The yield curve and forecasting recession in South Africa: does monetary
policy explain the yield spread’s predictive power?
By
Melvin Muzi Khomo*
And
Meshach Jesse Aziakpono
Abstract
The yield curve, as represented by the spread between long-term and short-term interest rates
has gained prominence in recent years as a useful tool for forecasting future economic
activity and the likelihood of recession. We apply the probit and modified probit models
proposed initially by Estrella and Mishkin (1996) in this paper to explore the yield curve’s
ability to predict recession in South Africa. We also test for the influence of monetary policy
on the yield spread’s predictive power in an effort to explain the source of the yield curve’s
forecasting abilities. The results show that the yield curve is still a simple and reliable
forecasting tool and recession indicator for both policymakers and private investors in South
Africa. In addition, the results show that monetary policy is an important determinant of the
term structure spread but the yield curve’s predictive power is also driven by other factors
independent of monetary policy.
Key Words: Yield curve, monetary policy, South Africa, probit model.
JEL Classification: C53, E3, F1.
*
Senior Lecturer, South African Reserve Bank College, P.O Box 427, Pretoria, South Africa, Tel +27 12 399
6914, E-mail: melvin.khomo@resbank.co.za

Corresponding author: Professor, Development Finance, University of Stellenbosch Business School, P.O.
Box 610, Bellville 7535, South Africa, Tel: +27 (021) 918 4261, E-mail: meshach.aziakpono@usb.ac.za
Disclaimer: The views presented in this paper are solely the responsibility of the authors and should not be
interpreted as reflecting the views of their respective employer institutions.
1. Introduction
Several studies have demonstrated that the slope of the yield curve or the term spread,
as represented by the difference between yields on long-term and short-term treasury
securities, is a useful indicator for future economic activity and thus a good leading economic
indicator. The inversion of the yield curve, where short term interest rates rise above longterm interest rates, has in the past provided a positive statistical relationship with the odds of
a recession ahead and is thus widely regarded as a harbinger for an economic downturn. Such
evidence is extensively documented in the United States and other developed countries with a
few studies also confirming such a behavior or relationship in South Africa ( Moolman 2002;
Khomo & Aziakpono 2007). The Fed consistently publishes GDP growth forecasts and
recession probabilities for the US economy based on the simple yield curve model 1. The
ability to predict future levels of economic activity is not only appealing to policymakers but
is also key to investors and all economic agents since good or accurate forecasts of economic
activity can directly translate into earnings.
Although empirical evidence on the ability of the yield curve to predict recession is
abundant (not in South Africa), considerably less attention has been paid the theoretical
reasons explaining the yield curve’s predictive power. The focus of this article is on the
usefulness of the term spread in forecasting the onset of recession in South Africa. Our aim is
to contribute to the literature by; i) revisiting the ability of the yield curve to predict recession
in South Africa following the recently experienced great recession and some observations
that the yield curve’s predictive power in some countries has deteriorated in recent years, ii)
providing some insights into whether monetary policy explains the yield curve’s predictive
power in South Africa. Evidence that monetary policy actions of the central bank explain the
yield’s curve’s predictive powers can provide support to building the theory that explains the
yield spread’s ability to predict recessions and its usefulness as a forecasting tool.
The paper is structured as follows; a brief theoretical and literature review is
presented in chapter 2; chapter 3 presents the empirical relationship between the business
cycle in South Africa, the yield spread and monetary policy; chapter 4 is the methodology
and chapter 5 presents the results and conclusion.
2. Theory and literature review
2.1 Theory
The yield curve can be purely defined as the relationship between interest rates with
different terms to maturity. It represents the term structure of interest rates and is normally
characterized by a plot of bond yields with the same risk, liquidity and tax considerations
(normally government bonds) against time to maturity. The shape and slope of the yield
curve changes daily and attracts the attention of everyone from analysts to economists and
1
The Cleveland Fed uses past values of the yield spread to calculate and post predictions of real GDP growth
and the probability that the US economy will be in recession one year forward. See
www.clevelandfed.org/research/data/yield_curve/index.cfm
forecasters since empirical studies have shown that changes in the shape of the yield curve is
closely linked to the movement of economic variables like inflation, future interest rates and
economic growth.
