IN-SAMPLE RESULTS

Page 81 of 119 Table 5.4: The in-sample estimations of foreign term spreads

k=1 k=2 k=3 k=4 k=5 k=6 k=7 k=8 CHINA RESULTS TERM SPREAD ( ) -0.7478 -1.1047 -1.2845 -1.1848 -0.9083 -0.5112 0.3996 1.2444 z-statistic -1.8627 -1.9139 -2.2845 -2.2793 -1.8855 -1.0204 -- -- p-value 0.0451 0.0556 0.0223 0.0226 0.0594 0.3075 -- --

LAGGED RECESSION INDICATOR ( )

2.6339 1.6949 0.8364 0.0408 -0.7219 -1.2393 -7.6191 -7.4605 z-statistic 3.1666 2.2659 1.2122 0.0612 -1.0313 -1.6009 -- -- p-value 0.0015 0.0235 0.2254 0.9512 0.3024 0.1094 -- -- Pseudo R-squared 0.7488 0.5956 0.4917 0.3502 0.2301 0.1696 0.4013 0.5872 Schwartz-Bayesian 0.9193 1.1359 1.2672 1.4265 1.5439 1.5818 1.2933 1.1292 RMSE 0.3035 0.3445 0.3663 0.4098 0.4446 0.4948 0.5189 0.3344 Variance Proportion 0.3035 0.2532 0.2496 0.2480 0.2790 0.3457 0.1481 0.1662

UNITED STATES RESULTS

TERM SPREAD ( )

0.0182 -0.1186 -0.1528 -0.2339 -0.2706 -0.2562 -0.2981 -0.2043

z-statistic 0.1239 -1.0149 -1.4022 -2.1366 -2.4397 -2.2757 -2.4068 -1.7580

p-value 0.9014 0.3101 0.1609 0.0326 0.0147 0.0229 0.0161 0.0787

LAGGED RECESSION INDICATOR ( )

2.5984 1.7814 1.1412 0.5883 0.0254 -0.3515 -0.6113 -0.6381 z-statistic 6.7962 5.4363 3.7758 2.0132 0.0874 -1.1986 -2.0343 -2.1332 p-value 0.0000 0.0000 0.0002 0.0441 0.9304 0.2307 0.0419 0.0329 Pseudo R-squared 0.6619 0.3860 0.1888 0.0970 0.0782 0.0935 0.1439 0.1128 Schwartz-Bayesian 0.7937 1.1358 1.3534 1.4498 1.4691 1.4531 1.4003 1.4364 RMSE 0.5134 0.4737 0.4824 0.4788 0.4772 0.4779 0.4865 0.4941 Variance Proportion 0.5913 0.6827 0.6839 0.6201 0.5880 0.5894 0.4911 0.5738 GERMANY RESULTS TERM SPREAD ( 0.0257 0.0265 0.0873 0.1530 0.2385 0.3419 0.4102 0.4440 z-statistic 0.1356 0.1674 0.5946 1.0738 1.6777 2.2646 2.5703 2.6927 p-value 0.8921 0.8671 0.5521 0.2829 0.0934 0.0235 0.0102 0.0071

LAGGED RECESSION INDICATOR ( )

2.7838 1.9301 1.3999 0.9639 0.5751 0.2974 0.0155 -0.1714 z-statistic 5.5878 4.6385 3.5813 2.5424 1.5376 0.7718 0.0395 -0.4336 p-value 0.0000 0.0000 0.0003 0.0110 0.1241 0.4402 0.9685 0.6646 Pseudo R-squared 0.7010 0.4350 0.2319 0.1001 0.0520 0.0874 0.1539 0.2068 Schwartz-Bayesian 0.7590 1.0973 1.3250 1.4631 1.5112 1.4736 1.4100 1.3592 RMSE 0.5663 0.4917 0.4944 0.4984 0.4927 0.4798 0.4619 0.4476 Variance Proportion 0.6239 0.7082 0.7003 0.6399 0.5591 0.4649 0.4223 0.4058

