Monetary policy in South Africa is carried out by the South African Reserve Bank (SARB) with the aim of keeping inflation within a target range of 3% – 6%. The SARB uses a variety of models to aid them, with the core model being the most significant.
The primary aim of this research is to determine whether the reverse yield gap (RYG) contains information that could be useful to the SARB when making monetary policy decisions.
The authors found no evidence that similar studies on the RYG have previously been done in the South African context. Since the yield curve has been found to be significant in South Africa at forecasting economic growth, yet insignificant in Europe, the results for this research may too be different to the global experience.
The authors tested for linear relationships between the RYG and economic growth and inflation over the period 1960–2014.
The results indicate that a slight linear relationship may exist in the case of economic growth, with the RYG based on earnings yields showing better out-of-sample forecasting abilities. Further investigation indicates that the linear relationship is stronger during times of economic upturn. The results for inflation forecasting, however, show no signs of a reasonable linear relationship.
There is evidence for the SARB to consider whether the RYG can replace other economic variables in its core model without loss of predictive ability. Interestingly, this study found evidence to suggest that the RYG has an inverse relationship to future economic growth in South Africa, which is not what was expected.
The reverse yield gap (RYG) is generally given to be the difference between the gross redemption yield on long-term government bonds and the dividend yield (Armah & Swanson
Research on the usefulness of the RYG in predicting economic conditions such as future economic growth and inflation (Armah & Swanson
Armah and Swanson (
The primary aim of this study was to determine if the RYG contains information that could be useful to the SARB when making monetary policy decisions. The focus of the research was not how the RYG could be used by the SARB, but rather to take the initial step of investigating how well the RYG can forecast economic conditions in South Africa.
The authors expect to accomplish this primary aim by achieving two subaims, the first being to investigate the ability of the RYG to forecast inflation levels in South Africa. The second is to determine the ability of the RYG to forecast economic, gross domestic product (GDP) growth in South Africa. Under this aim the relationship between the RYG and economic growth will be investigated over the full data set used in the study and then over periods that are classified as economic upwards phases and economic downwards phases.
This article has the following structure. The ‘economic implications of the reverse yield gap’ section describes the economic implication of the RYG; the ‘past research’ section is a literature review; ‘the data’ section gives a description of the data and variables; the ‘history of the reverse yield gap’ section reviews the history of the RYG; the ‘in-sample linear modelling’ section describes the in-sample linear modelling; the ‘out-of-sample forecasting’ section covers the out-of-sample forecasting models; the ‘forecasting gross domestic product over different economic periods’ section investigates forecasting economic growth during upwards and downwards business cycles; the ‘conclusions’ section details the authors’ conclusions.
The notion that a yield spread contains information on future market conditions is driven by the idea that asset prices are set by rational investors based on their expectations of the future (Nobili
Equity prices give an indication of the market’s expectations of future profitability, which should be affiliated to future economic growth (Davis & Fagan
One should note that the ideas presented in the ‘prices of financial assets’ section rely on the assumptions that, first, investors have access to all relevant information influencing future economic conditions and, second, that investors are rational and can accurately formulate expectations and price for them (Timmermann & Granger
A semi-strong form efficient market is one where all publicly available information is contained in asset prices, while a strong form efficient market is one where all public and privately available information is contained in asset prices (Fama
Investigating the level of efficiency of the South African market is beyond the scope of this article; however, it is worth noting that if the RYG is not predictive it may be a result of inefficiency in the market or that investors are not rational.
Monetary policy in South Africa is carried out by the SARB with the aim of keeping the rate of increase in the consumer price index (CPI) within a target range of 3% – 6%.