In essence, although a myriad of factors determines the general level of interest rates
in an economy, the focus of the yield curve is on those elements that define the yields on
bonds with different terms to maturity. It also makes sense to differentiate between short-term
(normally less than two years) and long-term sectors of the yield curve since different factors
appear to drive different segments of the curve and hence the shapes of the yield curve. The
difference between any two maturity sectors of the curve is termed the yield spread or
maturity spread and fluctuations in such spreads helps us infer changes in the slope and shape
of the yield curve and mainly for the purposes of this paper, the relationship between shortterm and long-term interest rates. High long-term interest rates relative to short-term rates
(positive spread) displays a normal or upward sloping yield curve, with a flat curve showing
similar yields regardless of maturity and a negative spread signalling an inverted yield curve
where short-term interest rates exceed long-term interest rates. Explanations for the term
structure of interest rates (i.e. the shape of the yield curve and relationship between long-term
and short-term interest rates) fall predominantly between two theories; the expectations
theory and the market segmentation theory (Fabozzi, 2012: 185). Fabozzi defines three forms
of the expectations theory which are the pure expectations theory, the liquidity theory and the
preferred-habitat theory. Given the objective of the study, we briefly review the fundamental
assumptions behind these theories in explaining the shape of the yield curve. We specifically
focus on the theoretical justification as to why the yield curve would invert before a recession
and hence its predictive powers.
The pure expectations theory explains the term structure in terms of expected future
short-term interest rates such that at any given moment in time, the yield curve reflects the
market’s current expectations of future short-term interest rates (Saunders & Cornett, 2011:
229). An upward sloping yield curve under this theory would reflect that the market expects
short-term rates to rise in the future whilst a flat term structure reflects expectations of
unchanged rates. An inverted yield curve would imply the market expects interest rates to
decline in the future. Since the yield curve has historically inverted prior to all observed
recessions in RSA, it could be a reflection of market expectations about a decline in interest
rates. Adrian et.al (2010:4) note that an inverted yield curve could be seen as a reflection of
market expectations of low future interest rates which in turn are attributed to weakness in
expected credit demand, diminished inflation expectations and central bank policy in
response to subdued economic conditions. Dueker (1997:42) notes that if investors expect a
recession to occur, the yield curves’ response will be determined by the market’s assessment
of the recession’s influence on short-term interest rates and the yield curve inversion will
mainly be driven by a decline in long-term interest rates.
Although the pure expectations theory explains the tendency of the yield curve to
invert at times, its fundamental drawback is that it does not account for the risk associated
with fixed income investments. In practice, it can be observed that the volatility of a bond’s
price (risk of holding that bond) is directly related to its term to maturity (i.e. long-term bonds
are more risky). The liquidity premium theory improves on the pure expectations theory by
asserting that investors will hold long-term bonds if they are offered a risk premium (also
called term premium) above expected future short-term interest rates to compensate for the
higher risk. The theory implies that long-term interest rates are a function of expected future
short-term interest rates plus a liquidity or risk premium and such premium will increase with
the maturity of the bond (Fabozzi; 2012:188). This theory explains well the observed
tendency or a bias towards a positively sloped shape of the yield curve since rational
investors would demand a premium for duration risk. This theory is however poor in
explaining the observed tendency of the yield curve to invert before recessions since its main
perceptive is that expectations of a steep decline in interest rates in the future might overcome
the term or liquidity premium associated with holding long-term bonds.
The preferred habitat theory is highly similar to the liquidity premium theory with its
major deviation being that the former rejects the assumption that the liquidity premium
increases with a bond’s duration or term. The theory proposes that the shape of the yield
curve is determined by expectations about future short-term interest rates plus a risk premium
(which can be either positive or negative) that is determined by the investors’ preferred
habitat at any given period in time (Fabozzi; 2012:189). According to this theory,
expectations of a steep decline in short-term interest in anticipation of monetary easing, lower
GDP growth or low inflation would induce investors to shift funds from short-term
instruments (the normally preferred habitat) to long-term bonds (in anticipation of higher
returns) and thus cause the yield curve to flatten and then finally invert.
All the three theories mentioned above emphasize on the importance of expectations
about future interest rates as the key determinant of the yield curve shape with an inverted
curve associated with an expected decline in short-term interest rates due to a countercyclical
monetary policy, lower GDP growth, lower inflation or a combination of any of the variables.
The last theorem; the segmented markets theory, assumes that investors regard the maturity
sectors of the yield curve as completely separate such that bonds with different maturities
cannot be regarded as substitutes (Mishkin 2004: 132). Demand and supply dynamics for a
particular maturity segment of the curve determines the yields for that portion of the yield
curve with no links to other maturities. The theory assumes that the shape of the yield curve
is determined by asset-liability management constraints of investors and issuers of bonds at
any maturity sector of the curve. The segmented markets theory does not explain the
tendency of the yield curve to invert before recession since it assumes investors will not shift
funds across maturity sectors (there is no relationship between demand and supply of shortversus long-term bonds) in anticipation of changes in interest rates, growth or inflation.
Given the term structure theories, Moneta (2003:10) provides three reasons for the
relationship between the term structure of interest rates and economic growth and hence the
yield curve’s information about future recessions. This relationship is generally positive and
mainly reflects the expectations of financial market participants about future economic
growth. Moneta attributes the relationship to market expectations about future interest rates,
monetary policy effects and investor hedging. Why would an inverted yield curve then
precede recessions? The answer lies in the expectations theory such that if financial market
participants expect slower growth, low inflation or even a recession ahead, they will lower or
reduce their forecasts of future short-term interest rates. Since long-term interest rates are
determined by expected future short-term interest rates, the yield curve will flatten and
eventually invert depending on how much the market expects interest rates to fall. Since
monetary policy determines short-term interest rates, the market will expect the central bank
to ease monetary policy (Rosenberg & Mauer 2011). We show later on in the paper that
monetary policy actions of the central bank in South Africa have an influence on the shape of
the yield curve and there is reason to believe monetary tightening might cause the yield curve
to invert before recession.
The investor hedging concept is sometimes referred to as the Consumption Capital
Asset Pricing Model and assumes movements in asset prices are associated with
developments in economic activity (Alessandrini, 2003:3). A general perception in the
financial markets that the economy is heading for a slowdown may cause investors to shift
their funds into financial instruments such as long-term bonds that will deliver payoffs during
the recession. The rush for long-term bonds will cause their prices to rise (and their yields to
decline). Further, to finance their purchases of long-term bonds, investors will liquidate their
holdings of short-term instruments and their yields will rise. The shifting of funds from shortterm to long-term securities in anticipation of a recession will cause the yield curve to flatten
and possibly invert. This explanation also ties with the preferred-habitat theory of the term
structure.
2.2 Literature
The literature on the yield curve’s ability to predict recessions is extensive with
several conclusions observable2. First and most importantly, there is still lack of a universally
acceptable theoretical explanation for this relationship (Estrella & Trubin, 2006:1); and this is
important for confidence to be built around this indicator. Benati and Goodhart (2008) (in
Wheelock & Wohar 2009:436) note that “much of the literature examines empirically how
well the term spread forecasts output growth and recessions, with less emphasis on why the
yield curve predicts economic activity”. Secondly, the probit model features prominently in
such studies whereby it is used to convert a measure of a yield curve’s steepness into the
probability of recession several quarters ahead. Thirdly, although empirical evidence on the
yield curve’s predictive power is clearly abundant; most studies have focused on developed
countries such as the United States and Europe with limited evidence from emerging markets
and South Africa in particular. Nel (1996), Moolman (2002) and Khomo & Aziakpono
(2007) have used South African data to determine the predictive ability of the yield curve.
All the studies mentioned above have mainly focused on proving the term spread’s
ability to forecast recession with limited attempts to explain why this happens. Wheelock and
Wohar (2009:423) note that the usefulness of the term spread for forecasting economic
activity remains a stylized fact in search of a theory. A few studies though make an attempt
into explaining the theory and there seems to be a general agreement in these studies that
central banks can directly influence the short-end of the yield curve in an effort to achieve
their long-term objectives of either low & stable inflation or output stabilization. A monetary
policy tightening in response to high inflation can lower expectations about future inflation,
interest rates and thus result in lower long-term interest rates (Wu, 2003). A monetary policy
induced rise in short-term interest rates could be expected to lead to lower future economic
activity and demand for credit thus exerting pressure on real interest rates (Estrella & Trubin:
2006). Expectations for future declines in short-term interest rates would cause long-term
interest rates to fall and thus the yield curve will flatten. This observation is consistent with
the expectations hypothesis of the term structure.
Estrella and Hardouvelis (1991), who pioneered the use of the yield spread to predict
recessions, argue that current monetary policy has a definite influence on the slope of the
yield curve. They state that a monetary policy contraction would raise the level of nominal,
Wheelock & Wohar (2009) provide a good comprehensive survey of the literature on the term spread’s ability to
predict output growth and recessions.
2
and with price rigidities, real short-term interest rates whilst leaving long-term rates intact
thus causing the yield curve to flatten. The high real rates would lead to low current
investment opportunities and lower future output, thus resulting in a positive relationship
between the yield slope and future output (Estrella & Hardouvelis, 1991:567). To assess the
effect of monetary policy on the yield curve’s predictive power, they add a variable that
represents the current monetary policy stance of the central bank (US Fed funds rate) to the
simple probit model to see if the yield curve correctly predicts recessions and continues to
have statistically significant regression coefficients. Their results showed that the predictive
power of the yield curve remained almost intact; implying that the information in the yield
slope is more about other variables than current monetary policy.
Estrella & Mishkin (1995) examine the relationship between the term structure of
interest rates, monetary policy instruments and subsequent economic activity and inflation in
the US and European countries. They estimate a multi-variate probit model that includes the
term spread, central bank rate, 3m TB rate and the real central bank rate to test whether there
is predictive power of the term spread over and above that provided by variables that reflect
the central bank’s monetary policy stance. They show that monetary policy is an important
determinant of the term structure spread but is unlikely to be the only factor. Estrella and
Mishkin conclude that the spread’s predictive power does not seem attributable solely to
monetary policy variables.
