interest rates movements also at short horizons. Empirical evidence suggests that the predictive
power of the spread increases with maturity in both the single and in the threshold regimes22.
■ BETA reg1 95% conf int
■ BETA reg2 95%> conf int
■ BETA reg1 abs — 95% conf i nt
■ BETA reg2 abs — 95% conf int
Figure 7
In the single regime the slope coefficient never reaches one though. Threshold estimates of the
slope coefficient are quite close to one; so that, in each regime the predictive power of the yield
spread is substantial. In particular, the 95% confidence interval at medium-long horizons contains
the expectations hypothesis value one (the horizontal dashed line).
The advantage of employing a threshold model can be shown by a kernel density estimate23 of the
short term rate (m = 3) distribution. In Figure 8 the shape of the density estimate makes clear the
convenience of adopting a multiple regime model, since the estimated empirical distribution of the
3-month yield in regime one is peaked (central panel); that is short term interest rates are easily
predictable. The left panel plots the kernel density for the 3-month yield in the entire sample, while
the right panel shows the empirical distribution in regime 2, characterized by high values of the
term premium. The standard deviation is much lower in regime one (below the estimated threshold)
than in the other regimes; whilst the kurtosis is much higher. In regime one, characterized by low
values of the term premium the empirical distribution of the short term rate is leptokurtic.
22 In regime two when the threshold is the absolute value of the term premium this result does not hold.
23 The Epanechnikov kernel density estimation is performed with automatic bandwidth selection. These results are
obtained by focusing on the pair of maturities (60, 3); similar results hold focusing on other couples of maturities (n, 3).
In the entire sample the standard deviation of the 3-month yields is 2.62, the kurtosis is 5. In regime one (below the
estimated threshold) the std. deviation is 2.08 and the kurtosis is 7.18. In regime 2 (above the estimated threshold) the
std. deviation is 2.90 and the kurtosis is 3.80.
21