66 SAJEMS NS Vol 4 (2001) No 1
An Empirical Capital Market Rate Function for
South Africa
Elna Pretorius and Charlotte du Toit
Department of Economics. University of Pretoria
ABSTRACT
The aim of this paper is to explain the detenninants of the South African long-
tenn interest rate. A market-related approach is followed which explains interest
rate detennination on the basis of the relationships between the capital maricet
and other domestic and international markets. Some implications for monetary
policy are derived.
JEL G 12
1 INTRODUCTION
Interest rates are the key detenninants in the flow of funds from the financial
sector to particular real investments in the real sector of the economy. If the
markets operate efficiently, funds flow to the most economically attractive real
investment opportunities, where attractiveness is detennined by the interest rate
offered and the probability of being repaid. In practice, money flows in large
amounts from lenders to different borrowers on the basis of fairly small changes
in interest rates. Relatively small changes in interest rates can therefore cause
huge flows of money from one sector to another. These flows, in tum, can be a
major detenninant of the amount of real economic activity that takes place and
in what sectors growth occurs. Even a percentage point increase can have a huge
impact on the present discounted value of future revenues, and thus on
investment decisions, output and jobs (Smith & Spudeck, 1993: 14). Interest
rates are therefore a vital part of the economy, and knowledge of the role of
interest rates and the reasons underlying their movements is crucial to an
understanding of financial developments and economic po Hcy.
Monetary authorities are particularly interested in the detennination of the long-
tenn interest rate and wish to understand to what extent they can influence it. In
South Africa the Reserve Bank plays a vital role in detennining the level of
short-term interest rates since these are closely related to the repo rate, which is
the interest rate at which the Reserve Bank lends money to commercial banks.
However, monetary authorities do not know .whether, and to what extent, they
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SAJEMS NS Vol 4 (2001) No 1 67
can influence the long-tenn interest rate. The aim of this paper is to determine
the factors underlying changes in the long-term interest rates in South Africa,
with specific reference to the implications for monetary policy.
Apart from analysing the univariate characteristics of the data and empirically
estimating the factors that influence the interest rate and the magnitudes of these
influences, the estimated function is subjected to rigorous diagnostic and
stability testing. The estimated function can be used to forecast the long-run
level of South African interest rates, and will form the linkage between the real
and fmancial sectors in the macroeconometric model of the Department of
Economics, University of Pretoria.
2 THE SOCIO-POLITICAL ENVIRONMENT IN SOUTH AFRICA
The course of South African interest rates could be influenced by the different
phases of monetary policy and the dramatic socio-political changes in the
country. Since the empirical function will be estimated for the period 1960 to
1998, the discussion will also be confined to this period.
During the 1960s, the South African Reserve Bank attempted to slow down an
excessive expansion of liquidity in the banking sector by introducing a required
liquid asset ratio in the Banks Act of 1965. After the promulgation of the Banks
Act, there were years of brisk economic activity, increasing inflationary
pressures and a rapidly expanding liquidity base of the banking system. During
his tenure, Dr De Jongb (Reserve Bank Governor from 1967 to 1980)
implemented a series of additional direct controls such as a ceiling on advances,
deposit rate controls, exchange control, import deposits and some direct
consumer credit controls in an effort to contain the persistent increases in money
supply and the inflationary tendency. The results were encouraging, and the
country enjoyed higb levels of real growth.
The controls of the 1960s and 1970s gave way in the 1980s to a general
recognition of the need to abolish as many restrictions as possible in a shift to
market-oriented policy. This was in line with the international thinking of the
time. During the 1980s, there was a definite shift across the globe in favour of
market-oriented policy measures. This shift in policy was further encouraged by
the liberalisation of international financial markets. South Africa likewise
followed this pattern, and under Dr De Kock (Reserve Bank Governor from
1981 to 1989), the Reserve Bank became more willing to align its policies to
market developments, rather than to try to force markets in a certain direction.
This was the most difficult decade in the history of the Reserve Bank, operating
as it did in the face of widespread international hostility and growing resistance
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68 SAJEMS NS Vol 4 (2001) No 1
to the consequences of the economic and racial policies of the government at the
time. After President PW Botha's so-called Rubicon speech, international
sanctions and a debt boycott were introduced against South Africa. and huge
amounts of capital flowed out of the country almost immediately. This period of
international isolation was characterised by high interest rates that attempted to
prevent capital outflow and attract foreign capital. (Botha, 1997; Fourie et al.,
1999: 314).
Although monetary policy did not change much in the 1990s - the Stals era
some most dramatic changes in the socio--political situation occurred during this
period. After the first democratic election in 1994, political barriers were
removed and South Africa became more exposed to world financial market
movements, as a result of the abolition of sanctions and the scrapping of
exchange controls on foreigners. Since 1994 in particular, South Africa has
adopted a clearly defined policy of actively participating in the process of
fmancial globalisation and implemented a number of economic policies to
facilitate its participation in globalisation (Stals, 1999).