Wu (2001) studies the relationship between the US Federal Reserve’s monetary
policy shocks and changes in the slope of the yield curve in the US. The study indicates that
there exists a strong correlation between monetary policy changes and the slope of the yield
curve in the very short run up to 2 months. Wu concludes that monetary policy tightening
leads to high nominal short-term interest rates, but due to its anti-inflationary effects, these
rates fall back since long-term rates have embedded expectations about the future behavior of
short-term rates. This therefore leads to a flattening of the curve when contractionary
monetary policy is implemented. Estrella (2005) uses an analytical rational expectations
model to investigate reasons for the empirical observation that the slope of the yield curve is
a significant predictor of output and real economic activity. He concludes that the extent to
which the yield curve is a good predictor of both future output and inflation depends on the
form of monetary policy reaction function, which in turn is influenced by the policy
objectives. The main implication from the model is that monetary policy does explain to
some extent the yield curve’s predictive power, but nonetheless it is not the only factor.
Since monetary policy changes directly influence short-term interest rates, Estrella
and Trubin (2006) use US data to assess if yield curve inversions that occurred prior to
recessions were highly influenced by changes in the short-term or long-term interest rates.
They observe that increases in short-term rates preceded all recessions observed, whilst
changes in long-term rates were not as consistent (2006:6). This implies that changes in the
slope of the yield curve were mainly driven by short-term interest rates which move in lockstep with the monetary policy rate. Wright (2007) estimates a number of probit models using
the yield curve combined with several variables to forecast recession, of which one of the
models includes the term spread and the nominal fed funds rate. He concludes that models
that use both the level of the fed funds rate and the term spread give better results than a
model with the yield spread alone (2007:10).
Kucko and Chin (2010) also investigate whether the yield spread is a predictor of
recessions in the US and European countries and augment the conventional two-variable
recession/yield curve specification with the fed funds rate. Their intention is to test the yield
curve’s predictive powers following the recent great recession and current conditions in
global bond markets and also to isolate the effect of changes in short-term interest rates
(monetary policy effect). Their findings are generally inconsistent across countries, with the
model correctly predicting recessions in the US, Germany and Sweden. With regards to
monetary policy effects, they find that adding the short-term rate to the simple probit model
resulted in a decrease in the economic and statistical significance of the yield spread.
Adrian, Estrella & Shin (2010: 15) note that the significant impact of changes in the
fed funds (monetary policy rate) rate is not on the level of long-term interest rates but on the
slope of the yield curve. They use data from the US to show a near perfect relationship
between changes in the fed funds rate and changes in the term spread. Their study proposes
an explanation of the yield curve’s predictive power from the balance sheet management of
financial intermediaries. Adrian et.al conclude that monetary policy tightening is associated
with a flattening of the yield curve and a reduction in net interest margins, which in turn
makes lending less possible, thus reducing the supply of credit. This then leads to slower
economic growth ahead.
With specific reference to South Africa, Nel (1996) used cointegration techniques to
test the relationship between the term structure of interest rates and growth in real economic
activity using data covering the period 1974 to 1993. He showed that the slope of the yield
curve is positively related to growth in real economic activity and concluded that the term
spread contains information about the real sector of the economy and may be used to forecast
future economic activity. Moolman (2002) uses the probit model to predict turning points of
the South African business cycle using the yield curve. Quarterly data for the period 1979 to
2001 is used in the analysis and Moolman finds that the probability of a recession in a
specific quarter is a negative function of the yield spread lagged two quarters (2002:48). The
results indicated that the yield curve successfully predicts turning points of the business cycle
in South Africa.
Khomo & Aziakpono (2007) also use the probit model to examine the ability of the
yield curve to predict recession in South Africa and its predictive power is compared to other
variables that include the growth rate of money supply, changes in stock prices and the index
of leading economic indicators. The study revealed that the yield spread was still a useful
indicator for predicting recession in South Africa and it produced better forecasts as
compared to the other variables. However, while these studies show the relevance of the yield
curve in predicting economic activities in South Africa, none of them attempted to explain
the reasons behind the predictive power of the yield and whether it can be attributed to the
role of monetary policy or not.
These studies, although not conclusive, do provide some form of credibility that
changes in monetary policy influences the slope of the yield curve and its ability to forecast
recessions. Adding a variable that represents the monetary policy stance of the central bank to
the two-variable probit model can be used to ascertain the influence of monetary policy on
the spread’s predictive power. In the next section we briefly review the evolution of the yield
spread, monetary policy cycle and business cycle in South Africa.