The use of various models is central to the process of monetary policy decision-making, with the core model being the most significant of these models (Aron & Muellbauer
The core model is used to quantify the impact on the South African economy of different monetary policy decisions, with the main components of the model aimed at explaining inflation, GDP and the exchange rate (Smal, Pretorius & Ehlers
Smal, Pretorius and Ehlers (
It is unlikely that the RYG alone can provide sufficient forecasting ability; however, it may contain some marginal forecasting ability. Thus, it may well be found that replacing a number of factors currently contained in the core model with the RYG could result in no significant loss of forecasting ability while at the same time reducing the number of variables and increasing the ease and simplicity of using the model.
Davis and Fagan (
Modelling techniques that allow for time variation of coefficients were used by Nobili (
The general consensus is that the RYG has poor out-of-sample performance in forecasting economic growth and inflation and that the estimated parameters are unstable over time (Davis & Fagan
Duarte, Venetis and Paya (
Investigating the use of non-linear models is, however, beyond the scope of this article.
Armah and Swanson (
The authors found no previous research on the usefulness of the RYG in predicting inflation or economic growth in South Africa.
Clay and Keeton (
Since the yield curve was found to be significant in South Africa at forecasting GDP levels and yet insignificant in Europe, this suggests that the results for the RYG in South Africa may too be different to that of Europe and the US.
As Davis and Fagan (
Furthermore, while the RYG showed no predictive abilities above those already contained in the models of Armah and Swanson (
Using the above reasoning, the authors believe that there is sufficient evidence to support the usefulness of this investigation within the South African environment. In addition, similar research has not yet been done in South Africa and the authors are of the view that it is of interest to explore this gap and, similar to the work by Clay and Keeton (
The investigation is done using quarterly data, or monthly data which has been converted into quarterly results. The period under investigation is from 1960:1 to 2014:1, where the notation Y:
For the purpose of this investigation, economic growth over a period of
Where:
Similarly, inflation over a period of
Where:
The quarterly yield was calculated as the average over each quarter of the monthly annual implied yields on government loan stock of term 10 years or more that are traded on the bond exchange.
For the purpose of this study, the yields on the equity market will be measured by the yields on the Financial Times Stock Exchange (FTSE) and/or Johannesburg Stock Exchange (JSE) All Share Index for the period 1995:2–2014:1. Prior to this, the yields on the JSE and/or Actuaries All Share Index were used, as the FTSE and /or JSE All Share only began in July 1995 (Hayes & Bertolis
Where:
The authors consider the RYG based on equity earnings yields or equity dividend yields. Contemporary corporate finance concepts recognise that dividends are a tool that can be manipulated by companies, discussed in ‘the re-emergence of the positive yield gap’ section and the ‘modelling gross domestic product’ section (Berk & DeMarzo
The RYG measures are calculated as follows:
Where:
Using the results given by Fukui and Kamiyama (
and
Where:
ERP is the equity risk premium.
The RYG can then be expressed as:
Before the early 1960s, both globally and in South Africa, it was generally true that the dividend yield on domestic equity was greater than that on conventional government bonds (Jesse
Business cycles became less pronounced and investors perceived a future with greater economic growth, which in turn meant greater dividend growth (Jesse
In
The reverse yield gap in South Africa from 1960 to 2014.
Since the financial crisis of 2008, developed countries once again experienced negative earnings yield RYGs (Fukui & Kamiyama
The RYG based on dividends yields appears to be smoother with less extreme dips than that of the RYG based on earnings yields. The likely explanation for this is dividend smoothing that describes a company’s practice of infrequently changing dividends, and generally upwards only, irrespective of the level of annual earnings (Berk & DeMarzo
To investigate whether or not there is a relationship between the RYG and future inflation or real GDP, linear models were constructed in a similar method to Duarte, Venetis and Paya (
Where:
The model coefficients were estimated for a number of different prediction horizons where
For clarity, when using a lag of 0 in the linear model defined by
For the remainder of this article, the RYG based on earnings yields will be denoted by RYG_{EY}, and by RYG_{DY} when based on dividend yields.
