The Predictive Power Of The Yield Spread In Sub-saharan And Northern Africa

The Predictive Power of the Yield Spread in Sub-Saharan and Northern Africa

May 2008

By Oluwasegun Popoola

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Table of Contents Abstract…………….………………………………………………………….……3

Section 1 Introduction……………………………………………………………...4 1.1 1.2 1.3

Background to the Study…………………………...4 Objectives of the Study..…………………………...6 Structure of the Study...…………………….……...6

Section 2 Literature Review and Theoretical Framework…………. ……………..7 2.1 2.2

Related Literature………………………..…………7 Theoretical Framework..…………………………....9

Section 3 Research Methodology, Empirical Analysis and Results……………...11 3.1 3.2 3.3

Data Description and Source(s)…………..….…….10 Predictive Power of the Yield Spread......................29 Forecasting Model Selection……............................44

Section 4 Summary of Research Findings, Recommendations and Conclusion…45 4.1 4.2

Summary of Research Findings……………………45 Conclusion..………………………………………..45

References…………………………………………………………………….…..48 2

Abstract The predictive power of the yield spread has been widely studied and documented in the United States and a number of countries outside the United States. However, little or no studies have been conducted in Africa. This paper studies the predictive power of the yield spread and ascertains its usefulness for predicting real economic growth in Africa. It buttresses the predictive ability of the yield spread particularly in South Africa where the results suggest that the yield spread as a predictive indicator of future economic activities performs better at longer horizons. The paper further identifies the appropriate model for forecasting the yield spread in Morocco, Nigeria and South Africa.

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SECTION 1 INTRODUCTION 1.1 Background to the Study The use of financial variables to predict real economic activity only took a serious turn in the Nineties when policymakers began to find alternative but more reliable ways of predicting economic conditions having being previously been limited by the faulty macroeconomic models which are often characterized by the lack of timely and accurate data and the complexity of the macroeconomic forecasting models.

The growing demand for such variables by policy makers fueled widening research into these variables and their usefulness in predicting future economic conditions. One of such financial variables is the yield spread, which is simply the difference between the long-term and short-term government instruments’ rates1.

Several studies have been conducted on the efficacy of the yield spread, which is often referred to as an indicator of the future direction of the economy. Generally, a positive yield spread (i.e. higher long-term interest rates than short-term rates) is associated with future economic expansion, while a negative yield spread (i.e. lower long-term interest rates than short-term rates) is associated with future economic contraction.

1

The widely used measure of the yield spread is the difference between the 10-year Treasury note and the 3-month Treasury bill.

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Harvey (1988) and several authors documented that there is information about future consumption and output growth in the yield spread. Bonser-Neal and Morley (1997) discovered that the predictive power of the yield spread is strongest in Canada, Germany and the United States having taken the study of the efficacy of the yield spread further by studying its implications in eleven OECD countries.

Perhaps, the closest semblance of a study of the yield spread and its predictive power in Africa was conducted by Khomo and Aziakpono (2007) who both compared the efficacy of the yield curve and other economic indicators as predictors of future economic activities (i.e. economic recessions and expansions) in South Africa.

The seeming lack of studies on the yield spread in Africa is largely due to the nature of the African monetary and financial markets which was largely seen as illiquid and sometimes not transparent because of the level and size of government intervention and controls.

In addition, the institutional development frameworks for financial and monetary regulators and players which were established about five decades ago in Sub-Saharan and Northern Africa (i.e. Morocco, Nigeria and South Africa) only began to take strong roots in the last two decades. As a result, the use of financial variables to forecast real economic activity was either absent or somewhat limited in most of the countries studied.

This study is therefore is an attempt to ascertain the predictive power or otherwise of the yield spread in three countries in Sub-Saharan and Northern Africa (i.e. Morocco, Nigeria and South Africa). The choice of the countries was based on two criteria. First, only countries in the top five bracket of largest countries

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in Africa in terms of real GDP were considered, Second, quarterly data on interest rates and (or) real economic activity had to be available for at least the last ten years.

1.2 Objectives of the Study The objectives of the study are: Highlight the importance2 of the yield spread and determine the forecasting power3 if any, of the yield spread in Sub-Saharan and Northern Africa; Appraise the theoretical underpinnings of the predictive capacity of the yield spread in SubSaharan and Northern Africa; and Consider the continued relevance of this financial variable in the light of constantly changing economic conditions and circumstances.

1.3 Structure of the Study The study covers the period 1963Q1 to 2006Q4. Section 2 contains a broad review of the existing and relevant literature related to the study. A theoretical framework is also provided. Section 3 provides a specification of the model, analysis of results obtained and the drawn generalizations from the findings. Section 4 contains the summary of research findings, recommendations and conclusion.

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Knowledge of the predictive ability of the yield spread enables businesses and policy makers to make better forecasts of real economic activity in the light of unprecedented economic growth being recorded in Sub-Saharan and Northern Africa in the last one decade. 3 As mentioned earlier, the yield spread is assumed to be a predictor of future economic conditions such as economic expansion or contraction.

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SECTION 2 RELATED LITERATURE AND THEORETICAL FRAMEWORK 2.1 Related Literature Predictive role of the yield spread in industrial countries Extensive studies on the predictive power of the yield spread and its predictive capacity began in the midsixties when Kessel (1965) noted the existence of relationship between the yield curve and future real economic activity. Ever since, researchers and analysts have continued to investigate the existence of a relationship between these two economic variables.

In the late eighties and nineties, several studies including Harvey (1989) found that the yield spread predicts real GDP growth in the United States. Stock and Watson (1989) empirically tested and established a predictive relationship4 in macroeconomics that when the difference in yields between long and short term interest rates in the United States is low or negative, future GDP growth tends to be slow or negative. This view is also corroborated in Bernanke and Blinder (1992). Haubrich and Dombrosky (1996) found that the yield spread is an excellent predictor of economic growth. Furthermore, Estrella and Mishkin (1996), Dueker (1997) and Dotsey (1998) compare the yield curve with a few other variables5 as a leading indicator of United States recessions and find generally supportive statistical evidence.

