The main reason behind our methodological choice stands in the key difference between threshold
modelling and a structural change model. Although conceptually similar, the difference between
these model is important. In a standard structural change (SC) model the sample is split at one point
in time, hence regimes are defined temporally. In this study, instead, we focus on the possibility that
regimes can switch back and forth depending on the value of a threshold variable. Threshold
modelling is a flexible tool which allows to capture switches in regime that occur frequently over
time, as it might happen in bond markets; interest rates dynamics are highly responsive to a
complex sequence of small macroeconomic and financial shocks, so that agents reformulate
continuously their expectations as soon as new information become available. SC and THR are
different also from a statistical point of view, since structural change models usually imply a time
trend, either in the explanatory or in the threshold variable (or both), that affects the distribution of
the threshold variable, which is, instead, stationary in THR models.
In the next Section we estimate a threshold model for term premia with two regimes:
n-m
m }ye
n ) q=0
m
t t+mq
n-m
m }∑E
n ) q=0
im
t t + mq
m nm
- it = α+ β(it - it )+ εt
m nm
- it = α+ β(it - it )+εt
th ≤ ^
th > ^
(6)
The threshold variable th is either the term premium tptn,m or its absolute value. The term premium
is computed as the unexpected change in short term rates, so that it captures the risk adverse attitude
of economic agents. The term premium is obtained by subtracting the short term yield from both
sides of Equation (2). Equation (1) shows that the yield spread can be decomposed into an
expectational component and a term premium9.
The threshold methodology allows us to match two salient features outlined in the empirical
literature regarding the EH. On the one hand, we allow the term premium to be time-varying; in
particular, the term premium is also assumed to be regime-dependent tp(τ, t, n, m). On the other
hand, we follow Mankiw and Miron (1986), who put forward the idea of using some measure for
uncertainty to separate regimes. They suggest that the predictive ability of the spread is conditional
on the agents’ capability of anticipating future movements in short rates; in particular, they argue
that the short term rate has become a martingale, and thus unpredictable, after the founding of the
Federal Reserve System: “the Fed has announced to stabilize -or even to peg- the interest rates”.
9 It is possible to demonstrate that the term premium is a function of the future path of the stochastic discount factor (or
pricing kernel) used to price any asset in the economy. The stochastic discount factor provides with a measure of the
intertemporal marginal rate of substitution.
11