Financial globalisation caused revolutionary and irreversible changes in capital
markets. International capital transactions have accelerated and international
financial interdependence increased substantially. Innovation and deregulation
have changed financial market structures. More instruments and markets have
developed, and technological change has made portfolios comprising
international assets universal. As a consequence of these transformations,
financial markets have become more efficient, but also more volatile and subject
to speculation. Some countries benefit greatly from the opportunity to attract
unprecedented inflows of capital. However, international markets tend to shun
countries that are not performing well. It is therefore not surprising that sub-
Saharan Africa. the region with the world's poorest growth record, is now a net
exporter of capital. Furthermore, capital flight is increasingly prevalent in
countries that are perceived not to provide competitive investment
opportunities. The international environment has simply become much more
averse to countries that do not foster competitive economies (Handley & Mills,
1996: 74).
In broad, monetary policy in South Africa since the 1960s can thus be divided
into the pre-1985 and post-1985 periods, with a shift from the use of direct
monetary instruments to more market-oriented monetary policy. This dramatic
policy shift implies that monetary variables such as interest rates will contain a
structural break, which should be reflected in the empirical estimation of such a
variable. The most significant socio-political events that impacted on the course
of South African interest rates, international sanctions and the process of
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SAJEMS NS Vol 4 (2001) No I 69
financial globalisation, also have to be reflected in the empirical estimation of
interest rates.
3 THE SOUTH AFRICAN CAPITAL MARKET
The capital market constitutes the long-term component of the financial system,
and can be regarded as the complex structure of institutions and mechanisms
involved in the trade of long-term securities (with maturity longer than one year)
(Fourie, Falkena & Kok, 1999: 183). It is not a physical market, but only the
abstract concept that includes all trade in long-term securities in the same way
that the money market includes all trade in short-term securities (Stapelberg,
1981: 23). The capital market can be broadly divided into two parts, namely the
primary and the secondary market New securities are issued in the primary
market, while previously issued securities are traded in the secondary market
3.1 The primary capital market
Securities are issued in the primary market by institutions wishing to borrow
money. Securities are issued in South Africa by the Treasury, public
corporations (e.g. Eskom), public utilities (e.g. Telkom and Transnet), local
authorities and private sector companies when they need to finance their
activities. The demand for the securities issued in the primary capital market is
generally by banks, building societies, insurance companies, pension funds,
mining houses, stockbrokers, and the Public Investment Commissioners (Fourie
eta!., 1992: 121).
The securities issued in the primary market can be either fixed- or variable-
interest-bearing securities. Fixed-interest-bearing securities such as government
bonds, annuities and debentures are characterised by a stipulated maturity date
and value (the nominal or face value) and contractually guaranteed interest
payments. These interest payments are based on a fixed and predetermined rate
(the coupon rate) paid on the nominal value of the bond (Fourie et aI., 1999:
172). If the security is issued at nominal value, its yield will be equal to this rate
of interest, since the interest payment will be the only income received from this
investment. However, if the security is issued at a price below the nominal
value, the yield to maturity will be higher than this rate of interest since the yield
will not only include the interest receipts but also a capital gain. The interest
rates on variable-interest securities (e.g. long-term loans), shares and negotiable
documents fluctuate sharply, particularly when the inflation rate changes
frequently. In South Africa, a variable-interest loan normally remains a contract
solely between the lender and the borrower.
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70 SAJEMS NS Vol 4 (200 I) No I
The way in which secuntIes are issued depends on the type of security.
Government bonds are sold on a tap or tender basis. In the case of a tap issue,
the Reserve Bank buys stock from the Treasury at a rate at which the Bank can
sell a fairly large volume to the market, and then resell it to the public. In the
case of a tender issue, the date of the issue and amount of stock available are
announced to the public, and sold to the highest bidders. Other fixed-interest
securities as well as all variable-interest securities are either sold by the issuer or
by an underwriter, usually a merchant bank, acting on behalf of the issuer. The
issue may either be by way of a public issue where the terms and conditions are
announced to the public at large, or by way of a private issue where it is offered
only to selected investors (Fourie et al., 1999: 185; Fabozzi, 1992: 523).
3.2 The secondary capital market
The securities issued in the primary market are traded in the secondary market.
The financial intermediary sector is the principal supplier of funds to the
secondary capital market, in particular insurers, pension funds and building
societies, which simply channel surplus funds of the household sector into
appropriate invesnnents. Other banking institutions, the Public Invesnnent
Commissioners, and other financial intermediaries such as participation
mortgage bond schemes and the National Housing Commission are also lenders
in the capital market (Fourie et al., 1992: 41). The main traders of securities in
the secondary capital market are divided into five categories, namely fmancial
intermediaries, the government, corporate business enterprises, households and
the foreign sector. Foreign participants, in other words foreign households,
businesses, institutional investors and governments, act in the South African
capital market in the same way as domestic households, businesses, investors
and the government. However, technological development and the process of
globalisation have dramatically increased the importance and role of foreign
participants in the domestic capital and other fmancial markets. Globalisation
bas resulted in the acceleration of international capital transactions, and
international fmancial interdependence has increased substantially. In
consequence, fmancial markets have become more efficient, but also more
volatile and subject to speculation practices. Advances in computer technology,
coupled with advanced telecommunication systems, link market participants
throughout the world and allow the transmission of real-time information on
security prices and other key information to many participants in many places.