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Recent findings however, indicate the relative weakness of the predictive power of yield curves and spreads to forecast economic growth and future interest rates in the United States. For instance, the yield spread failed to predict the 1990-1991 recession. Popoola (2007) 5 Alternative indicators are stock prices, stock returns, interest rates, dividend yields and exchange rates.

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The early and mid-nineties also saw the emergence of a couple of studies on the predictive power of the yield spread outside the United States. Estrella and Hardouvelis (1991) found that the yield spread predicts real GDP growth in the United States and a number of European countries. Hu (1993), Caporale (1994), Plosser and Rouwenhorst (1994) and Estrella and Mishkin (1995) all attempted to ascertain the predictive power of the yield spread within and outside the United States. To the author’s best knowledge, the most extensive multi-country analysis of the yield spread and its predictive capacity known to date was conducted by Bonser-Neal and Morley (1997)6.

Predictive role of the yield spread in Africa While extensive studies on the yield curve exist for the United States and a number of industrialized countries, very little advancements have been made to study the yield curve and its predictive power in other countries. Study on emerging economies let alone African countries are almost non-existent. This view was buttressed by Mehl (2006).

Two works that specifically dwell on the yield spread and its predictive capacity relating to sub-Saharan Africa were written by Mehl (2006) whose work was on the use of the slope of the yield curve to predict domestic inflation and growth in South Africa among other emerging countries; while Khomo and Aziakpono (2007) compared the efficacy of the yield curve and other economic indicators as predictors of future economic activities (i.e. economic expansions or recessions) in South Africa.

Contribution Interestingly, very few of the previous studies explored the possibility of appraising the theoretical underpinnings of the predictive capacity of the yield spread in spite of the extensive literature available on 6

Bonser-Neal and Morley (1997) studied eleven OECD countries in their paper.

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the subject matter. The only study known to the author was by Hamilton and Kim (2002) which attempted to theoretically show evidence to buttress why the yield spread helps in forecasting the business cycle. In addition, there has been no extensive work on the predictive capacity of the yield spread in African countries except South Africa.

To the author’s best knowledge, this study is the first attempt to investigate and study the predictive power of the yield spread in Morocco and Nigeria and provide an appropriate model for forecasting the yield spread in Morocco, Nigeria and South Africa.

2.2 Theoretical Framework The predictive capacity of the yield spread is embodied in an understanding of the relationship existing between the yield curve, its movements and how it impacts economic conditions.7 A yield curve is the graphical distribution of the yields of treasury securities with different maturities (i.e. 3-month, 6-month, 2, 3, 5, 10 and 20-year). The yield spread as described earlier is the difference between the long-term and short-term government instruments’ rates. It is widely believed that the difference between the short and long-term rates indicates the steepness or the slope of the yield curve.

A positive yield spread (i.e. long term rates are higher than short term rates; positively sloped yield curve) is associated with a potential future increase in real economic activity while negative yield spread (i.e. short term rates are higher than long term rates; negatively sloped or inverted yield curve) is associated with a potential future decrease in real economic activity. Resultantly, the size of the yield spread indicates the potential future increase or decline in real economic activity. 7

Guiding thoughts from Bonser-Neal and Morley (1997)

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The following reasons have been adduced for the empirical relationship between the yield spread and its predictive capacity: The yield spread reflects the stance of monetary policy; The yield spread reflects market expectations of future economic growth; The yield spread reflects credit market conditions and in addition, reflects the changes in expected inflation, fiscal situation and investors’ risk preferences.

Studies have consistently shown that all the theories listed above may have some merit. Estrella and Hardovelis (1991) and Estrella and Mishkin (1995), for example, show that proxies for current monetary policy do help forecast future real GDP growth; however, the inclusion of these proxies does not eliminate the significance of the yield curve. These results suggest the yield curve reflects more than just the effects of current monetary policy actions.

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SECTION 3 RESEARCH METHODOLOGY, EMPIRICAL ANALYSIS AND RESULTS 3.1 Data Description and Source(s) The author studied three countries in Africa as previously documented in section one of the paper.

Real GDP is observed quarterly in South Africa and thus the sample is quarterly from 1963 through the end of 2005 (i.e. 1963.01 to 2006.04). The author also obtained the 10-year government bond yield and 3month Treasury bill rate.

Quarterly real GDP for Morocco and Nigeria was unavailable. As a result, the author was unable to test the predictive power of the yield spread. The author, however, obtained the quarterly 15-year Treasury bond yield8 and 3-month Treasury bill rate for Morocco and deposit rate9 and 3-month Treasury bill rate for Nigeria in order to derive the yield spread.

All the data sets used for this study was sourced from the International Monetary Fund (IMF) data and statistics electronic database.

8

15-year Treasury bond yield used in the absence of 10-year Treasury bond yield in Morocco. The deposit rate was used as Nigeria discontinued the issuance of long term bonds only to have them re-introduced about five years ago. 9

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Figure 3.1 displays the time series plot of the annualized rate of growth of real GDP in South Africa over the next four quarters which suggests that annualized growth rate in real GDP has been relatively unstable over time. Fig 3.1: Annualized Real GDP Growth Rates, 1963.01 – 2006.04 (South Africa) 5 4 3 2 1 0 -1 -2 65

70

75

80

85

90

95

00

05

GDP GROWTH RATE

Fig 3.2: Time series of T-bill rate and Government Bond Yield, 1963.01 – 2006.04 (South Africa) 24 20 16 12 8 4 0 65

70

75

80

TREASURY BILL RATE

85

90

95

00

05

GOVERNMENT BOND YIELD

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Fig 3.3: The Yield Spread and Real GDP growth rate, 1963.01 – 2006.04 (South Africa) 8 6 4 2 0 -2 -4 -6 65

70

75

80

85

90

GDP GROWTH RATE

95

00

05

SPREAD

Fig 3.4: The Yield Spread, Real GDP growth rate and Periods of negative Real GDP growth rate, 1963.01 – 2006.04 (South Africa)

8 6 4 2 0 -2 -4 -6 65

70

75

80

85

GDP GROWTH RATE

90

95

00

05

SPREAD

Figure 3.2 and 3.3 displays the time series of the T-bill rate and government bond yield rate and the yield spread and real GDP respectively. Figure 3.4 displays the time series of the yield spread and real GDP.

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The author observed that the yield spread declined into negative territory just before the real GDP turns negative indicating the presence of predictive power in South Africa’s yield spread.

