but the null of no cointegration could not be rejected even at 10 % level of significance. Similar conclusions were also reached based on both the Bierens (1997) and Breitung (2002) nonparametric cointegration tests, as these tests too failed to reject the null of no cointegration. Note that both these tests allow for nonlinearity of an unknown form in the short-run dynamics of the the two variables. Interestingly, even though no cointegration could be detected, estimates of θ 1 based on the dynamic ordinary least squares (DOLS) or the Johansen (1991) methods are not significantly different from unity. However, this result, perhaps, explains as to why we detect stationarity for the EPRR based on the unit root tests with a prespecified cointegrating vector of (1, −1)\(^{\prime}\). Further, using the nonparametric nonlinear co-trending analysis developed by Bierens (2000), the null hypothesis that there exists one co-trending vector between the nominal Treasury bill and the inflation rate could not be rejected. These results are available upon request from the authors.

  13. Until recently, researchers used models of cointegration that assumed both the cointegrating relationship and short-run dynamics to be linear. But now studies have started to relax these linearity assumptions based on nonlinear cointegration or threshold dynamics, which in turn, allow the cointegrating relationship and mean reversion to be contingent on the current values of the variables. Given this, when we tested for nonlinear cointegration between the 3-month Treasury bill rate and the the inflation rate based on the test proposed by Li and Lee (2010), the null of no cointegration could not be rejected even at the 10 % level of significance. This result is available upon request from the authors. It must be pointed out that, although evidence of threshold behavior could be interesting, these models do not obviate the persistence in the EPRR, since there are still regimes where the real interest rate behaves like an unit root process.

  14. Similar results were obtained for the fractional integration parameter of EPRR using the Geweke and Porter-Hudak (1983) and the Robinson (1992) methods, though the latter estimation strategy produced a relatively lower value of d. In addition, when we used the modified R/S statistic developed by Lo (1991), we confirmed the EPRR to be a long-memory process. These results are available upon request from the authors.

  15. This short-memory behavior of the per capita consumption growth rate was also confirmed by the Geweke and Porter-Hudak (1983) and the Robinson (1992) estimation of d, as well as by the modified R/S statistic which failed to reject the null hypothesis of the per capita consumption growth being a short-memory process. These results are available upon request from the authors.

  16. Note that in Table 3, we see that F(2|1) is rejected meaning that we reject 1 break in favor of 2 breaks. Also, F(3|2) is not significant, implying that we cannot reject 2 breaks in favor of 3 breaks. These results suggest 2 breaks. However, the 10 % confidence interval around the endpoint of the first break, identified at 1974:1, so was so wide that it included the starting point of the sample. In light of this, we decided to choose one break rather than 2 for the EPRR. Further, if we allowed for two breaks, suggesting three regimes, the estimate of the mean EPRR (0.89) under the first regime was insignificant with a t-statistic of 1.42. The details of these results are available upon request from the authors.

  17. In contrast to this evidence of a unique break in the EPRR, the Bai and Perron (1998) methodology obtained no structural break in the mean of per capita consumption growth. These results are available upon request from the authors.

  18. Note that, when we conducted the Zivot and Andrews (1992) unit root test allowing for a break in the intercept, it rejected the null of unit root at the 10 % level of significance for the EPRR. This test identified a break for the series at 1987:Q4. In addition, the Lee and Strazicich (2003) unit root test allowing for 2 breaks, also rejected the null hypothesis of unit root test, with the breaks identified in 1972:Q3 and 1999:Q3.

  19. Refer to Ludi and Ground (2006) for a detail discussion of the history of monetary policy in South Africa.

  20. Using a measure of monetary policy surprise developed by Reid (2009) and Gupta and Reid (forthcoming), we analyzed the impulse response function of the EPRR obtained from an autoregressive distributed lag (ARDL) model following a contractionary monetary policy shock over the period of 2002:Q2-2010:Q4. The results, based on Romer and Romer’s (2004) Monte Carlo methods to generate confidence bands for the impulse response functions, indicated a delayed very short-lived (1 quarter) positive effect on the EPRR, suggesting again a weak monetary explanation of the persistence of the real rate—a result in line with the findings of Amusa et al. (forthcoming). The impulse response functions from the ARDL model is available upon request from the authors. Note, Reid (2009) and Gupta and Reid (forthcoming) used the change in the 3-months Banker’s Acceptance rate on the day after the monetary policy committee makes its statement as a proxy for the surprise component of monetary policy. This event-based data was converted to a quarterly frequency by averaging the shocks over a three month period.

  21. We used the bcp package in R, developed by Erdman and Emerson (2007), to implement the algorithm of Barry and Hartigan (1993).

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Authors and Affiliations

  1. Logistics and Quantitative Methods, CSIR Built Environment, P.O. Box: 395, Pretoria, 0001, South Africa

    Sonali Das

  2. Department of Economics, University of Pretoria, Pretoria, 0002, South Africa

    Rangan Gupta, Patrick T. Kanda, Christian K. Tipoy & Mulatu F. Zerihun

  3. Department of Economics, University of Stellenbosch, Private Bag X1, Matieland, 7602, South Africa

    Monique Reid

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  1. Sonali Das
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Das, S., Gupta, R., Kanda, P.T. et al. Real interest rate persistence in South Africa: evidence and implications. Econ Change Restruct 47, 41–62 (2014). https://doi.org/10.1007/s10644-012-9132-5

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