In order to narrow down the set of considered models, the authors choose models for each value of
The significance of the RYG measures as predictor variables is measured using Newey-West standard errors to test for the significance of the slope parameter estimate,
The
Summary of results for the linear models of gross domestic product using the RYG_{EY}.
1 | 2 | 3 | 4 | 5 | 6 | 8 | 12 | |
---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
−0.1036 | −0.1248 | −0.1284 | −0.1334 | −0.1361 | −0.1462 | −0.1543 | −0.1570 | |
Newey-West standard error | 0.1018 | 0.0946 | 0.0819 | 0.1175 | 0.0694 |
0.0827 |
0.1006 | 0.0909 |
0.0014 | 0.0059 | 0.0153 | 0.0534 | 0.0348 | 0.0442 | 0.1106 | 0.1507 | |
Root mean squared error | 0.1269 | 0.0754 | 0.0481 | 0.0263 | 0.0336 | 0.0319 | 0.0206 | 0.0178 |
Note: The values of
, significant at the 5% level;
, significant at the 10% level.
Summary of results for the linear models of gross domestic product using the RYG_{DY}.
1 | 2 | 3 | 4 | 5 | 6 | 8 | 12 | |
---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
−0.2687 | −0.2756 | −0.2715 | −0.2636 | −0.2630 | −0.2661 | −0.2606 | −0.2510 | |
Newey-West standard error | 0.0819 |
0.0808 |
0.0856 |
0.1079 |
0.0652 |
0.0819 |
0.1286 |
0.1332 |
0.0078 | 0.0232 | 0.0552 | 0.1686 | 0.1050 | 0.1181 | 0.2545 | 0.3105 | |
Root mean squared error | 0.1265 | 0.0748 | 0.0471 | 0.0246 | 0.0323 | 0.0307 | 0.0189 | 0.0160 |
, values of the Newey-West standard errors, indicate that the estimates
, significant at the 5% level;
, significant at the 10% level.
For both RYG measures, the value of the lag parameter that minimises the AIC for all values of
There are two interesting results to take note of. First, all of the slope parameter estimates are negative. When considering
The second interesting result is that all of the model statistics used indicate that the RYG_{DY} is better at explaining the GDP data than the RYG_{EY}. This is unexpected since, as mentioned in the ‘reverse yield gap’ section, earnings yields are less open to direct manipulation. A possible reason for this result is the ‘dividend signalling hypothesis’ that states that managers declare dividends on the basis of future expectations in earnings, rather than current earnings that may be distorted through, for example, a once-off large expense (Berk & DeMarzo
The general pattern of results for the two sets of models is the same. The
It appears that the best model fits occur when modelling GDP growth over 12 quarters (3 years) ahead, with the overall best model being that for the RYG_{DY}. This model explained 31% of the variation in the 12 quarters (3 years) ahead GDP growth over the period of observation.
Summary of results for the linear models of inflation using the RYG_{EY}.
1 | 2 | 3 | 4 | 5 | 6 | 8 | 12 | |
---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
0.2228 | 0.2106 | 0.2016 | 0.1943 | 0.1840 | 0.1764 | 0.1543 | 0.0904 | |
Newey-West standard error | 0.1738 | 0.2167 | 0.2572 | 0.2669 | 0.2523 | 0.2891 | 0.3332 | 0.3568 |
0.0224 | 0.0325 | 0.0363 | 0.0379 | 0.0362 | 0.0348 | 0.0289 | 0.0110 | |
Root mean squared error | 0.0683 | 0.0535 | 0.0485 | 0.0458 | 0.0445 | 0.0436 | 0.0422 | 0.0408 |
Note: The values of
Summary of results for the linear models of inflation using the RYG_{DY}.
