1038 The Econometrics of Exchange Rates
post-war periods. His evidence suggests that there are few profitable violations of
CIP, even during periods of market uncertainty and turbulence, which contrasts
with the results in earlier studies, thus illustrating the crucial role that appropriately
sampled data can play.
A second method for testing CIP widely used in the early literature is to employ
regression analysis and test whetherα=0 andβ=1 in the regression:
ft−st=α+β(it−i∗t)+ut. (22.28)If CIP holds, on average we should obtain estimates ofαandβdiffering insignifi-
cantly from zero and one, respectively. However, as noted by Taylor (1987),̂α= 0
and̂β=1 is a necessary but not a sufficient condition for CIP to hold. These
restrictions could be met but the error term might be of such magnitude as to
permit substantial arbitrage possibilities.
A more recent approach to modeling deviations from CIP is to employ univari-
ate threshold models (see Balke and Wohar, 1998; Peel and Taylor, 2002).^37 The
rationale of the univariate threshold model is, of course, to capture the transac-
tions band that arbitrageurs face in reality. This method of analysis was explained
in section 22.2. A complementary method is to model the dynamics of adjustment
of each component of CIP by the threshold error correction model set out by Balke
and Fomby (1997).
Peel and Taylor (2002) applied this model, as well as the univariate threshold
model, to weekly data in the interwar period 1922–25. We outline their method
for estimating the threshold error correction model. If we define the vectorXt=
(it,i∗t,ft−st)′, the deviation from CIP,δt, may be viewed as an error correction term
relating the three elements ofXt, sinceδt=ft−st−(it−i∗t). A simple first-order
threshold vector error correction model (TVECM) may be written as:
Xt=⎧
⎪⎪
⎨
⎪⎪⎩Et if∣∣
δt− 1∣∣
<κ,
θ+δt− 1 +Et ifδt− 1 ≥κ,
−θ+δt− 1 +Et ifδt− 1 ≤−κ,(22.29)whereEtisa(3×1) disturbance vector, andandθare (3×1) parameter vectors.
Within the band, the error correction term has no effect on any of the variables
and there is no tendency to adjust toward CIP. However, once outside the band,
we expect at least one of the elements into be non-zero. In that case, one or
more offt−st,it, andi∗tadjust toward CIP so thatδtalso adjusts. The statistical
significance and relative size of the estimated elements of, the error correction
parameters, should give an indication of the relative speeds of adjustment of the
components of CIP to large deviations from CIP.
If we define the indicator variables 1 (|δt− 1 |<κ), 1 (δt− 1 ≥κ)and 1 (δt− 1 ≤−κ),
each of which takes the value unity when the inequality indicated in parentheses
is satisfied, and zero otherwise, the TVECM may be written as a set of dummy
variable regressions:
Xt= 1 (δt− 1 ≥κ)θ− 1 (δt− 1 ≤−κ)θ+[ 1 − 1 (|δt− 1 |<κ]δt− 1 +Et. (22.30)