3. The yield spread and the business cycle in South Africa
Figure 1: the yield spread and business cycle in RSA
Shaded areas indicate
official recession periods
as identified by the SARB
Figure 1 shows the movement of the yield spread (as represented by the difference
between yields on the 10-year RSA government bond and the 91-day Treasury bill) across the
business cycle in South Africa since 1980. The graph provides some evidence that a
relationship has indeed existed in South Africa between changes in the shape of the yield
curve and the various phases of the business cycle with the yield curve flattening and
eventually becoming inverted (yield spread becomes negative) prior to all five recession
periods observed over this period. This relationship is consistent even with the most recent
recession over the period 2007 to 2009 thus confirming the value of the yield spread as a
good leading economic indicator. Since the predictive power of the yield curve is most likely
influenced by the monetary policy stance of the central bank, the relationship between the
business cycle and the SARB’s repo rate is shown in Figure 2 below. The idea is to explore
the movement of the policy interest rate over the business cycle and before the onset of past
recessions in RSA.
We follow the approach by Adrain et al (2010) and define the end of a monetary
policy tightening cycle as when either one of the following criteria is met: (1) the repo rate is
higher than at any time from 12 months before to 9 months after and is at least 50 basis points
higher than at the beginning of the period or (2) the repo rate is higher than at any time from
6 months before to 6 months after and is 150 basis points higher than the average at these
points. Both these criteria show six monetary policy tightening cycles since 1980 (Figure 2)
and all monetary contraction cycles except for one (2004) were followed by official
recession. The lag between the end of the tightening cycle and the onset of recession is not
consistent over the different periods but interest rates have in the past normally peaked well
into the recession. This means the central bank could do better by improving its forecasts for
business cycle turning points.
Figure 2: repo rate, monetary policy tightening cycles & business cycle in RSA
Shaded areas indicate official
recession periods
Red lines indicate the end of a
monetary policy tightening cycle
Figure 3 below shows the movement of the term spread against its individual
components (short-term vs. long-term rates) over the business cycle. The idea is to ascertain
if changes in the yield spread are highly driven by movements in the shorter or longer end of
the curve. An inversion of the yield curve can be caused by either a rise in short term interest
rates, a decline in long term interest rates or a combination of both. Figure 3 shows that in the
period studied, long-term and short term interest rates have generally moved together in the
past (0.74 positive correlation) with the only difference being the magnitude of changes in
both.
Short-term rates have generally risen faster than long-term rates during a tightening
cycle and causing the yield curve to flatten and then invert prior to recessions. In the most
recent recession (2007 – 2009), short-term interest rates rose by 207 basis points compared to
an increase of 67 basis points in long-term rates in the 12 months before the onset of the
recession in December 2007. The same is observable in the previous recession of 1996 where
short-term rates rose by 206 basis points in the 12 months before the start of the recession
compared to a rise of 153 basis points in long-term rates. One can conclude from this analysis
that the inversion of the yield curve before past recessions is partly explained by a rise in
short-term interest rates which move in direct proportion to the SARB’s repo rate (Estrella &
Trubin (2006) find a similar link in the US).
Figure 3: the yield spread components and business cycle in RSA
10Y Yield
Term Spread
Figure 4 shows the relationship between changes in the repo rate and changes in the yield
spread, and confirms the existence of relationship between the two. Changes in the repo rate
have in the past exhibited a strong negative relationship with the yield spread; implying that
increases in the repo rate have to a great extent explained the inversion of the yield curve
before all recessions observed. Changes in long-term interest rates appear to have no
relationship with changes in the spread (Figure 6). One can conclude that long-term bond
yields are independent of current monetary policy and are driven by a wide range of factors.
Market expectations about future monetary policy actions of the central bank would however
play a role in determining long-term bond yields.
Figure 4: change in the repo rate versus yield spread
Figure 5: change in 10Y yields versus the yield spread
4. Data and model estimation
In this section, we present the probit methodology used in estimating the likelihood of
recession given the slope of the yield curve.
4.1 Indicators and data used
a) Yield Spread: since the yield curve normally inverts prior to recessions, an inverse
relationship should be observable between the yield spread and the probability of a
recession. The yield spread in the paper is calculated as the difference in yields between
the 10-year government bond and the 91-day Treasury bill in South Africa (10-year rate
minus the 91-day rate). An inverted yield curve will be observable where short-term
interest rates are higher than long-term interest rates.
b) Monetary policy stance: this is represented by the SARB’s repo rate and an increase in
the central bank rate should normally cause the yield spread to decline and the probability
of recession to increase. Monthly data from January 1980 to July 2012 is used in the
study with all data obtained from the South African Reserve Bank.
c) Recession indicator: The recession indicator in the study is obtained from the SARB’s
official recession dates. The central bank applies the National Bureau of Economic
Research (NBER) methodology3 in dating official downswings of the business cycle and
this method goes beyond the general two consecutive quarters of declining GDP.