Source: Eviews results

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Observe the results for the Chinese term spreads in the above table. The optimal lag of the best-fit model is at 1 quarter earlier (i.e. k =1). This lag is characterized by the

highest of 0.7488, the lowest SIC of 0.9193 and the lowest RMSE of 0.3035

compared to measures at other lags (i.e. from k=2 to k=8). These RMSE and values are similar to those produced by the S.A. best-fit model. At the optimal lag both the coefficients of the term spread and the lagged recession indicator are statistically significant at both 5% and 10% at significant levels with z- statistics of -1.8627 and 3.1666 respectively and at p-values of 0.0451 and 0.0015 respectively. This suggests that the Chinese term spread is best at predicting S.A. recessions, given the Chinese spread and the S.A. recession indicator 1 quarter earlier. As such, the best-fit model for China is presented below:

The equation above quantifies the probability of a recession in S.A. given the Chinese spread and the S.A. recession indicator 1 quarter earlier.

View the result for the U.S. term spread in Table 5.4 above. The optimal lag of the best- fit model is represented by k=5. This is because at this lag, despite the of 0.0782 not being the lowest, and the SIC of 1.4691 not being the lowest, the lag is selected based on the lowest RMSE of 0.4772 compared to other lags. This high RMSE might be due to the fact that the lagged recession variable from an emerging country such as S.A. is modelled with the term spread from a developed country such as the U.S. As such, this suggests that the U.S. term spread predictions of S.A. recessions might not be accurate. At the optimal lag of 5, the t-statistics of -2.4397 is statistically significant at 5% and 10% significant levels indicated by the p-value of 0.0147. However, the lagged recession indicator is insignificant even at 10% significance level with a p-value of 0.5880. As such the best-fit model is as follows:

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The above best-fit equation provides the probabilities of S.A. being in a recession given the U.S term spread and the S.A. recession indicator 5 quarters earlier.

Finally, examine Table 5.4 for the German term spread results. The best-fit model optimal lag is at 8 quarters (i.e. k = 8). Also in this case, the of 0.2068 is not the highest and the SIC of 1.3592 is not the lowest. But the RMSE of 0.4476 is the lowest compared to other lags. The high RMSE suggests that the German term spread might be accurate in predicting S.A. recessions. This might be due to a similar reason as in the case for the U.S. that the lagged recession variable from an emerging country such as S.A. is modelled with the term spread from a developed country such as Germany. However, the t-statistics are significant at this lag with a p-value of 0.0071. As such, the best-fit model is represented as follows:

This model generates the probabilities of S.A. recessions, given the German spread and the S.A. recession indicator 8 quarters earlier. Table 5.5 below illustrates the use of the Chinese, U.S. and Germany best-fit models in generating the predictions for S.A. recessions. The term spreads used are in the period from 1995:Q2 to 1998:Q1. Part of the period indicates the time when S.A. was not in a recession (i.e. indicated by 0) and the other part indicates the time when S.A. was in recession (i.e. indicated by 100).

Page 84 of 119 Table 5.5: Probabilities of recession from the foreign best-fit models

QUARTERS 1995/2 1995/3 1995/4 19961 1996/2 1996/3 1996/4 1997/1 1997/2 1997/3 1997/4 1998/1 ACTUAL PROBABILITY (Yt) % 0 0 0 0 0 0 100 100 100 100 100 100 CHINA TERM SPREAD SLOPE (Xt-1) 0.55 -0.27 -0.26 -0.53 0.21 0.58 0.73 -0.02 -0.29 -1.33 -1.11 -1.14 PROBABILITY (t) % 7.55 15.59 15.43 18.89 10.39 7.33 86.76 93.33 94.94 98.50 98.02 98.10 U.S TERM SPREAD SLOPE ((Xt-5) 0.63 0.75 0.49 1.18 1.55 1.67 1.25 1.59 1.32 1.00 0.45 0.523 PROBABILITY (t) % 64.12 62.90 65.53 58.43 54.49 53.20 58.68 55.07 57.94 61.29 66.85 66.13 GERMANY TERM SPREAD SLOPE (Xt-8) 2.39 2.41 1.94 3.05 3.26 3 2.66 2.77 2.64 2.41 1.81 1.47 PROBABILITY (t)% 75.62 75.89 68.94 83.82 86.00 83.27 73.97 75.53 73.68 70.25 60.45 54.54

Source: Calculated Probabilities using the best-fit model equations (5.2, 5.3 and 5.4) (=NORMSDIST

( ))

Table 5.5 above indicates that in 1995Q2 given the S.A. recession indicator and the Chinese, U.S. and German term spreads at 1, 5 and 8 quarters earlier respectively, the probabilities were about 7.55%, 64.12% and 75.62% respectively that S.A. would be in a recession. Similarly, in 1997Q3 the probabilities were about 98.50%, 61.29% and 70.25% respectively. As the literature suggests that recessions are signalled by a negatively sloped yield curve, observe from the Table above that the slope of the Chinese term spread was positive in the periods of no recessions, from 1995Q2 to 1996Q4. This is indicated by the term spread values increasing in that period until 1996Q4. However, during the recession periods, the slope of the Chinese term spread was positive, indicated by term spread values decreasing until 1997Q3, and started

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increasing from that period, as S.A. was exiting the recession. Similarly, the U.S. term spread started decreasing from 1997Q1 as S.A. was entering the recession, and began to increase in 1998Q1, indicating a recovery. The probabilities of recession in this period remained above 55%. However, the high probabilities in no recession periods incorrectly predicted the occurrence of a recession. In the case of Germany, despite the negatively sloped yield curve in the recession periods accompanied by high probability levels, the probability levels were as high as about 70% in periods where S.A. was not in a recession. The implication is that the German term spread did not follow accurately the expected behaviour as observed in the literature when forecasting S.A. recessions.

It is important, however, to evaluate how well the estimated best-fit models of China, the U.S. and Germany predicted the S.A. recessionary events in the entire in-sample time frame. Figures 5.4, 5.5 and 5.6 illustrate this.

Figure 5.4: The probabilities of recessions from the Chinese best-fit model

0.0 0.2 0.4 0.6 0.8 1.0 1995 1996 1997 1998 1999 2000 y ears /quarters Pr ob ab ilit ie s

Source: Eviews prediction in_sample forecasts

Figure 5.4 represents the S.A. recessionary predictive performance as found by China. The general observation from the graph shows that the Chinese best-fit model in this instance accurately predicted the 1996 S.A. recession as early as about 2 quarters earlier. Before the recession the graph shows that the probability graph was above 60% about 2 quarters before the 1996 recession, correctly indicating a looming future recession. At the start of the recession, the graph decreased just below 60% and sharply increased to about above 80% during the recession, accurately predicting the

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occurrence of a recession. The probability graph remained high above 80% during the recession and decreased to below 20% after the recession.

Figure 5.5: The probabilities of recessions from the U.S. best-fit model

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 y ears /quarters Pr ob ab ilit ies

Source: Eviews prediction in_sample forecasts

Figure 5.5 indicates that U.S. term spread somewhat predicted some S.A. recessions and not so many others. The graph shows that before the 1992 recession, the probability graph increased from just above 40% to about 60% probability at the start of the recession. The graph remained above 70% during the recession and decreased to below 50% after the recession. At the start of the 1989 recession, the graph shows that the probabilities were just above the 40% and increased to above 70% during the recession. The graph decreased as S.A. was recovering from the recession. During the 1996 recession, the probability graph remained at above 50% and above 60% towards the end of the recession, and seemed to be decreasing after the recession. However, the U.S. term spreads provided probabilities above 50% around 1981, 1983 and 1987 of S.A. being in a recession. According to the recession rule stated by Moolman (2003:300) that a probability of above 50% is regarded as a predicted recession, these predictions by the U.S. best-fit model were incorrect.

Page 87 of 119 Figure 5.6: The probabilities of recessions from the German best-fit model

.1 .2 .3 .4 .5 .6 .7 .8 .9 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 y ears /quarters Pr ob ab ilit ie s

Source: Eviews prediction in_sample forecasts

Shown in Figure 5.6 is the performance of the German term spread. Observing the graph it indicates that during the recession periods, the probability graph was as high as above the 70% probability. This was the case for recessions in 1985, 1989 and 1996. However, around late 1986 the probability graph provided was as high as about 60%, which provided an incorrect probability of S.A. being in a recession. Observe as well that around halfway during the recession of 1989, the probability graph dropped to below 40%, despite S.A. being in a recession in that period. The following section presents the results for the out-of-sample S.A. recessions as forecast by each of the foreign term spreads.