---CS (60,3) roll60
stderr
----p-val
---CS (120,3) roll60
stderr
----p-val
Figure 5
These results, coupled with the statistical tests performed in Section 4, suggest the presence of non
linearity in the empirical equation used to test the expectations hypothesis15. In particular, the slope
estimates tend to be statistically not significant when both the level and the volatility of term premia
are large16.
There is broad consensus on the role played by that time-varying term premia in explaining the
empirical failure of the expectation hypothesis (Fama, 1986; Cook and Hahn, 1989; Campbell,
1995; Lee, 1995; Tzavalis and Wickens, 1997). In the expectational model the term premia effect is
captured partially by the residual term and partially by the intercept of the model. Consequently, a
change in the level of term premia, due for instance to changing conditions of the economy, affects
the empirical assessment of the expectations theory; the term premia effect cause a shift in the
intercept of the model, which in turns generates a bias in the slope estimate; we thus suggest that
linear models are not appropriate to test the EH.
In order to deal with this evidence we suggest estimating the Campbell-Shiller equation with a
threshold model; hence, we allow the term premium to be, not only time-varying, but also regime-
dependent ( tpt, m (f ) ); in particular, regimes are determined by the value of the term premium as
shown below:
15 Equation (9) has been estimated in the entire sample (between 1964 and 2002); then we have performed the Chow
breakpoint test performed to check for structural breaks. The test has failed to reject the null hypothesis of absence of
structural break for the dates when the term premium displays highest local volatility. In addition, residuals obtained by
the OLS estimation of (9) are both serially correlated and heteroscedastic; the Newey and West correction help to deal
with this problem.
16 Mankiw and Miron (1986) point out that the uncertainty regarding the future path of interest rates can explain the
empirical failure of the expectations theory. In particular, they argue that the random walk behaviour of the short term
rate, due to the interest rate smoothing policy of the Federal Reserve, affect the predictability of short rates. They
identify the breakpoint with the creation of the Fed in 1914.
17