A further investigation on the usefulness of adopting a threshold model is provided by the statistical
results of the Wald test. In the two regime framework the probability of rejecting the null
hypothesis of β = 1 occurs less frequently, as show in Table 7.
Wald Test H0: β = 1
|
linear |
th = tptn,m |
th = |
tp" ’ m | |||
|
(p-val) |
reg. |
(p-val) |
reg |
(p-val) | ||
|
(120,3)* |
(0.0355) |
1 |
(0.0002) |
1 |
(0.3784) | |
|
2 |
(0.6925) |
2 |
(0.9896) | |||
|
(60,3) |
(0.0434) |
1 |
(0.7948) |
1 |
(0.0006) | |
|
2 |
(0.1901) |
2 |
(0.9643) | |||
|
(36,3) |
(0.0085) |
1 |
(0.0154) |
1 |
(0.0005) | |
|
2 |
(0.0897) |
2 |
(0.0000) | |||
|
(24,3) |
(0.0011) |
1 |
(0.0002) |
1 |
(0.0000) | |
|
2 |
(0.0892) |
2 |
(0.0001) | |||
|
(12,3) |
(0.0000) |
1 |
(0.0010) |
1 |
(0.0058) | |
|
2 |
(0.0020) |
2 |
(0.0000) | |||
|
(6,3) |
(0.0000) |
1 |
(0.0018) |
1 |
(0.0000) | |
|
2 |
/ |
2 |
/ | |||
sample jan64-sep02; *jan64-mar97. p-values in parenthesis
Table 7
Finally, as a further robustness check we run a rolling estimate of the Campbell-Shiller equation in
both regimes. The following figures show the time-varying behaviour of the slope coefficient in
each regime (regime one in the left panel; regime two in the right panel). Estimates are obtained by
estimating a rolling OLS (Newey-West corrected) on sequential samples of 50 observations. The
plot of βt over time is smooth and stands closely around one (horizontal solid line). Furthermore,
in each regime the slope coefficients are statistically significant as opposed to the rolling βt
estimates obtained in the single regime setting (Figure 6). Figure 9.a is obtained from rolling the
22
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