This enables many investors to monitor global markets and simultaneously
assess how this information will impact on the risk/reward profile of their
portfolios (Fabozzi, 1995: IS).
The securities that are issued in the primary market are traded in the secondary
market. The number of new securities issued in the primary market bas a
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SAJEMS NS Vol 4 (2001) No I 71
considerable influence on the demand for and price of securities in the
secondary market. The secondary market serves as a barometer of changes in the
markets and reflects these changes in the prices and volumes of traded
securities. This gives the issuers in the primary market a good idea of the correct
price and interest rate at which they should issue new securities which is vital to
a successful issue. The secondary market also guarantees investors that they will
be able to resell their securities and adjust their portfolios, provides an indication
of the general availability of funds and enables the Reserve Bank to buy and sell
securities in order to influence the liquidity of financial markets (Fourie,
1999:13; Faure et al .• 1991: 10).
There are active markets in many of the securities issued in the primary market,
but they differ in terms of so-called "breadth" and "depth". Mainly fixed-
interest-bearing securities are traded in the secondary market, while there is
virtually no secondary market for variable-interest securities because of the
uncertainty of their variable pattern of income which makes it difficult to
discount their future earnings. Institutions trade in the secondary market in the
attempt to maximise their expected portfolio returns while bearing minimum
risk. Investment is therefore a risk-return trade-off.
The nominal rate of return (R) on a security is not the absolute rand return, but is
R sl - So + d d . f th . calculated as = , where So an s} are the pnce 0 e secunty at
So
the beginning and the end of the investment and d, any dividends or interest
payments in the interim (Kobold, 1986: 67). Since the rate of return is uncertain,
the investor has to take into account the risk that the expected return may not be
realised. Risk is the variation of actual return from expected return and may be
caused by broad economic forces such as recession, unemployment and
inflation, or attributable to causes that are peculiar to the specific security or
issuing company. There are several risks associated with investing in bonds.
Interest-rate risk is the risk that if an investor has to sell a bond prior to the
maturity date, an increase in interest rates will mean a capital loss (F abozzi &
Modigliani, 1996: 5). Reinvestment risk is the variability in the reinvestment
rate of a given strategy because of changes in market interest rates (Fabozzi &
Modigliani, 1996: 5). Default or credit risk is the risk that the issuer of a bond
may default, in other words be unable to make timely principal and interest
payments on the issue. Inflation or purchasing power risk arises as a result of the
variation in the value of cash flows from a security because of inflation, as
measured in terms of purchasing power of money (Fabozzi & Modigliani, 1996:
7). The risk that the currency in which the flows are paid will depreciate relative
to the rand, is the exchange rate or currency risk (Fabozzi & Modigliani, 1996:
7). Liquidity or marketability risk depends on the ease with which an issue can
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72 SAJEMS NS Vol 4 (2001) No 1
be sold at or near its value, usually measured by the size of the spread between
the bid price and the ask price quoted by a dealer (Fabozzi & Modigliani, 1996:
7).
Risk and return are always the criteria for investment, but investors can choose
between the efficient market hypothesis (EMH), Markowitz's portfolio choice
theory and the capital asset pricing model (CAPM) (Dobbins, Witt & Fielding,
1994: 18). Security prices conform to the law of demand and the law of supply
like any other price. Since the demand and supply of a security are determined
by the behaviour of investors, their behaviour will also influence security prices
and therefore interest rates.
4 AN EMPIRICAL FUNCTIONIMODEL FOR THE LONG-TERM
INTEREST RATE
In this section the determinants of the long-term interest rate are empirically
estimated by means of annual data. Although the yield on the R150 long-term
government bond is the leading long-term interest rate in South Africa, it was
issued in 1987 and expires in 2004, which means that only a minute sample of
12 observations is currently available. The Rl50 yield is also extremely volatile,
which makes empirical estimation rather difficult Hence in this study the yield
on the Eskom 168 (EI68) security is used instead to proxy the general level of
long-run interest rates in South Africa (see Figure I).
The E 168 is a security issued by Eskom. It has biannual interest payments fixed
at II per cent on the nominal value. and it matures on I June 2008. Unlike the
RI50 and other government bonds, the government does not guarantee Eskorn
securities. The guarantee of Eskorn securities lies in the size of Eskom. the fifth
largest utility in the world, and the nature of its business, namely the provision
of electricity to Southern Africa (http://www.eskom.co.za). Hence Eskom
securities, like government bonds, are not subject to default risk. Since the EI68
long-term Eskom security has no default risk, is actively traded in the South· .
