The name is absent

Figure 4 plots the F sequence to test for the presence of a threshold. The null hypothesis of linearity
is rejected against the alternative of one threshold if the F sequence exceeds the 5% critical value
line. In both cases, i.e. for both couples of maturities (60, 3) and (120,3), there is clear evidence of
non linearity.

In this paper, asymmetry can be regarded as any non-constant effect of the yield spread on the
theoretical spread. In testing for non linearity, Andrews (1993) points out that searching over a grid
invalidates standard statistical inference: assessing the significance of the threshold with the usual t-
statistics is actually not feasible. Hansen (1996) has proposed a method to overcome this issue. He
suggests making inference using p-values obtained by estimating an asymptotic distribution of the
test statistic through bootstrapping. In this work, we use 1000 bootstrap replications to simulate the
asymptotic distribution. In Table 3 we report the bootstrap probability values. The null hypothesis
of absence of threshold effect (linearity) is rejected in favour of a multiple regime model. The
threshold variables tested for non linearity in the Campbell-Shiller equation are both the term
premium and its absolute value, respectively in the first and in the second row of Table 3.

Test for Non Lineairty
long term maturity ( n )

6      12      24      36      60     120*

_t n, m

^tpt (0.001)  (0.000)  (0.000)  (0.000)  (0.000)  (0.000)

∖^tpn^t  I (0.022)  (0.000)  (0.000)  (0.000)  (0.000)  (0.000)

sample jan64-sep02; bootstrapped p -values; *400 obs

Table 3

In the following part of this Section we provide some further evidence of non linearity in the
equation to test the EH. Parameter instability in Equation (5) would eventually provide a
justification for estimating a non linear econometric model. Hansen (1992) has proposed a test to
check for parameter constancy in linear models which does not require any prior knowledge of the
timing of the structural break; this feature makes the test appealing compared to the popular Chow

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