3.2 Predictive Power of the Yield Spread The author followed the standard regression methodology adopted in previous studies, such as Estrella and Hardouvelis (1991), Estrella and Mishkin (1997) and Bonser-Neal and Morley (1997).

Model Specification (ΔY) t, t+k = α + β*spreadt + error, Where ΔY is the change in real economic activity and defined as the annualized growth rate in real GDP. The subscript k denotes the forecasting horizon in quarters and the spread is defined as the difference between the long-term and short-term rates.

Results The results reported in Table 3.1 indicates the yield spread explains roughly between 5% and 7% of the variation in the following period’s real GDP (i.e. t + k). In addition, the results seem to support the findings, in Khomo and Aziakpono (2007) that the yield spread as a predictive indicator of future economic activities performs better at longer horizons compared to other leading indicators in South Africa.

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Table 3.1: Explanatory Power of the Yield Spread for Real GDP

Forecasting Horizon; k Quarters Ahead 1 2 3 4 5 6 7 8 12 16 20

Explanatory Power of the Yield Spread for Real GDP

5.66 6.10 6.23 6.27 6.27 6.27 6.30 6.37 6.47 6.60 6.74

3.3 Forecasting Model Selection The author applied a number of models including trend, seasonality and ARMA regression models to choose the best model to forecast yield spread from January to December 2006.

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Trend Regression Model Linear Trend Model Yt =

o+

1Timet

+

t

Table 3.2: Linear Trend Regression (South Africa) Dependent Variable: SPREAD Method: Least Squares Date: 05/04/08 Time: 23:29 Sample: 1963Q1 2005Q4 Included observations: 172 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C TIME

2.854042 -0.011156

0.357074 0.003612

7.992849 -3.089045

0.0000 0.0023

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.053147 0.047578 2.351711 940.1927 -390.1362 0.159212

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

1.900193 2.409735 4.559723 4.596322 9.542199 0.002346

Table 3.3: Linear Trend Regression (Morocco) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 01:18 Sample: 1998Q1 2005Q4 Included observations: 32 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C TIME

1.442309 0.027815

0.183345 0.010162

7.866632 2.737035

0.0000 0.0103

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.199816 0.173143 0.530782 8.451888 -24.10450 0.488715

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

1.873437 0.583715 1.631531 1.723139 7.491363 0.010319

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Table 3.4: Linear Trend Regression (Nigeria) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 02:54 Sample: 1992Q1 2005Q4 Included observations: 56 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C TIME

1.250543 0.000645

0.690317 0.021641

1.811548 0.029795

0.0756 0.9763

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.000016 -0.018502 2.617602 369.9995 -132.3288 0.584429

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

1.268275 2.593718 4.797456 4.869790 0.000888 0.976341

Quadratic Trend Model Yt =

o+

1Timet

+

2Timet

2

+

t

Table 3.5: Quadratic Trend Regression (South Africa) Dependent Variable: SPREAD Method: Least Squares Date: 05/04/08 Time: 23:36 Sample: 1963Q1 2005Q4 Included observations: 172 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C TIME TIME^2

2.480436 0.002030 -7.71E-05

0.531913 0.014373 8.14E-05

4.663240 0.141239 -0.947883

0.0000 0.8878 0.3445

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.058155 0.047009 2.352414 935.2207 -389.6802 0.160069

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

1.900193 2.409735 4.566049 4.620947 5.217491 0.006328

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Table 3.6: Quadratic Trend Regression (Morocco) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 01:19 Sample: 1998Q1 2005Q4 Included observations: 32 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C TIME TIME^2

1.028893 0.110498 -0.002667

0.247380 0.036936 0.001151

4.159157 2.991644 -2.316430

0.0003 0.0056 0.0278

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.324756 0.278187 0.495922 7.132218 -21.38822 0.577224

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

1.873437 0.583715 1.524263 1.661676 6.973708 0.003367

Table 3.7: Quadratic Trend Regression (Nigeria) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 02:54 Sample: 1992Q1 2005Q4 Included observations: 56 Variable

Coefficient

Std. Error

t-Statistic

Prob.

C TIME TIME^2

-2.035820 0.365796 -0.006639

0.815493 0.068563 0.001206

-2.496430 5.335170 -5.506504

0.0157 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat

0.363921 0.339918 2.107278 235.3529 -119.6611 0.915792

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-statistic Prob(F-statistic)

1.268275 2.593718 4.380754 4.489255 15.16148 0.000006

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Exponential Trend Model Yt =

oe

1Timet

+

t

Table 3.8: Exponential Trend Regression (South Africa) Dependent Variable: SPREAD Method: Least Squares Date: 05/04/08 Time: 23:40 Sample: 1963Q1 2005Q4 Included observations: 172 Convergence achieved after 6 iterations SPREAD=C(1)*EXP(C(2)*TIME)

C(1) C(2) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Coefficient

Std. Error

t-Statistic

Prob.

2.893209 -0.005262

0.438064 0.001986

6.604528 -2.649734

0.0000 0.0088

0.048053 0.042454 2.358029 945.2509 -390.5976

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.900193 2.409735 4.565089 4.601688 0.158361

Table 3.9: Exponential Trend Regression (Morocco) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 01:21 Sample: 1998Q1 2005Q4 Included observations: 32 Convergence achieved after 9 iterations SPREAD=C(1)*EXP(C(2)*TIME)

C(1) C(2) R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Coefficient

Std. Error

t-Statistic

Prob.

1.511348 0.013417

0.167015 0.005542

9.049159 2.420939

0.0000 0.0217

0.181001 0.153701 0.536986 8.650618 -24.47635

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.873437 0.583715 1.654772 1.746380 0.477824

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Table 3.10: Exponential Trend Regression (Nigeria) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 03:03 Sample: 1992Q1 2005Q4 Included observations: 56 Convergence achieved after 6 iterations SPREAD=C(1)*EXP(C(2)*TIME)

C(1) C(2)

R-squared

Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

Coefficient

Std. Error

t-Statistic

Prob.

-4.67E-13 0.702880

5.30E-12 2.95E-06

-0.088176 238064.3

0.9301 0.0000

2959146.6 08949 3013945.6 38744 4502.882 1.09E+09 -549.5407

Mean dependent var

1.268275

S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

2.593718 19.69788 19.77022 0.255009

Table 3.11: Comparing AIC and SIC (South Africa) Trend AIC SIC Linear 4.5377 4.5737 Quadratic 4.5433 4.5974 Exponential 4.5439 4.5800

Table 3.12: Comparing AIC and SIC (Morocco)

Trend Linear Quadratic Exponential

AIC 1.6315 1.5242 1.6548

SIC 1.7231 1.6617 1.7464

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Table 3.13: Comparing AIC and SIC (Nigeria)

Trend Linear Quadratic Exponential

AIC 4.7975 4.3808 19.6979

SIC 4.8698 4.4892 19.7702

Having considered the three models (i.e. linear, quadratic and exponential), we adopt the linear model for South Africa and the quadratic model for Morocco and Nigeria10.

A cursory look at the regression statistics produced by the linear trend model for South Africa and quadratic model for Morocco and Nigeria reveal the following: Linear Trend Model – South Africa The linear term is significant11. R2 indicates that the trend is only responsible for about 5.3% of the variation in the yield spread. A Durbin-Watson statistic of 0.159 indicates the presence of positive serial correlation.

The linear trend regression residual plot in figure 3.5 reveals that the fitted trend remains relatively stable throughout. As a result, it is difficult to notice any obvious seasonality or cyclical patterns.

Quadratic Model – Morocco The linear and quadratic terms are significant.

10 11

The model with the lowest SIC and AIC for each country is selected in this instance. Except otherwise stated, test of significance is at the 95% confidence interval.

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R2 indicates that the trend is only responsible for about 32% of the variation in the yield spread. A Durbin-Watson statistic of 0.5772 indicates the presence of positive serial correlation.

The fitted trend remains stable throughout as can be seen from the quadratic trend regression residual plot in figure 3.7. As a result, it is difficult to notice any obvious seasonality or cyclical patterns.

Quadratic Model – Nigeria The linear and quadratic terms are significant. R2 indicates that the trend is only responsible for about 36% of the variation in the yield spread. A Durbin-Watson statistic of 0.9158 indicates the presence of positive serial correlation.

The fitted trend remains stable as can be seen from the quadratic trend regression residual plot in figure 3.9. As a result, it is difficult to notice any obvious seasonality or cyclical patterns.

The residual correlograms and its graphs (i.e. figure 3.6, 3.7 and 3.8) reveal the residual sample autocorrelation and partial autocorrelation function has spikes in the 1st, 2nd, 9th and 11th lags for South Africa; 1st and 2nd lags for Morocco and 1st, 2nd, 9th and 11th lags for Nigeria. Additionally, it can been seen that the Ljung-Box statistic rejects the white noise null hypothesis even at very small, non-seasonal displacements which means there is still some useful information contained in the residuals which can be extracted.

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Fig 3.5: Linear Trend Residual Plot

8

8

4

4

0

0

-4

-4

-8

-8 1965 1970 1975 1980 1985 1990 1995 2000 2005 Residual

Actual

Fitted

Fig 3.6: Linear Trend Regression, Residual Correlogram

Date: 05/04/08 Time: 23:58 Sample: 1963Q1 2005Q4 Included observations: 172 Autocorrelation .|*******| .|****** | .|***** | .|*** | .|** | .|* | .|. | *|. | **|. | ***|. | ***|. | ****|. | ****|. |

Partial Correlation .|*******| ****|. | *|. | .|. | *|. | *|. | .|. | .|. | *|. | *|. | **|. | .|. | .|. |

1 2 3 4 5 6 7 8 9 10 11 12 13

AC

PAC

Q-Stat

Prob

0.920 0.774 0.599 0.429 0.271 0.124 -0.009 -0.123 -0.226 -0.320 -0.419 -0.504 -0.559

0.920 -0.479 -0.116 0.016 -0.074 -0.125 -0.051 -0.033 -0.152 -0.111 -0.221 -0.013 -0.024

148.26 253.68 317.19 349.90 363.09 365.86 365.88 368.63 378.01 396.97 429.67 477.09 535.98

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

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Fig 3.7: Quadratic Trend Residual Plot (Morocco)

3

2 1.0 1

0.5 0.0

0

-0.5 -1.0 -1.5 -2.0 1998 1999 2000 2001 2002 2003 2004 2005 Residual

Actual

Fitted

Fig 3.8: Quadratic Trend Regression, Residual Correlogram (Morocco)

Date: 05/06/08 Time: 01:31 Sample: 1998Q1 2005Q4 Included observations: 32 Autocorrelation . |***** | . |**. | . *| . | .**| . | .**| . |

Partial Correlation . |***** | ****| . | . |* . | .**| . | . | . |

1 2 3 4 5

AC

PAC

Q-Stat

Prob

0.693 0.224 -0.069 -0.241 -0.308

0.693 -0.493 0.103 -0.264 0.010

16.871 18.699 18.878 21.140 24.965

0.000 0.000 0.000 0.000 0.000

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Fig 3.9: Quadratic Trend Residual Plot

8 4 8

0

4

-4

0

-8

-4 -8 92 93 94 95 96 97 98 99 00 01 02 03 04 05 Residual

Actual

Fitted

Fig 3.10: Quadratic Trend Regression, Residual Correlogram

Date: 05/06/08 Time: 03:10 Sample: 1992Q1 2005Q4 Included observations: 56 Autocorrelation . |**** . |*. .|. .|. .|. .|. .|. .|. .*| . **| . **| . .*| . .*| .

| | | | | | | | | | | | |

Partial Correlation . |**** .*| . .|. .|. .|. .|. .|. .*| . .*| . .*| . .|. .|. .|.

| | | | | | | | | | | | |

1 2 3 4 5 6 7 8 9 10 11 12 13

AC

PAC

Q-Stat

Prob

0.532 0.165 0.044 0.009 0.002 -0.000 0.043 0.013 -0.064 -0.197 -0.211 -0.153 -0.059

0.532 -0.165 0.043 -0.014 0.005 -0.002 0.064 -0.061 -0.066 -0.178 -0.018 -0.035 0.048

16.734 18.370 18.490 18.495 18.496 18.496 18.619 18.630 18.911 21.661 24.862 26.601 26.866

0.000 0.000 0.000 0.001 0.002 0.005 0.009 0.017 0.026 0.017 0.010 0.009 0.013

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Modeling Seasonality

In order to test for seasonality, the author generated four dummy variables for the quarters in a year and performed a regression using both the linear trend and seasonal dummies in the case of South Africa and quadratic trend and seasonal dummies in the case of Morocco and Nigeria.

