pt is the probability that the state of economy will switch from the current state A to a
new state B at t + 1. Suppose the current state is preserved. Then the forecast error
can be decomposed into two components, the rational expectations forecast error and the
unfulfilled expectations about the policy change, as:
stA+1 - Etst+1 = ηtA+1 + pt∆e st+1 (8)
where ηtA+1 = stA+1-Et(st+1 |A) is the rational expectations forecast error, ∆e st+1 = Et(st+1|A)-
Et(st+1|B) represents the expectations about the policy change, and the superscript A de-
notes state A. Accordingly, using equation (3b), together with equation (8), implies the
following estimable UIP equation:
stA+1 - st = β0 + β1 (ft1 - st) + εt+1 (9)
where εt+1 = ηtA+1 + pt∆e st+1 + ut+1, and ut+1 is a white noise error term. Note that εt+1
is no longer a zero-mean stationary process since it depends not only on white-noise error
terms, ηtA+1 and ut+1, but also on expected policy changes, pt∆e st+1. Accordingly, under the
assumptions of risk neutrality and independently-formed exchange rate expectations over
the two states, one can show that
cov(εt+1, ft1 - st) = pt [(1 -pt) var(Et(st+1|A)) -pt var(Et(st+1|B))] 6= 0 (10)
which implies a biased slope term when equation (3b) is estimated under the incorrect
assumption that the error term is white-noise. Moreover, it can be shown that when the
probability, pt , is sufficiently high, the peso problem causes a downward bias in the slope
term.
As this bias dissipates when the state changes from A to B, it is possible to compare the
results of the two regressions: the one that excludes the period in which the state is expected
to change, i.e. the peso problem prevails, and the other that uses the whole sample. This
approach has been pursued by Flood and Rose (1996) and Sachsida et al. (2001).
Flood and Rose (1996) document for the countries in the European Monetary System
that the exclusion of the realignment dates of bilateral DM central parities implies a 0.5
15
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