1 | 2 | 3 | 4 | 5 | 6 | 8 | 12 | |
---|---|---|---|---|---|---|---|---|
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
0.4873 | 0.4700 | 0.4573 | 0.4445 | 0.4309 | 0.4193 | 0.3927 | 0.3222 | |
Newey-West standard error | 0.1689 |
0.1886 |
0.2418 |
0.2931 | 0.2898 | 0.3128 | 0.3496 | 0.3852 |
0.0867 | 0.1307 | 0.1509 | 0.1604 | 0.1605 | 0.1588 | 0.1509 | 0.1130 | |
Root mean squared error | 0.0660 | 0.0507 | 0.0455 | 0.0428 | 0.0415 | 0.0407 | 0.0395 | 0.0386 |
, values of the Newey-West standard errors, indicate that the estimates
, significant at the 5% level;
, significant at the 10% level.
Again the value of the lag parameter that minimises the AIC for all values of
All of the inflation model slope parameters are now positive. One possible explanation for this positive relationship is that if investors believe that inflation is going to increase in the future, but are unsure of the magnitude of this change, this could lead to an increase in demand for inflation protecting assets like equities. This would lead to a decrease in dividend or earnings yields relative to gross redemption yields on government bonds and hence an increasing RYG; see
The maximum
It is not clear that there is any one best fit model out of the tested models for inflation; however, one can say that the results for the RYG_{DY} models appear better than those of the RYG_{EY.}
The out-of-sample forecasting is done by removing from the data the observations from 1996:1 to 2014:1. Linear models for both GDP and inflation of the same form as
This process is followed for each considered value of
The size of the RMSE value will be somewhat swayed by the absolute values of the observations. Thus, because the scale of the real GDP and inflation underlying data is different, one cannot compare directly the RMSE values between the two sets of models, but rather only between the various models within each GDP and inflation category. A summary of the forecasting results can be seen in
Out-of-sample forecasting results.
Root mean squared error |
||||
---|---|---|---|---|
GDP models |
Inflation models |
|||
RYG_{EY} | RYG_{DY} | RYG_{EY} | RYG_{DY} | |
1 | 0.1074 | 0.1677 | 0.0543 | 0.0580 |
2 | 0.0588 | 0.0592 | 0.0460 | 0.0504 |
3 | 0.0401 | 0.0405 | 0.0439 | 0.0486 |
4 | 0.0188 | 0.0198 | 0.0420 | 0.0470 |
5 | 0.0270 | 0.0277 | 0.0412 | 0.0464 |
6 | 0.0246 | 0.0254 | 0.0402 | 0.0455 |
8 | 0.0154 | 0.0168 | 0.0388 | 0.0444 |
12 |
Note: Root mean squared error values in bold indicate the minimum value for a particular set of models.
RYG, reverse yield gap; GDP, gross domestic product.
For each RYG measure, the minimum RMSE values were obtained when forecasting GDP growth over 12 quarter periods (3 years). This is in line with the results found in
When comparing the error terms for the RYG_{EY} and RYG_{DY} forecasting models where
In the ‘forecasting gross domestic product over different economic periods’ section, the authors investigate the nature of the relationship between the RYG_{EY} and future economic growth during periods of upwards or downwards growth. The results indicate that the RYG_{EY} has an improved linear relationship with future GDP growth during upwards economic cycles and little, if any, linear relationship with future GDP during downwards cycles. By reference to the upwards and downwards economic cycle periods obtained from the SARB, at least 74% of the months over this forecasting period are considered to be in an upwards cycle, whereas for the data before this period, only 57% are contained in upwards cycles.
It is also observed that the period over which the RYG_{DY} performs at its worst compared to the RYG_{EY} is during the time of the Asian economic crisis, and that over this period there was actually a general pattern of increasing three-year economic growth in South Africa. It is possible that market participants expected this crisis to result in a lower than observed growth rate in South Africa and, as dividends are set by companies, this incorrect expectation was more pronounced in the RYG_{DY} than in the RYG_{EY}.
Overall it is likely that the rapid economic growth experienced in South Africa over the period 1996:1–2013:4 resulted in the better performance of the RYG_{EY} model compared to the RYG_{DY} model over this period.