African capital market and a relatively large sample is available, it may be used
to proxy long-term interest rates in South Africa.
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SAJEMS NS Vol 4 (2001) No I 73
Figure 1 The Eskom rate
20
18
16
14
12
10
8
6
4
60 65 70 75 80 85 90 95
4.1 The theoretical model
The process of globalisation dramatically changed the way in which small open
economies, such as South Africa, function. They no longer function in an
isolated environment, for their financial markets are driven by developments in
international markets. The market approach (see Gayed 1990 and Murphy 1991)
is therefore regarded as the most appropriate analytical method in a small open
economy where the interaction between the various domestic and international
markets predominantly determines interest rates. Studies on interest rate
determination in small open economies, such as Harmse and Du Toit (1999) and
Hodgson, Kremmer and Lee (1998), are therefore based on the market approach,
which explains interest rate determination on the basis of the relationship
between the various domestic and international markets. On the other hand,
interest rates in large economies are mainly determined by the traditional
demand and supply factors. Studies such as Tran and Sawbney (1998), Mehra
(1995) and Mehra (1994) on interest rate determination in industrialised
countries are thus based on the economic approach which explains interest rate
determination by the demand and supply of money or loanable funds. This study
will however follow the market approach, since South Africa has a small open
economy where interest rates are determined by movements in international and
domestic markets.
A priori theory suggests the following about the relevant variables and their
coefficients:
(i) The long-term interest rate should be positively related to international
interest rates. As the South African fmancial markets become more
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74 SAJEMS NS Vol 4 (2001) No I
integrated with the international fmancial system, the relationship
between domestic and international interest rates becomes increasingly
important. Domestic interest rates that are too low will eventually be
reflected in a weak currency, and also cause further depreciation of the
rand. Conversely, interest rates that are too high will encourage
speculative short-term foreign capital that will cause undesirable
appreciation of the currency and/or an unhealthy expansion of domestic
liquidity (SARB, 1999). Various studies such as that of Pain and Thomas
(1997), Hodgson, Kremmer and Lee (1998) and Awad and Goodwin, have
shown that the US long-bond rate is the most influential in the world and
can be regarded as the leading rate. It is also used in most studies of small
open economies such as Harmse and Du Toit (1999) and Hodgson,
Kremmer and Lee (1998) to represent the international level of interest
rates. Hence in this study, the US long-bond rate is also used to represent
the level of international interest rates.
(n) The short-term interest rates are determined in the money market. If the
long-term interest rate does not rise when the short-term interest rates rise,
investors will substitute their long-term bonds for money market
securities. An increase in the short-term rate should therefore cause an
increase in the long-term rate.
(iii) According to the Fisher effect, the rate of inflation causes the nominal
interest rate to change so that the real rate is unaffected by the rate of
inflation. An increase in expected inflation should therefore result in a
proportional increase in the nominal interest rate.
This results in the following specification for the interest rate function (See
Appendix 2 for an explanation of the pneumonic variables):
RL = £{US, E(INFL), RS)
(+ + +)
4.2 Thedata
All the data were obtained from the Quarterly Bulletin of the South African
Reserve Bank, except the US interest rate which was obtained from the
International Financial Statistics of the International Monetary Fund. All the
variables were transformed into the naturallogaritbmic form. Annual data from
1960 to 1998 were used.
The yield on the E 168 Eskom bond was used as the representative long-term
interest rate in South Africa. The three-month banker's acceptance rate is
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SAJEMS NS Vol 4 (200 I) No 1 75
considered to be the representative short-tenn interest rate and the yield on 30-
year US government bonds is used as the long-tenn interest rate of the USA.
Kalman filter predictions of the expected one-period-ahead inflation rate were
used as inflationary expectations. The specification, including the lagged
inflation rate, interest rate and exchange rate, was based on the specification of
Koekemoer (2000) for Kalman filter predictions of the expected one-period-
ahead price expectations. In the specification the rand-dollar exchange rate was
used as the exchange rate, and the Eskom rate as the interest rate. A dummy
variable was created to represent the years 1985 to 1990 during which there
were international sanctions and disinvestment actions against South Afiica.
During this period, interest rates were kept at a high level in an attempt to
prevent capital outflow and to attract foreign capital.
Models that contain potentially non-stationary variables can result in a spurious
regression, indicating statistically significant relationships where there are none.
The statistical significance obtained from standard regression techniques with
non-stationary variables is picking up is the existence of contemporaneous
correlation in the variables due to their trending over time, rather than a
meaningful causal relationship between them. It is therefore vital to detennine
the order of integration of all the variables used in the econometric analysis,
since this will detennine the correct estimation technique to use. In this study,
the augmented Dickey Fuller (ADF) (1979) and Phillips-Perron (PP) (1988)
tests were used in conjunction with data plots to establish the order of
integration of the variables. The ADF test assumes that the errors are statistically
independent and have a constant variance, while the PP test allows the
disturbances to be weakly dependent and heterogeneously distributed (Enders,
1995: 239). The PP test also has greater power to reject the false null hypothesis
of a unit root, except when the errors have a moving average (MA) structure, in
which case this test tends to reject the null hypothesis whether it is true or false.
Since the structure of the error terms is usually unknown, it is preferable to use
both tests. Hence both the augmented Dickey Fuller (ADF) and the Phillips-
Perron (PP) tests were used in this study to establish the order of integration of
the variables. When there are structural breaks, however, the ADF and PP test
statistics are biased towards the non-rejection of a unit root, and the Perron
(1989) test for unit roots in the presence of a structural break should be used
instead (Enders, 1995: 261; Charernza & Deadman, 1997: 119). Appendix 3
summarises the results of the unit root tests.
A priori theory suggests a possible structural break in South Afiican long-tenn
interest rate in 1985 when monetary policy changed dramatically from direct to
market-oriented monetary instruments. The graph of the long-tenn interest rate
series (see figure I) confinns that a possible structural break occurred in 1985.
The results of the ADF and PP test are invalidated by the occurrence of a
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76 SAJEMS NS Vol 4 (2001) No 1
structural break - hence the Perron test for testing unit roots in the presence of a
structural break was used to test the stationarity of the Eskom series. The results,
which are summarised in Appendix 3, confirm that the long-term interest rate is
trend-stationary with a structural break in 1985.
Visual inspection of the graph of the long-term US interest rate (see Appendix 1)
suggests a possible structural break. The Perron test for a unit root in the
presence of a structural break confirms that the US long-term interest rate is in
fact trend-stationary with a structural break (see Appendix 3).
The ADF and PP tests rejected the null hypothesis of a unit root against the
alternative of trend stationarity for the short-term interest rate. Therefore, if a
trend is included in the regression, the short-term interest rate can be directly
included in the OLS-regression.
In contrast to a priori expectations, both the ADF and PP tests could not reject
the null hypothesis of a unit root for the inflationary expectations in levels
(E(lNFL)). However, if there is a structural break in the inflation rate and
inflationary expectations as suggested by the graphs, it invalidates the results of
the ADF and PP tests. The results of the Perron test for unit roots in the presence
of a structural break render expected inflation trend-stationary with a structural
break in 1985. Inflationary expectations are therefore regarded as integrated of
order zero.
4.3 Empirical estimation of tbe long-term interest rate function for South
Africa
The dependent variable tested trend-stationary with a structural break in 1985,
which implies that ordinary least squares (OLS) is the appropriate technique to
use, with a trend dummy (TIME) and a dummy allowing for the new trend (DT)
included. With the trend and the new trend dummies included, the South African
short-term and US long-term interest rates can be regarded as stationary and
therefore included without any transformation.
Both the long-run equilibrium equation and the short-run dynamics or deviations
from equilibrium are simultaneously included when OLS is used - in other
words an ECM structure such as that of Mehra (1994), Mehra (1995) and
Harmse and Du Toit (1999) is considered to be inappropriate in this context.
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SAJEMS NS Vol 4 (2001) No 1 77
Table 1 Estimation results of OLS-regression, dependent variable: SA
long-term interest rate
Coefficient Standard t-value p-values
Variable Error
US 0.225712 0.084908 2.658324 0.0125
RS 0.241269 0.047219 5.109571 0.0000
TIME 0.000491 0.036744 3.752138 0.0000
DT 0.020408 0.005954 3.427301 0.0018
E(INFL) 0.984009 5.35E-05 9.177556 0.0557
DUM- 0.165878 0.494351 1.990508 0.0004
SANCT
RS(-2) 0.138707 0.041299 4.016492 i 0.0008
Sample period (adjusted): 1964 to 1998
iP =0.9578 DW= 1.9696
s.e. = 0.0756 F == 136.9639
With the natural logarithmic form, coefficients may be interpreted as elasticities.
The coefficient of each explanatory variable can be interpreted as follows:
i) US long-term interest rate (US). A one per cent increase in the long-term
interest rate of the US results in a 0.225712 per cent increase in the
domestic (SA) long-term interest rate.
ii) Short-term interest rate (RS). A one per cent increase in the short-term
interest rate results in a 0.241269 per cent increase in the long-term
interest rate. Apart from this contemporaneous effect, a one per cent
increase in the short-term interest rate two years ago will also cause a
0.138707 per cent increase in the current long-term interest rate. The
short-term rate one period ago was insignificant.
iii) Inflationary expectations «E(INFL». A one per cent increase in the one-
period-ahead inflationary expectations results in a 0.984009 per cent
increase in the long-term interest rate. When the null hypothesis that the
coefficient is not equal to one was tested against the alternative hypothesis
that it is equal to one, it was rejected. The coefficient is therefore assumed
to be one, which conforms to the a priori expectation.
iv) Sanctions (DUM-SANCT). During the period of sanctions against South
Africa, interest rates were on average 0.165878 percentage points above
the equilibrium path. This implies that South Africa was extremely
sensitive to international sentiment at that time.
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v) Time trend (TIME). The coefficient of the trend in the equation is
0.000491 which means that the long-tenn interest rate grows on average
by 0.000491 per cent every year.
vi) New trend (DT). The coefficient of the variable that measures the new
trend after 1985 is 0.020408, which means that the interest rate grows on
average 0.020408 per cent faster than before.
5 EVALUATION OF THE RESULTS
5.1 Economic evaluation of the estimated function
Except for the coefficient of inflationary expectations that should be one,
economic theory provides only a priori information on the sign of the
coefficients and not on the size of the coefficients. As explained in section 4.1,
the long-term US interest rate, the domestic short-term interest rate, inflationary
expectations and sanctions should have a positive effect on the long-tenn
interest rate. The results in Table 1 indicate that the influence of all the variables
conforms to the requirements of economic theory. It can therefore be concluded
that this function is an acceptable representation of the long-tenn interest rate of
South Africa.
5.2 Statistical evaluation of the estimated function
Since all the variables in the regression are stationary, the assumptions of
classical regression analysis are fulfilled. Consequently standard diagnostic and
other statistical tests can be used to evaluate this function statistically.
The adjusted R-squared (iP) of 0.957736 indicates that 95.7736 per cent of the
variation in the long-term interest rate is explained by the variation in the
dependent variables, which is evidence of a very good fit. The F-statistic of
136.9639 indicates that the dependent variables are jointly significant in ..
explaining the long-tenn interest rate. The Durban-Watson (OW) statistic of
1.969636 fails to reject the null hypothesis of no serial correlation. The t-
statistics testing the significance of the individual coefficients indicate that all
the coefficients are significantly different from zero, and should therefore be
included in the function. Table 2 summarizes the results of the diagnostic tests
performed on the function.
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Table 2 Diagnostic test results
Test performed Test Test-statistic Probability
for
Normality Jarque-Bera 0.367785 0.832025
Heteroscedasticity ARCH 0.005304 0.941945
White 8.983760 0.774169
Serial correlation Breuch-Godfrey 2.424835 0.297477
LM
Specification Ramsey Reset 1.648535 0.210456
Parameter CUSUM Stable
stability CUSUM
2 Stable
These diagnostic tests proved that
i) the error terms are normally distributed
ii) there is no heteroscedasticity present in the error terms
iii) there is no serial correlation in the error terms
iv) no variables have been omitted, and the specification of the functional
form is correct
v) the parameters are stable
5.3 Dynamic simulation
To obtain an indication of the goodness of fit of the model, an initial dynamic
simulation was performed. A graphical representation of the actual and
simulated values for the derived equation provides a good indication whether the
function is a good representation of the true data-generating process. The close
correlation between the actual and simulated values of the long-term interest rate
(see Figure 2) suggests that the function is a good representation of the true data-
generating process.
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Figure 2 Actual and simulated values of tbe long-term interest rate
20~--------------------------~
18
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10
8
6
65 70 75 80 85 90 95
The model was subsequently subjected to two different types of shocks. In the
first place the sensitivity of the model was tested by increasing the explanatory
variables by 10 per cent. If the model is stable, these shocks should result in
consistent long-run elasticity effects. This means that the simulated value must
increase by 10 per cent of the original coefficient when one of the long-run
explanatory variables is shocked by 10 per cent. When one of the short-term
explanatory variables is increased, there should be an initial movement away
from the long-run equilibrium path, but eventually the model should return to
the original equilibrium path. The dynamics of the model are driven by the
short-term interest rate and the sanction dummy, and they are the only variables
giving dynamic feedback. In the second place, the stability of the model was
tested by shocking each of the variables only in one period to test how long the
system takes to return to equilibrium. The effect of the sensitivity and stability
shocks on the US rate are illustrated in Figures 3 and 4. Although now shown
here, similar shocks were performed on all the other explanatory variables, and ..
all of them illustrated that the function is stable.
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Figure 3 Difference between sbocked and original simulated interest
rates wben a stability test is performed on tbe US interest rate
0.025...-----------------,
0.020
0.015
0.010
0.005
As may be seen from the graph, the difference between the initial and shocked
simulations disappears almost immediately. This means that the effect of a
shock will not persist, and that the model is therefore extremely stable.
A typical sensitivity test shocks the explanatory variables in the model, one at a
time, by increasing them by 10 per cent. The shocks in the long-run variables
must result in a convergence of the dependent variable on 10 per cent of the
estimated coefficient of the shocked variable - in other words 10 per cent of the
elasticity effect. A shock in the short-run variables, however, must result in an
initial shock, after which the dependent variable must converge on the original
equilibrium path. The first shock was performed on the US long-tenn rate, by
increasing it by 10 per cent from 1967. The difference between the original and
shocked simulations is illustrated in Figure 4. The shock results in an immediate
movement away from the long-run equilibrium path to a new equilibrium path.