Applying this convention, the SARB identified five recessions since 1980 in the
3
The NBER, the organisation responsible for officially dating the beginnings and ends of US recessions, defines
a recession as “a broad decline in aggregate economic activity (which is measured as a common movement in
output, income, employment and trade), using lasting from six months to a year, and marked by widespread
contractions in many sectors of the economy” (Filardo, 1999:36).
following periods; September 1981 to March 1983, July 1984 to March 1986, March
1989 to May 1993, December 1996 to August 1999 and December 2007 to August 2009.
4.2 Model and estimation methods
Following previous studies, we estimate a non-linear probit model that directly estimates the
probability of a recession at a given time horizon based on the steepness of the yield curve.
The main input into the model is the value of the term spread; i.e. the difference between
long-term and short-term interest rates at time t-k, and the output is the probability of a
recession occurring at time t. The probit model is therefore used in the study to relate the
probability of a recession in South Africa as dated by the SARB during the current period to
the slope of the yield curve observed several months earlier. The probability of a recession at
time t, with a forecast horizon of k periods is given by the following probit model that is
estimated:
Prob(Rt = 1) = Φ(c0 + c1Xt-k)
(A)
Where Φ(..) denotes the normal cumulative distribution function and X is the set of
explanatory variables (only the term spread in this case) used to forecast recession. The
parameters c0 and c1 are estimated by maximizing the log-likelihood function (Atta-Mensah
and Tkacz, 1998:5). If the coefficient c1 is statistically significant, then the term spread, Xt-k
is deemed useful for forecasting recession in periods ahead (Wheelock & Wohar, 2009:432).
Dueker (1997:45) notes that the general probit model stated above (A) assumes the
random shocks in the model are independent and identically distributed with a mean of zero,
whilst for many time series applications this is not a plausible assumption. According to
Estrella and Mishkin (1998:47), the probit model has an overlapping data problem such that
the forecast errors are likely to be serially correlated. Dueker proposes a method to remove
the serial correlation in the error term by adding a lag of Rt to the probit model (A) stated
above4. He observes that adding a lag of the dependent variable increases the validity of the
assumption that the error term has a mean of zero, conditional on availability of information
over time t+k. The new probit model proposed by Dueker stated below is also estimated to
remove potential serial correlation:
Prob(Rt = 1) = Φ(c0 + c1Xt-k +c2Rt-k )
(B)
Since the main objective of this study is to test for the influence of monetary policy on the
yield spread’s predictive power, we follow Kucho and Chin (2010) and augment the
modified probit model (B) with the a variable that represents the current level of short-term
interest rates (SARB’s repo rate in this case) as follows;
Prob(Rt = 1) = Φ(c0 + c1Xt-k +c2Rt-k +c3REPOt-k ) (C)
4
Karunaratne (1999), Atta-Mensha and Tkacz (1998), and Moneta (2003) also recommend this approach and
when applied in Khomo &Aziakpono (2007) it produced better results than the ordinary probit model.
The objective is to isolate the effect of changes in official interest rates and test whether there
is extra information in the slope of the yield curve over and above the information which the
slope carries about current monetary policy actions (Estrella & Hardouvellis; 1991:566). If c1
is statistically significant in equations (A) and (B) but not in equation (C), then the ability of
the spread to predict recessions is not robust to the inclusion of a variable that represents the
current monetary policy stance of the central bank. An opposite observation however would
imply that the predictive power of the yield spread goes beyond the current monetary policy
stance of the central bank and is explained by other factors.
The principal measure of the goodness-of fit for the probit model estimation
suggested by Estrella (1995) and subsequently used in several studies that include Dueker
(1997), Bernard and Gerlach (1996), Estrella and Mishkin (1998) and Moneta (2003) is used
in the paper. The pseudo R², a measure of the goodness of fit of the estimated equation that
corresponds intuitively to the coefficient of determination in a standard linear regression
(Estrella and Mishkin, 1998:47) is defined as;
Pseudo R² = 1 - (Lu/Lc) –(2/N) Lc
Where Lu is the value of the log-likelihood of the estimated model (unrestricted) and Lc is the
value of a constrained model containing only the constant term (all coefficients are zero
except constant). N is the number of observations. The pseudo R2 is used together with t
statistics from the estimated regressions to find the lags that give the best fit for all the
variables studied.
5. Empirical Analysis
5.1 The yield spread and recession in South Africa
Presented in this section are the results based on the 3 probit equations estimated. The simple
probit model with only the yield spread as an explanatory variable (A) is estimated first and
results are presented in Table 1 below. We report the estimated coefficients (z-statistics), pvalues, pseudo R2, root mean squared error (RMSE) and variance proportion (VP) for the
model at different forecasting lags. The results indicate that the slope coefficients of the
spread conform to the theoretical expectations as they exhibit an inverse relationship between
the term spread and the probability of a recession occurring. The results are also statistically
significant up to 18 months with the lag representing the best fit observed at around 2
quarters (highest pseudo R2 is at 5 months). The probit model therefore still allows us to
estimate the probability that the South African economy will be in recession in a given month
on the basis of the interest rate spread observed some months earlier.
Table 1: probit results: Prob(Rt = 1) = Φ(c0 + c1Xt-k)
Lags
k=1
k=3
k=5
k=6
k=9
k = 12
k = 15
k = 18
k = 21
Z-Stat
Prob
Pseudo R²
-9.7392
0.0000
0.2980
-10.4699
0.0000
0.3810
-10.6691
0.0000
0.4145
-10.6945
0.0000
0.4133
-10.0596
0.0000
0.3315
-8.5431
0.0000
0.2148
-5.9977
0.0000
0.0989
-3.4660
0.0005
0.0324
-1.4726
0.1408
0.0058
RMSE
VP
0.4075
0.3163
0.3868
0.2617
0.3775
0.2440
0.3761
0.2490
0.3966
0.3046
0.4281
0.3984
0.4606
0.5392
0.479
0.7015
0.4861
0.8596
Adding a dynamic structure to the simple model (A) through a lagged dependent variable
should improve the forecasting power of the model by making the residuals free of serial
correlation (Karunaratne 1999:11). Table 2 below presents results from the modified probit
model that includes the yield spread and a lagged dependant variable (B).
Table 2: probit results: Prob(Rt = 1) = Φ(c0 + c1Xt-k +c2Rt-k )
Variables
SPREAD
Z-Stat
Prob
LAG Dep.
Z-Stat
Prob
k=1
k=3
k=5
k=6
k=9
k = 12
k = 15
k = 18
-3.7465
0.0002
-6.2895
0.0000
-7.3034
0.0000
-7.5691
0.0000
-7.3914
0.0000
-6.6071
0.0000
-5.1791
0.0000
-3.7283
0.0002
11.3393
0.0000
11.2895
0.0000
10.0882
0.0000
8.8769
0.0000
5.3616
0.0000
2.4305
0.0151
0.1213
0.9035
-1.5045
0.1324
Pseudo R²
RMSE
VP
0.0510
0.4277
0.0188
0.1450
0.3746
0.0568
0.1813
0.3734
0.1530
0.1892
0.3777
0.2037
0.1669
0.4075
0.3341
0.1263
0.4341
0.4381
0.0747
0.4276
0.5423
0.0381
0.4752
0.6501
Several observations can be made from the results of the modified probit model presented in
Table 2 above. The yield spread does not lose its statistical significance and its forecasting
power over the 18-month horizon. Coefficients of the lagged dependent variable are
statistically significant up to 12 months and the lag that presents the best fit remains 5 months
as the value of the pseudo R2 is the highest at 0.1892. The estimated probabilities of recession
obtained from running model B (dynamic probit) are plotted in Figure 6 together with past
recession periods. This is compared to the estimated probabilities obtained previously
running the standard probit model (A) based on a 6 months horizon which is the best forecast
lag for both models
Figure 6: Probability of RSA recession 6M ahead as predicted by yield spread
Figure 6 shows that both probit models correctly predicted past recessions over 6m horizons,
with the dynamic model appearing to exhibit a greater degree of fit. The modified probit
model appears to improve the forecasting power of the probit model as it predicts better the
occurrence, severity and duration of observed recessions. Figure 6 shows how both models (A
& B) performed in predicting past recessions and confirms that the modified model produces
better forecasts. As an example, the dynamic model showed a 94% chance of recession in
April 2009, compared to an 84% chance from the simple model. Although both models give a
false signal in 2004, the extent of the misnomer is lower for the modified probit model than in
the bi-variate probit model. Based on the analysis above, we can therefore confirm that the
yield curve is still a valuable economic leading indicator and an increase in the yield spread
in negatively associated with the odds of a recession in South Africa.
5.2 Monetary policy and the predictive power of the yield spread
It is without doubt that the central bank’s current monetary policy stance has an influence on
the slope of the term spread, mainly through direct influences on short-term interest rates
(section 3 above). Movements in the repo rate are in lock-step with the 91-day TB rates (98%
correlation in the data used) whilst there is also a positive relationship between the repo rate
and the 10-year bond yield (we found a 75% positive correlation in the same data). It can be
safely postulated that the SARB’s current monetary policy at any given moment in time may
cause the slope of the yield curve and future real output (the likelihood of recession in this
study) to move in the opposite direction and hence the observed association between an
inverted yield curve and a positive probability of recession. The fundamental question
however, is whether or not there is extra information in the slope of the yield curve about
future economic developments over and above the information which the slope carries about
current policy actions of the central bank (Estrella & Hardouvellis, 1991:566).
Table 3: probit results: Prob(Rt = 1) = Φ(c0 + c1Xt-k +c2Rt-k +c3REPOt-k )
Variables
SPREAD
Z-Stat
Prob
LAG DEP.
Z-Stat
Prob
REPO RATE
Z-Stat
Prob
k=1
k=3
k=5
k=6
k=9
k = 12
k = 15
k = 18
-2.2893
0.0221
-3.9635
0.0001
-4.4652
0.0000
-4.5719
0.0000
-4.2348
0.0000
-3.6314
0.0000
-2.6127
0.0090
-1.5279
0.1265
10.3041
0.0000
9.9002
0.0000
7.5134
0.0000
6.0479
0.0000
2.4161
0.0157
0.0884
0.9296
-1.6042
0.1087
-2.8513
0.0044
2.1486
0.0317
3.6488
0.0003
4.4666
0.0000
4.7411
0.0000
5.0118
0.0000
4.4095
0.0000
3.7101
0.0002
3.3311
0.0009
Pseudo R²
RMSE
VP
0.0667
0.3589
0.0202
0.1900
0.3287
0.0555
0.2434
0.3316
0.1165
0.2570
0.3364
0.1498
0.2369
0.3703
0.2481
0.1782
0.4085
0.3490
0.1114
0.4467
0.4402
0.0682
0.4677
0.5221
Primarily, a positive relationship is expected between the repo rate and the probability
of a recession. An increase in interest rates should lower future economic growth and
increase the probability of a recession whilst a reduction in the repo rate is expected to have
the opposite effect. In order to isolate the possible effects of monetary policy on the yield
spread’s predictive power, we estimate the third model (C), and add a variable that represents
the central bank’s current monetary policy stance to the modified probit model. Table 3
above displays the results from this model.
Table 3 confirms that increases in the repo rate by the SARB in South Africa are
positively associated with the odds for a recession in the future. The repo rate parameter in
the model is statistically significant at 5% over a period of 3 years. This positive correlation
is supported by the monetary policy transmission mechanism since higher interest rates can
imply lower investment and consumption expenditure and hence lower future real output.
Such developments should lead to an increase in the odds for recession. The more interesting
observation from the findings above is that the predictive power of the yield spread remains
almost intact when the repo rate is added. The yield spread parameters are nonetheless
statistically insignificant (at 1%) over a shorter horizon of up to 15 months (it was up to 22
months in model B).
Most importantly, the forecasting power of the modified probit model does not
improve with the inclusion of the variable indicating the current monetary policy stance of
the Reserve Bank. The dynamic probit model with the yield spread and lagged dependent
variable as regressors produces the best forecasts. This leads us to conclude that current
monetary policy does not dominate the yield spread and the information in the yield spread
for predicting recessions is mostly about other variables other than the SARB’s monetary
policy stance. Figure 7 below compares the estimated recession probabilities and shows that
forecasts do not improve with the addition of the repo rate to the modified probit model.
Figure 7: Probability of recession: modified probit vs. modified probit + repo
5.3 Conclusion
In this paper, we present further evidence that movements in the yield curve still possess
significant predictive power for distinguishing between economic expansions and
contractions in South Africa. A non-linear probit model that directly estimates the probability
of a recession at a given time horizon based on the steepness of the yield curve is used in the
study. Changes in the shape of the yield curve, especially its inversion, still provides a good
indicator of a possible future recession in South Africa and such an indicator can still play a
role in economic forecasting for policy makers, economic researchers and market
participants. Although there is reason to believe that monetary policy has an influence on the
yield curve, it is only one part of the explanation since the slope of the yield curve is driven
by other factors as well. Although we find evidence of a positive relationship between the
repo rate and the likelihood of recession, our findings suggest that current monetary policy
actions of the SARB are not primarily responsible for the yield curve’s predictive powers.
A word of caution though as Fernandez and Nikolsko-Rzhevskyy (2011:4) point out
that “no standard theoretical approach exists to relate the yield curve to forecasts of future
economic activity….and the curve’s close association with subsequent changes in production,
consumption, investment and other components of real GDP remains purely empirical”. The
ability of the yield curve to predict recession is not necessarily policy invariant and there is
no guarantee its performance will continue unaffected in the current global economic phase
and the near future. There is reason to believe that in countries like the US, the yield spread
indicator has been compromised by the unusual run of monetary policy in recent years. With
US short-term interest rates virtually zero since late-2008, an inverted yield curve is highly
unlikely to be experienced. Furthermore, other nonconventional monetary policies like
Quantitative Easing, Permanent Open Market Operations and “Operational Twist” that are
specifically targeted at suppressing the yield curve raise questions about the information that
one can read from current yield curve shapes. For emerging markets like South Africa that
offer attractive fixed income market yields relative to the developed markets, substantial
global capital inflows in search for better returns would indeed have an impact on the yield
curve. But even under the best of circumstances, relying on one economic indicator is risky.
More robust models that combine multiple predictors might prove useful. A model that
captures the influence of current plus expected future actions of the central bank might yield
better clues about the impact of monetary policy on the yield curve.
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