Estimation results of model (10) are reported in the second and third columns of Table 6. The left
panel of Table 6 shows the single-regime (entire sample) slope estimates of the traditional
Campbell-Shiller equation; the central panel reports the threshold estimates when the threshold
variable is the term premium; finally, in the right column the estimates are obtained from threshold
model in which the absolute value of the term premium determines the regime shifting.
Interest Rates Prediction
|
Linear Threshold: tptn,m Threshold |
tpt ■m |
|
(n. m) |
obs R2 |
β |
τ |
reg |
obs R2 |
β |
τ |
reg |
obs R2 |
β |
|
(120,3)* |
400 |
0.5846 |
1.223 |
1 |
196 |
1.2489 |
2.183 |
1 |
227 |
0.9418 |
|
0.107 |
(0.001) |
0.800 |
0.753 |
(0.000) |
0.746 |
0.475 |
(0.000) | |||
|
2 |
204 |
1.0247 |
2 |
173 |
1.0008 | |||||
|
0.562 |
(0.000) |
0.573 |
(0.000) | |||||||
|
(60,3) |
465 |
0.6592 |
1.460 |
1 |
275 |
0.9724 |
3.801 |
1 |
415 |
0.7472 |
|
0.127 |
(0.000) |
0.683 |
0.384 |
(0.000) |
0.423 |
0.202 |
(0.000) | |||
|
2 |
190 |
1.0802 |
2 |
50 |
0.9966 | |||||
|
0.594 |
(0.000) |
0.784 |
(0.000) | |||||||
|
(36,3) |
465 |
0.4761 |
1.184 |
1 |
270 |
0.6860 |
2.762 |
1 |
371 |
0.7371 |
|
0.059 |
(0.010) |
0.676 |
0.2405 |
(0.000) |
0.346 |
0.206 |
(0.000) | |||
|
2 |
195 |
0.8738 |
2 |
94 |
-0.1342 | |||||
|
0.424 |
(0.0000) |
0.005 |
(0.611) | |||||||
|
(24,3) |
465 |
0.3800 |
0.907 |
1 |
268 |
0.6898 |
1.972 |
1 |
349 |
0.6378 |
|
0.036 |
(0.032) |
0.641 |
0.218 |
(0.000) |
0.351 |
0.183 |
(0.000) | |||
|
2 |
197 |
0.8480 |
2 |
116 |
0.2096 | |||||
|
0.357 |
(0.000) |
0.010 |
(0.292) | |||||||
|
(12,3) |
465 |
0.3252 |
0.537 |
1 |
276 |
0.6263 |
0.924 |
1 |
313 |
0.8200 |
|
0.027 |
(0.032) |
0.528 |
0.148 |
(0.000) |
0.285 |
0.341 |
(0.000) | |||
|
2 |
189 |
0.6747 |
2 |
152 |
0.1001 | |||||
|
0.219 |
(0.000) |
0.003 |
(0.555) | |||||||
|
76,3) |
465 |
0.0716 |
0.403 |
1 |
347 |
0.6548 |
1.964 |
1 |
458 |
0.3708 |
|
0.001 |
(0.700) |
0.383 |
0.115 |
(0.000) |
0.350 |
0.038 |
(0.001) | |||
|
2 |
118 |
0.2784 |
2 |
7 |
1.6461 | |||||
|
0.022 |
(0.313) |
0.348 |
(0.018) |
sample jan64-sep02; *jan64-mar97.
The estimated value of the threshold variable (τ), the joint20 goodness of fit (j-R2), the number of
observations (obs.), the goodness of fit in each regime (R2), the slope estimated coefficient ( β) and
the associated p-values of the t-test (in parenthesis) are shown for each regime (reg).
Table 6
The estimated slope coefficient in the entire sample (left panel) tends to increase with maturity n. In
the single regime setting, at the very short end the spread is not informative about future movements
of short term interest rates; results substantially improve in the threshold setting, as long as in both
regimes β estimates increase and become statistically significant. The joint goodness of fit is much
20 The joint goodness of fit (j-R2) is computed as “one minus the ratio between the sum of the residual sum of squares in
both regimes and the total sum of squares in the single regime”. The goodness of fit measures the proportion of the
variability in the dependent variable which can be explained by the explanatory variables.
19