The results of the regression on seasonal dummies for South Afirca, Moroco and Nigeria are shown in Tables 3.14, 3.15 and 3.16 respectively. The seasonal dummy model is 4

Yt =

i=1

i

Dit +

t

Table 3.14: Seasonal Dummy Variable Model (South Africa) Dependent Variable: SPREAD Method: Least Squares Date: 05/05/08 Time: 00:38 Sample: 1963Q1 2005Q4 Included observations: 172 Variable

Coefficient

Std. Error

t-Statistic

Prob.

D1 D2 D3 D4

1.811237 1.975157 1.876001 1.938377

0.370623 0.370623 0.370623 0.370623

4.887012 5.329295 5.061756 5.230057

0.0000 0.0000 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.000675 -0.017171 2.430335 992.2965 -394.7748

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.900193 2.409735 4.636916 4.710114 0.147940

26

Table 3.15: Seasonal Dummy Variable Model (Morocco) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 01:36 Sample: 1998Q1 2005Q4 Included observations: 32 Variable

Coefficient

Std. Error

t-Statistic

Prob.

D1 D2 D3 D4

1.974584 1.917082 1.793750 1.808333

0.215272 0.215272 0.215272 0.215272

9.172499 8.905389 8.332475 8.400215

0.0000 0.0000 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.017211 -0.088087 0.608882 10.38063 -27.39333

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.873437 0.583715 1.962083 2.145300 0.351156

Table 3.16: Seasonal Dummy Variable Model (Nigeria) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 03:13 Sample: 1992Q1 2005Q4 Included observations: 56 Variable

Coefficient

Std. Error

t-Statistic

Prob.

D1 D2 D3 D4

1.697393 1.585945 0.613574 1.176188

0.703108 0.703108 0.703108 0.703108

2.414127 2.255619 0.872658 1.672840

0.0193 0.0283 0.3869 0.1004

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.027325 -0.028791 2.630791 359.8952 -131.5535

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.268275 2.593718 4.841195 4.985863 0.545425

27

The dummies account for less than 1 percent of the variation in the yield spread for the three countries. As a result, the author considered the linear trend model and the dummies below for South Africa and the quadratic trend model and dummies below for Morocco and South Africa.

Yt =

o+

1Timet

+

Yt =

o+

1Timet

+

i

Dit +

2Timet

2

South Africa

t

+

i

Dit +

i=1

t

Morocco and Nigeria

Table 3.17: Shows the Linear Trend and Seasonal Dummy Variable Regression Results (South Africa) Dependent Variable: SPREAD Method: Least Squares Date: 05/05/08 Time: 00:44 Sample: 1963Q1 2005Q4 Included observations: 172 Variable

Coefficient

Std. Error

t-Statistic

Prob.

TIME D1 D2 D3 D4

-0.011176 2.750030 2.925126 2.837146 2.910699

0.003643 0.473774 0.476135 0.478512 0.480906

-3.067731 5.804524 6.143482 5.929098 6.052537

0.0025 0.0000 0.0000 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.053985 0.031326 2.371690 939.3606 -390.0601

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.900193 2.409735 4.593722 4.685219 0.156185

28

Table 3.18: Shows the Quadratic Trend and Seasonal Dummy Variable Regression Results (Morocco)

Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 01:38 Sample: 1998Q1 2005Q4 Included observations: 32 Variable

Coefficient

Std. Error

t-Statistic

Prob.

TIME TIME^2 D1 D2 D3 D4

0.111948 -0.002671 1.155124 1.063127 0.910640 0.901410

0.038035 0.001185 0.291318 0.297569 0.302575 0.306396

2.943313 -2.253588 3.965169 3.572709 3.009637 2.941973

0.0068 0.0329 0.0005 0.0014 0.0057 0.0068

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.358772 0.235459 0.510389 6.772923 -20.56118

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.873437 0.583715 1.660074 1.934899 0.535745

Table 3.19: Shows the Quadratic Trend and Seasonal Dummy Variable Regression Results (Nigeria) Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 03:15 Sample: 1992Q1 2005Q4 Included observations: 56 Variable

Coefficient

Std. Error

t-Statistic

Prob.

TIME TIME^2 D1 D2 D3 D4

0.367195 -0.006642 -1.632462 -1.759062 -2.733301 -2.159269

0.069042 0.001214 0.943469 0.953645 0.962518 0.970127

5.318423 -5.471797 -1.730276 -1.844568 -2.839738 -2.225759

0.0000 0.0000 0.0897 0.0710 0.0065 0.0306

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.391712 0.330883 2.121650 225.0700 -118.4102

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.268275 2.593718 4.443223 4.660225 0.867988

29

From the foregoing results, the inclusion of the dummy variables provides little or no explanation for the variation in the yield spread at least in the case of South Africa. The author therefore excludes the dummy variables from the forecast model for South Africa but includes the dummy variables in the forecast models for Morocco and Nigeria.

Incorporating the ARMA Model AR (p) model yt = c +

1yt-1

+

2yt-2

+ …….. +

pyt-p

+

t

MA (q) model yt =

+

t+

1 t-1

+

2 t-2

+ ………. +

q t-q

Tables 3.20 to 3.26 provide the AIC and SIC estimates for various AR and MA processes. Table 3.20: AIC Values, ARMA Models (South Africa)

0 AR Order

0 1 2 3 4

2.696736 2.473483 2.484050 2.496814

MA Order 1 3.836832 2.535904 2.479649 2.462456 2.477522

2 3.213445 2.478719 2.486647 2.474071 2.486658

3 2.847858 2.481130 2.498621 2.484896 2.511902

4 2.666828 2.492796 2.476628 2.495511 2.507652

2 3.268343 2.552208 2.578876 2.585191 2.616823

3 2.921056 2.572992 2.609296 2.614537 2.660663

4 2.758325 2.603030 2.605750 2.643672 2.675007

Table 3.21: SIC Values, ARMA Models (South Africa)

0 AR Order

0 1 2 3 4

2.733481 2.528821 2.558131 2.589789

MA Order 1 3.873431 2.591021 2.553432 2.555057 2.589092

30

Table 3.22: AIC Values, ARMA Models (Morocco)

0

MA Order 1 4.107412 4.108774 3.986706 4.018662 4.038840

2 4.096161 3.975994 3.976569 4.131278 4.002267

3 4.127168 4.101645 3.991413 4.082619 4.061713

4 4.161448 4.125594 3.906611 4.123159 3.984842

MA Order 1 4.360581 4.400750 4.318203 4.390415 4.451603

2 4.385497 4.304467 4.344900 4.540207 4.452554

3 4.452671 4.466615 4.396576 4.528722 4.549524

4 4.523118 4.527061 4.348607 4.606439 4.510177

Table 3.24: AIC Values, ARMA Models (Nigeria) MA Order 0 1 0 4.107412 AR Order 1 4.102316 4.108774 2 4.125950 3.986706 3 4.172017 4.018662 4 4.231887 4.038840

2 4.096161 3.975994 3.976569 4.131278 4.002267

3 4.127168 4.101645 3.991413 4.082619 4.061713

4 4.161448 4.125594 3.906611 4.123159 3.984842

2 4.385497 4.304467 4.344900 4.540207 4.452554

3 4.452671 4.466615 4.396576 4.528722 4.549524

4 4.523118 4.527061 4.348607 4.606439 4.510177

AR Order

0 1 2 3 4

4.102316 4.125950 4.172017 4.231887

Table 3.23: SIC Values, ARMA Models (Morocco)

0 AR Order

0 1 2 3 4

4.357795 4.420615 4.506595 4.607126

Table 3.25: SIC Values, ARMA Models (Nigeria)

0 AR Order

0 1 2 3 4

4.357795 4.420615 4.506595 4.607126

MA Order 1 4.360581 4.400750 4.318203 4.390415 4.451603

31

Based on the results from the AIC and SIC, we select the ARMA (2, 0) for South Africa; ARMA (3, 2) for Morocco and ARMA (1, 2) for Nigeria. This suggests that the best model to regress yield spread is the ARMA (2, 0) model inclusive of the linear trend but excluding the seasonal dummies for South Africa; ARMA (3, 2) and ARMA (1, 2) model inclusive of the quadratic trend and seasonal dummies for Morocco and Nigeria respectively.

As such, the new model adopted is: Yt =

o+

1Timet

+

Yt =

o+

1Timet

+

2yt-2

+

t

2 2Timet

South Africa i=1

+ i=1

i

Dit +

2yt-2

+

t

Morocco and Nigeria

Table 3.26: Linear Trend Regression and ARMA (2, 0) Disturbances (South Africa) Dependent Variable: SPREAD Method: Least Squares Date: 05/05/08 Time: 05:22 Sample (adjusted): 1963Q3 2005Q4 Included observations: 170 after adjustments Convergence achieved after 4 iterations Variable

Coefficient

Std. Error

t-Statistic

Prob.

TIME AR(1) AR(2)

0.012936 1.375742 -0.461797

0.007089 0.068624 0.068463

1.824890 20.04747 -6.745181

0.0698 0.0000 0.0000

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Inverted AR Roots

0.885042 0.883665 0.826181 113.9900 -207.2461 .79

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.890489 2.422260 2.473483 2.528821 2.074602

.58

32

Table 3.27: Quadratic Trend Regression, Seasonal Dummies and ARMA (3, 2) Disturbances (Morocco)

Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 02:14 Sample (adjusted): 1998Q4 2005Q4 Included observations: 29 after adjustments Convergence achieved after 108 iterations Backcast: OFF (Roots of MA process too large) Variable

Coefficient

Std. Error

t-Statistic

Prob.

TIME TIME^2 D1 D2 D3 D4 AR(1) AR(2) AR(3) MA(1) MA(2)

0.226916 -0.005621 0.207156 0.116748 -0.099565 0.001071 0.940373 -0.070506 -0.240043 -0.099211 -2.035910

0.068170 0.001904 0.525318 0.545711 0.552776 0.536030 0.233439 0.354592 0.231763 0.613869 0.656769

3.328678 -2.951913 0.394343 0.213937 -0.180118 0.001999 4.028352 -0.198838 -1.035722 -0.161617 -3.099885

0.0037 0.0085 0.6980 0.8330 0.8591 0.9984 0.0008 0.8446 0.3140 0.8734 0.0062

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Inverted AR Roots Inverted MA Roots

0.964129 0.944201 0.143649 0.371428 22.03736

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.897816 0.608116 -0.761197 -0.242568 2.197198

.67-.39i .67+.39i -.40 1.48 -1.38 Estimated MA process is noninvertible

33

Table 3.28: Quadratic Trend Regression, Seasonal Dummies and ARMA (1, 2) Disturbances (Nigeria)

Dependent Variable: SPREAD Method: Least Squares Date: 05/06/08 Time: 04:09 Sample (adjusted): 1992Q2 2005Q4 Included observations: 55 after adjustments Convergence achieved after 20 iterations Backcast: 1991Q4 1992Q1 Variable

Coefficient

Std. Error

t-Statistic

Prob.

TIME TIME^2 D1 D2 D3 D4 AR(1) MA(1) MA(2)

0.791903 -0.012240 -8.977489 -9.143115 -10.05746 -9.410579 0.850948 -0.441986 -0.553947

0.204280 0.002623 3.965062 4.000570 3.972891 3.927692 0.063813 0.124828 0.127364

3.876562 -4.665945 -2.264148 -2.285453 -2.531523 -2.395956 13.33502 -3.540754 -4.349324

0.0003 0.0000 0.0283 0.0269 0.0148 0.0207 0.0000 0.0009 0.0001

R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood

0.664313 0.605933 1.640118 123.7394 -100.3398

Inverted AR Roots Inverted MA Roots

.85 1.00

Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion Durbin-Watson stat

1.289516 2.612704 3.975994 4.304467 1.882480

-.56

Table 3.26 shows the regression results from the linear trend and ARMA (2, 0) model. Each of the coefficients is significant. R2 for the model is now 88.37 percent. The Durbin-Watson statistic is now very acceptable and the standard error of the regression is now reduced to 0.8262. Table 3.27 shows the regression results from the quadratic trend and ARMA (3, 2) model. In spite of the fact that some of the coefficients are insignificant, the R2 for the model is now 96 percent. The DurbinWatson statistic is now very acceptable and the standard error of the regression is now reduced to 0.1436.

34

Table 3.28 shows the regression results from the Linear Trend and ARMA (1, 2) model. Each of the coefficients, except for the linear trend coefficients is significant. Even though the linear trend coefficient is now insignificant, the adjusted R2 for the model is now 88.37 percent. The Durbin-Watson statistic is now very acceptable and the standard error of the regression is now reduced to 0.8262.

Figures 3.11, 3.13 and 3.15 shows the residual plots for the selected models for South Africa, Morocco and Nigeria, which looks like white noise and this is also confirmed by the residual correlograms (figures 3.12, 3.14 and 3.16). The sample autocorrelations and partial autocorrelations show no more patterns and are mostly within the standard error bounds. Each of the Q-stats is insignificant thereby providing evidence that white noise does exist. As such, the model is able to capture the elements explaining the variation in the yield spread. Fig 3.11: Linear Trend Regression and ARMA (2, 0) Residual Plot

8 4 0 4

-4

2

-8

0 -2 -4 1965 1970 1975 1980 1985 1990 1995 2000 2005 Residual

Actual

Fitted 35

Fig 3.12: Linear Trend Regression and ARMA (2, 0), Residual Correlogram

Date: 05/05/08 Time: 06:32 Sample: 1963Q3 2005Q4 Included observations: 170 Q-statistic probabilities adjusted for 2 ARMA term(s) Autocorrelation .|. .|* .|. .|. .|. .|. *|. .|. *|. .|* .|. *|. *|.

| | | | | | | | | | | | |

Partial Correlation .|. .|* .|. .|. .|. .|. *|. .|. *|. .|* .|. *|. *|.

| | | | | | | | | | | | |

1 2 3 4 5 6 7 8 9 10 11 12 13

AC

PAC

Q-Stat

Prob

-0.043 0.081 -0.048 -0.020 0.038 0.017 -0.078 0.048 -0.103 0.146 -0.048 -0.077 -0.142

-0.043 0.079 -0.042 -0.030 0.044 0.022 -0.086 0.043 -0.084 0.128 -0.029 -0.104 -0.140

0.3169 1.4477 1.8538 1.9249 2.1795 2.2300 3.3172 3.7245 5.6338 9.5331 9.9597 11.050 14.794

0.173 0.382 0.536 0.694 0.651 0.714 0.583 0.299 0.354 0.354 0.192

36

Fig 3.13: Quadratic Trend, Seasonality and ARMA (3, 2) Regression Residual Plot (Morocco)

3 2 1 .2 0

.1 .0 -.1 -.2 -.3 -.4 1999

2000

2001

2002

Residual

2003

Actual

2004

2005

Fitted

Fig 3.14: Quadratic Trend, Seasonality and ARMA (3, 2) Regression, Residual Correlogram (Morocco)

Date: 05/06/08 Time: 02:16 Sample: 1998Q4 2005Q4 Included observations: 29 Q-statistic probabilities adjusted for 5 ARMA term(s) Autocorrelation . *| . .**| . . *| . . *| . . |* .

| | | | |

Partial Correlation . *| .**| . *| .**| . *|

. . . . .

| | | | |

1 2 3 4 5

AC

PAC

Q-Stat

-0.132 -0.265 -0.083 -0.074 0.078

-0.132 -0.288 -0.184 -0.232 -0.082

0.5622 2.9062 3.1432 3.3412 3.5716

Prob

37

Fig 3.15: Quadratic Trend, Seasonality and ARMA (1, 2) Regression Residual Plot (Nigeria)

8 4 0

6 4

-4

2

-8

0 -2 -4 92 93 94 95 96 97 98 99 00 01 02 03 04 05 Residual

Actual

Fitted

Fig 3.16: Quadratic Trend, Seasonality and ARMA (1, 2) Regression, Residual Correlogram (Nigeria) Date: 05/06/08 Time: 04:16 Sample: 1992Q2 2005Q4 Included observations: 55 Q-statistic probabilities adjusted for 3 ARMA term(s) Autocorrelation .|. . |*. .*| . .*| . .*| . .*| . .|. .|. .|. .*| . .|. .*| . . |*.

| | | | | | | | | | | | |

Partial Correlation .|. . |*. .*| . .*| . .*| . .*| . .|. .|. .*| . .*| . .|. .*| . .|.

| | | | | | | | | | | | |

1 2 3 4 5 6 7 8 9 10 11 12 13

AC

PAC

Q-Stat

Prob

0.045 0.088 -0.136 -0.088 -0.109 -0.079 -0.032 -0.011 -0.037 -0.118 -0.030 -0.092 0.092

0.045 0.086 -0.145 -0.085 -0.078 -0.078 -0.035 -0.029 -0.071 -0.151 -0.047 -0.112 0.042

0.1186 0.5769 1.6942 2.1702 2.9142 3.3096 3.3757 3.3832 3.4759 4.4484 4.5146 5.1250 5.7546

0.141 0.233 0.346 0.497 0.641 0.747 0.727 0.808 0.823 0.835

38

The selected models for the respective countries in the earlier pages prove adequate to forecast the yield spread. Figures 3.17, 3.18 and 3.19 show the history of the yield spread and the four quarters-ahead forecast. It is apparent that the model forecasts well and adequately picks up all relevant elements in the series as the realization fits within the confidence intervals shown by the lower and upper limits.

Fig 3.17: 4-Quarters Forecast (South Africa)

6 Forecast: SPREADF Actual: SPREAD Forecast sample: 2006Q1 2006Q4 Included observations: 4

5 4 3

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

2 1 0 -1

0.865454 0.597711 185.0955 0.434289 0.476973 0.164668 0.358359

-2 -3 2006Q1

2006Q2

2006Q3

2006Q4

SPREADF

39

Fig 3.18: History and 4-Quarters-Ahead Forecast

6

4

2

0

-2

-4 2002

2003

2004

FORECAST HISTORY LOWER

2005

2006

UPPER ACTUAL

40

Fig 3.19: 4-Quarters Forecast (Morocco)

4 Forecast: SPREADF Actual: SPREAD Forecast sample: 2001Q1 2006Q4 Included observations: 24

3

2

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

1

0

0.477077 0.292781 61.45160 0.117914 0.094263 0.663533 0.242204

-1 2001

2002

2003

2004

2005

2006

SPREADF

41

Fig 3.20: History and 4-Quarters-Ahead Forecast (Morocco)

2.8 2.4 2.0 1.6 1.2 0.8 0.4 0.0 -0.4 -0.8 2002

2003 ACTUAL HISTORY LOWER

2004

2005

2006

UPPER FORECAST

42

Fig 3.21: 4-Quarters Forecast (Nigeria) 2 Forecast: SPREADF Actual: SPREAD Forecast sample: 2006Q1 2006Q4 Included observations: 4

0 -2

Root Mean Squared Error Mean Absolute Error Mean Abs. Percent Error Theil Inequality Coefficient Bias Proportion Variance Proportion Covariance Proportion

-4 -6 -8 -10 2006Q1

2006Q2

2006Q3

4.766529 4.211038 453.0544 0.623990 0.780502 0.186027 0.033472

2006Q4

SPREADF

43

Fig 3.22: History and 4-Quarters-Ahead Forecast (Nigeria)

8

4

0

-4

-8

-12 2002

2003

2004

FORECAST ACTUAL UPPER

2005

2006

LOWER HISTORY

44

SECTION 4 SUMMARY OF RESEARCH FINDINGS, RECOMMENDATIONS AND CONCLUSION

Summary of Research Findings The author’s findings reveal the robustness of the yield spread and its predictive ability particularly in South Africa where the results suggest that the yield spread as a predictive indicator of future economic activities performs better at longer horizons.

In addition, the author’s attempt at determining the best forecasting model to explain the dynamics in the yield spread provided a number of revelations on how the yield spread fluctuates rapidly as a result of constantly changing economic conditions and circumstances.

Conclusion The paper found evidence to suggest that the yield spread is a predictive indicator of future economic activities in South Africa. Also, the paper reveals that the linear trend with ARMA (2, 0) is the best model12 to forecast the yield spread in South Africa. In Morocco, the quadratic trend with seasonal dummies and ARMA (3, 2) is the best model to forecast the yield spread and in Nigeria, the quadratic trend with seasonal dummies and ARMA (1, 2) is the best model to forecast the yield spread.

12

The author has only employed trend, seasonality and ARMA regression models in this study.

45

However, a clear suggestion from the forecasting model results particularly for Morocco and Nigeria is the possibility that there are other variables, which I have not considered in this study that may further explain the variation in the yield spread.

This gives credence to the author’s views that several financial and non-financial variables may have a strong influence on the yield spread. The author is also of the opinion that variables such as inflation expectations via the consumer price index (CPI), money supply, exchange rate, monetary asset values and consumer sentiment13, may be very good determinants to consider in terms of their influence on the yield spread.

While the African continent is particularly different from the United States, the continent is not entirely insulated from the market and macroeconomic fundamentals from abroad. It is believed that the reliability and predictive power of yield spreads in the United States has diminished significantly compared to the past due to the following14: The determinants of the yield spread today are materially different from the determinants that generated the yield spread during prior decades. The impact of changes in international capital flows and inflation expectations have changed considerably overtime. Developments in the financial sector. Reduction in the risk premiums of long term bonds caused by considerable improvement in the fiscal balance may have distorted the predictive power of the yield spread of government bonds.

13 14

Consumer sentiment is presently not being measured in any of the three countries of focus The listed factors were influenced by the Saito and Takeda paper. See reference section for further details.

46

In addition to the points listed above, there are arguments on the inappropriateness of using data before 1990 to measure the connection between the yield spread and future economic activities as some of the countries in consideration particularly Morocco and Nigeria have not had a long history of accurate and complete data collection.

Looking ahead, more work may be needed to understand how the yield spread is influenced by other variables including the ones mentioned earlier. Further regressions on these variables and their relationship with the yield spread may be advanced in the future.

While the author has attempted to provide interpretation for the results, the author suggests the results should be treated with caution because of the obvious data limitations and sometimes small sample size. As Alan Greenspan15 rightly suggested, yield curves should be interpreted carefully.

15

Source of the Greenspan quote is: Alan Greenspan, 2005. Letter to the Honorable Jim Saxson (Nov. 28).

47

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Bonser-Neal, Catherine and Timothy R. Morley., “Does the Yield Spread Predict Real Economic Activity? A Multicountry Analysis,” “Federal Reserve Bank of Kansas City, Economic Review, (Third Quarter 1997), 37-53.

Caporale, Guglielmo M. 1994. “The Term Structure as a Predictor of Real Economic Activity: Some Empirical Evidence”, London Business School, Discussion Paper no. 4-94, February.

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Dueker, Michael. 1997. “Strenthening the Case for the Yield Curve as a Predictor of U.S. Recession, “Federal Reserve Bank of St. Louis, Review, March/April, pp.41-50.

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Estrella, Arturo, and Frederic Mishkin. 1996. “Predicting U.S. Recessions: Financial Varaibles as Leading Indicators,” Federal Reserve Bank of New York, working paper no. 9609, May.

48

Estrella, Arturo, and Gikas A. Hardouvelis. “The Term Structure as a Predictor of Real Economic Activity,” Journal of Finance 46 (1991), 553-76.

Harvey, Campbell 1988. “The real term structure and Consumption Growth,” Journal of Financial Economics, 22, Dec, 305-333

Haubrich, Joseph G., and Ann M. Dombrosky. 1996. “Predicting Real Growth Using the Yield Curve”, Federal Reserve Bank of Cleveland, Economic Review, First Quarter, pp. 26-35.

Hu, Zuliu, 1993. “The Yield Curve and Real Activity,” IMF Staff Papers, 40, Dec, 781-806

Kessel, Reuben A. 1965. “The Cyclical Behavior of the Term Structure of Interest Rates,” National Bureau of Economic Research, Occasional Paper 91.

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