Plot of annual forces of real gross domestic product over a 12 quarter ahead period.
There appears to be little difference between the two models, except over the period 1996 to around 2001. Both forecast models seem to follow the general trend of GDP growth but do not exhibit the extreme peaks and troughs as found in reality. This is disappointing, since what is of key interest when forecasting GDP growth is to be able to predict economic troughs and peaks. The SARB in particular would probably be interested in modelling the extreme possible future outcomes as a result of changes in current economic conditions. Of particular concern is the steep decline in actual GDP growth over 2005–2009 where both forecast models seem to show almost level growth over this period.
It is noteworthy that the forecasts under the EY and DY models are similar. Brill and Toerien (2011) found that directors in South Africa generally believe that reducing dividends leads to negative consequences and that maintaining consistency with historic dividend policies is important. There is evidence of dividend smoothing in
Overall, it appears that while there may be some relationship between future GDP growth and the value of RYG_{EY} and RYG_{DY}, these variables alone are not sufficient to reasonably assist the SARB in monetary policy decision-making.
The models that performed best at forecasting inflation were again the models with a forecasting horizon of 12 quarters. This is interesting as the results in
Plot of annual forces of inflation over a 12 quarter ahead period.
From
Davis and Fagan (
The business phases begin and end on a monthly basis; thus, the quarterly data used in this study is allocated to a specific business cycle period only if the full quarter considered is contained within that cycle. Similarly, when considering the GDP growth over a period of
The modelling process followed is the same as that in the ‘in-sample linear modelling’ section with the same model structure as
Note the developed models for each different value of
The lag parameters that minimise the AIC values are no longer all 0 as was the case in
Summary of results for upwards business cycle linear models of gross domestic product with RYG_{EY}.
1 | 2 | 3 | 4 | 5 | 6 | 8 | 12 | |
---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 6 | 6 | 6 | 1 | 0 | |
−0.1966 | −0.2411 | −0.2271 | −0.1909 | −0.1969 | −0.2129 | −0.2305 | −0.2043 | |
Newey-West standard error | 0.0613 |
0.0696 |
0.0594 |
0.0651 |
0.0507 |
0.0417 |
0.0564 |
0.1037 |
0.0042 | 0.0229 | 0.0514 | 0.2369 | 0.1030 | 0.1656 | 0.4277 | 0.3875 | |
Root mean squared error | 0.1293 | 0.0686 | 0.0434 | 0.0166 | 0.0286 | 0.0239 | 0.0119 | 0.0105 |
Note: The values of
, values of the Newey-West standard errors, indicate that the estimates
, significant at the 5% level.
Summary of results for downwards business cycle linear models of gross domestic product with RYG_{EY}.
1 | 2 | 3 | 4 | 5 | 6 | 8 | 12 | |
---|---|---|---|---|---|---|---|---|
0 | 1 | 0 | 0 | 7 | 7 | 0 | 2 | |
−0.0367 | −0.0156 | −0.0827 | −0.0743 | 0.1500 | 0.1427 | −0.1228 | −0.4004 | |
Newey-West standard error | 0.1080 | 0.1242 | 0.0895 | 0.0850 | 0.1198 | 0.0752 |
0.1362 | 0.0183 |
0.0003 | 0.0001 | 0.0112 | 0.0388 | 0.0431 | 0.0408 | 0.1695 | 0.9761 | |
Root mean squared error | 0.1240 | 0.0769 | 0.0420 | 0.0190 | 0.0291 | 0.0285 | 0.0122 | 0.0015 |
, values of the Newey-West standard errors, indicate that the estimates
, significant at the 10% level.
While the majority of slope parameters are negative, those for the downwards phase models where
The large
A general rule of thumb is that for a model to be able to credibly forecast results it should contain at least 20 observations (Clemen & Winkler
Out-of-sample gross domestic product forecasting results for different business cycles.