The difference between the original and shocked simulations is 10 per cent of
the coefficient of the US interest rate, which is consistent with the elasticity
effect. Although not shown here, similar shocks were perfonned on all the other
explanatory variables, and they all indicated that the function is stable.
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Figure 4 Difference between shocked and original simulated interest
rates when a sensitivity test is performed on the US long-term
interest rate
0.025,-------------------,
0.020
0.015
0.010
0.005
0.000+r-,...,....,.,.+~..,.......,........,....".~,...,....,~.,.."~.,...,,...,....,...,....,...,....,....1
60 65 70 75 80 85 90 95
The function has passed economic and statistical evaluation and can therefore be
regarded as a true representation of the determination of the South African long-
term interest rate. The results showed that the long-term interest rate is mainly
determined by inflationary expectations, but that the US long-term rate and the
domestic short-term rate also have important influences on the long-term rate.
Interest rates increased significantly during the sanction era, which shows that
South Africa is extremely vulnerable to international sentiment. These results
have important policy implications, which are discussed in the next section.
6 THE EFFECT ON MONETARY POLICY
Monetary policy makers want to know whether and to what extent they are able
to influence long-term interest rates, and which instruments they should use. The
results of the empirical estimation indicate that the South African long-term'
interest rate reacts mainly to changes in international interest rates, the short-
term interest rate and inflationary expectations. This has several important
policy implications.
The South African Reserve Bank plays a vital role in determining the level of
short-term interest rates, because they are closely related to the rates at which
the Bank lends money to private sector banks (SARB, 1999). Since the
empirical results showed that the long-term interest rate reacts to changes in the
short-term interest rate, monetary authorities can influence the long-term rate by
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SAJEMS NS Vol 4 (2001) No I 83
changing the short-term rate. However, the influence of the Reserve Bank on the
long-term interest rate through changes in the short-term interest rate is limited.
Owing to fmancial globalisation, the monetary authorities in a small open
economy such as that of South Africa cannot force interest rates, especially
long-term interest rates, in a direction other than that dictated by the markets. If
the monetary authorities try to do that, investors and borrowers simply go to
other countries with competitive opportunities.
The influence of the US rate is almost as great as the influence of the domestic
short-term rate. This means that, as in other small open economies, the South
African long-term rate is extremely sensitive to movements in international
markets. This emphasises the fact that the South African capital market is not a
price leader but a price follower, and that the authorities cannot force domestic
interest rates in a direction other than that dictated by the markets. The upward
pressure on interest rates during the sanctions era also emphasises the sensitivity
of South African interest rates to international sentiment.
The empirical results indicated that the influence of inflationary expectations is
far greater than that of the short-term or foreign interest rates. This shows that
the monetary authorities can have a greater effect on the long-term interest rate
if they can influence inflationary expectations. As part of a new approach to
monetary policy and price stabilisation, the government and the Reserve Bank
announced an inflation target band in February 2000. The inflation-targeting
framework does not require significant changes in monetary policy, but the aim
is to reduce the inflationary expectations of consumers, producers, employers
and workers (RSA, 2000: 3). The experiences of other countries that adopted
inflation targets show that this increases stability in nominal interest rates. The
results of this study show that nominal interest rates in South Africa will also be
stabilised if the monetary authorities can convince the public that the inflation
target will be reached.
The monetary authorities can influence the long-term interest rate by changing
the short-term interest rate and inflationary expectations. The influence of
inflationary expectations on the long-term interest rate is greater than that of the
short-term interest rate, and therefore the recently introduced inflation-targeting
framework can have a significant impact on the long-term interest rate if it
reduces inflationary expectations. As in other small open economies, the South
African interest rate is sensitive to changes in international interest rates and
therefore the monetary authorities cannot force interest rates in a direction other
than that which the markets dictate.
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7 CONCLUSION
A market-related approach was followed in this study to explain the
detennination of long-term interest rate in South Africa. Apart from the
theoretical factors, the political and economic environment in which interest
rates are determined plays a key role in the process of interest rate
detennination.
Broadly put, since the 1960s South African monetary policy may be divided into
the pre-1985 and post-1985 periods with the shift from the use of direct
monetary instruments to market-oriented monetary policy. This shift was in line
with the global shift in the 1980s to market-oriented policy, and was encouraged
by the liberalisation of international fmancial markets.
The most significant socio-political events that impacted on the course of South
African interest rates were the international sanctions during the 1980s, and the
process of fmancial globalisation during the 1990s. The sanctions period was
characterised by high interest rates in the attempt to prevent capital outflow and
attract foreign capital. Owing to fmancial globalisation, international fmandal
interdependence has increased substantially, and also become more volatile and
subject to speculation.
The factors that influence the South African long-term interest rate and the
magnitudes of these influences were empirically estimated on the basis of a
market-related approach, with annual data from 1960 to 1998. The results
indicated that there was a structural break in the long-term interest rate in 1985
when monetary policy in South Africa changed, in line with the rest of the
world, from direct to market-oriented policy. The long-term interest rate is
detennined by the US long-term rate, the domestic short-term rate and
inflationary expectations, of which inflationary expectations have the greatest
influence. This means that the monetary authorities can affect long-term interest
rates by either changing short-term interest rates or influencing inflationary
expectations. but they cannot force interest rates in a direction other than that
indicated by the markets because domestic rates are sensitive to changes in
international markets.
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APPENDIXl
Graphical representation of data series employed in estimations
20 25
18
20
16
14 15
12
10 10
8
5
6
4 0
00 65 70 75 80 65 00 95 00 65 70 75 80 65 00 95
- SAIong-IErm_rlIIJiI - SA shcrt-term interest rlIIJiI
14 600
12 600
10 400
8 !l(lO
6 200
4 100
2 0
00 65 70 75 80 00 95 70 75 80
- us Ialg-term i_ rate R-I ...:Ilenge rlIIJiI
25 20
20
15
15
10
10
5 5
65 70 75 80 65 00 95 75 80 65 00 95
- E>peded Inflaticn -lnIIaIlcn
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APPENDIX 1
List ofvariables
Series Description
RL Nominal SA long-tenn interest rate (Eskom rate)
US Nominal rate of US long-tenn government bonds
RS Nominal SA short-tenn interest rate (3-month banker's
acceptance rate)
DUM-SANCT Dummy created to represent years of sanctions and
disinvestment actions against South Africa
E(INFL) Kalman filter prediction of expected one-period-ahead
• consumer price level
DT Dummy for the new trend since structural break in 1985
TIME Trend
APPENDIX 3
Order of integration
Table A Augmented Dickey-Fuller and Phillips-Perron tests for non-
stationarity, levels, 1960-1998 (all data series in natural
logaritbmic form)
Series Model Lagsl
RS
*
**
***
Trend 1
Constant 4
None 4
Slgmficant at a 10% level
Significant at a 5% level
Significant at a 1 % level
'tn 'tl1• 't ~~ PpZ
-4.196** 5.98*** -3.190*
-1.76 3.166 -1.540
1.23 2.57 0.4968
TableD Augmented Dickey-Fuller and Pbillips-Perron Tests for non-
stationarity, first differenced, 1960-1998 (aU series in natural·
logaritbmic form)
Series Model Lags
E(INFL) Trend 3
*
**
***
Constant 0
None 0
Significant at a 10% level
Significant at a 5% level
Significant at a I % level
't" 'tu,'t ~'.1
IpP
0.4366 2.11 -0.606
-1.66 i 2.78 -1.570
-0.427 -0.316
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Table C Perron Tesf for non-stationarity in the presence of a structural
break4, levels, 1960-1998 (all data series in naturallogaritbmic
form)
Series TB I.. K ~ ~ y as tr(a-l)
(t,J (t~) (tT) (ta )
RL 1985 0.64 0 -84.899 0.04416 -0.0475 0.21614 ! -30.57*
(-18.14) (18.63) (-7.028) (-4.85**) i
US 1985° 0.7 3 -85.663 0.04439 -0.1069 0.27123 -32.79*
(-18.66) (19.07) (-13.69) (-3.93*)
E 0 -12.419 0.00633 -0.0129 0.17428 -32.20*
(INFL)
1985 10.64
(-14.42) (14.52) (-lD.71) (-4.78**)
'"
"''''
SlgDlficant at a 5% level
Significant at a 1 % level
ENDNOTES
The number of lags used in the estimated equations was determined
according to the method suggested by Said and Dickey (1984), which
means starting with TI/3 lags and using sequential t-tests to exclude the last
lag if insignificant.
2 The number of truncation lags used in the Banlett kernel was detennined
as suggested by Newey-West. For this sample size Newey-West suggested
3.
3 The version that tests Ho:Yt=J.It+Yt-I+(Jl2-JlI)DUt+et against Ha:
Yt=Jl+l3lt+(I3z-131)DTt·+et, where DUt=1 if t>TB and 0 otherwise and
DTt·=t ift>TB and 0 otherwise, was used.
4 The parameters given are from the model:
k
Yt Ii + f1 + jDT· t +Yt ;Yt = ayt-l + .L ci~Yt-i + &t
1=1
5 Phillips and Ouliaris (1990) showed that t ratio procedures diverge under
that alternative at a slower rate than direct coefficient tests, which means
that direct coefficient tests should have superior power properties over t
ratio tests. Therefore the T{ a-I) test might have higher power than the a
test and therefore both are reported. However, in this study they gave the
same results.
6 Visual inspection of the data suggests a possible structural break in 1981,
and the Perron test confirmed this by rejecting the null hypothesis of a unit
root against the alternative of trend stationarity with a structural break in
1981. However, to keep the specification parsimonious, the Perron test
was also conducted to test the null of a unit root against the alternative of
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trend stationarity with a structural break in 1985.
7 Data from 1954 to 1998 were used to test the stationarity of the US
interest rate.
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