Upwards business phase |
Downwards business phase |
|||
---|---|---|---|---|
RMSE |
RMSE |
|||
1 | 1 | 0.1378 | 0 | 0.2675 |
2 | 1 | 0.0735 | 1 | 0.0777 |
3 | 1 | 0.0538 | 0 | 0.0448 |
4 | 6 | 0.0175 | 0 | |
5 | 6 | 0.0300 | 7 | 0.0295 |
6 | 6 | 0.0285 | 7 | 0.0228 |
8 | 1 | 0 | 0.0240 | |
12 | 0 | 0.0127 | – | – |
, RMSE values in bold indicate the minimum value for a particular set of models; RMSE, root mean squared error.
The minimum RMSE for the upwards phase models is obtained when
Graphs of these two best forecast models are given in
Plot of ordered observations of annual forces of real GDP growth over an eight quarter ahead period during upwards business cycles.
Plot of ordered observations of annual forces of real GDP growth over a four quarter ahead period during downwards business cycles.
Neither of the above graphs shows any signs of the forecasting models having a reasonable forecasting ability, and in fact neither seems to even produce a graph with a clearly upward sloping trend throughout. This indicates that it is unlikely that the RYG_{EY} as a linear predictor of GDP growth will be a reasonably useful single tool to the SARB when considering the use of different models over upwards and downwards business cycles.
A high RYG should indicate a high expected rate of future dividend or earnings growth, relative to the equity risk premium. The authors therefore reason that a high expected future growth rate in equity yields should indicate an expectation of high future profits and hence, ceteris paribus, higher GDP growth. From the in-sample linear modelling, however, all of the slope parameter estimates are negative indicating the opposite, which is unexpected.
When considering the linear relationship between the two RYG measures and GDP growth over the entire investigation period, the RYG_{EY} models have superior out-of-sample forecasting abilities and the relationship seems strongest with a lag parameter of 0 and a forecasting horizon of 12 quarters (3 years).
The forecasted models, however, did not capture the extreme changes in GDP growth that sometimes occur in reality. This is disadvantageous as these extreme values are likely the ones the SARB is most interested in predicting.
When modelling GDP growth over different business cycles it was found that the linear relationship between the RYG_{EY} and GDP growth is strongest during upwards economic cycles, although when looking at the out-of-sample forecasted model, this linear relationship does not appear strong.
The RYG_{EY} may still be useful to the SARB since it appears to capture some aspects of the general trend in GDP growth and it may be found that the information contained within the RYG_{EY}, although insufficient on its own, could replace a number of variables in the SARB’s core model without any significant loss in forecasting ability.
There does not appear to be any linear relationship between future inflation and either of the two RYG measures. The minimum RMSE value was found when forecasting inflation over 12 quarters (3 years) with the RYG_{EY} value at the current time
The following areas of research could be pursued to further the results found in this article:
Testing the RYG as a predictor of real GDP growth alongside other variables already considered by the SARB.
Testing if the forecasting ability of the RYG could be improved by use of non-linear models, such as was done by Duarte, Venetis and Paya (
Testing the ability of the RYG to forecast inflation during different times in the economic or inflationary cycle.
The authors thank Mr G. Haltmann for assisting with some of the coding that was used to compute the models and model statistics. We also thank the anonymous reviewers for their helpful comments.
The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.
K.A.G. was the principal author, who instituted the study and undertook initial analyses and inferences. M.G.H. supervised the principal author and co-wrote additional analyses and inferences, with supporting references
This information was obtained from the South African Reserve Bank’s official website and can be found at:
The SARB online database can be accessed at the following address:
Deloitte, Haskins & Sells (1987). A guide to the recommendations of the Margo Commission of Inquiry into the tax structure of the Republic of South Africa.
The published dates for the South African business phases can be found on page S-157 of the Statistical Tables section of the SARB Quarterly Bulletin June 2015, which can be viewed at: