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BUS 10123 Lecture 39: • Switching models IIExam

Business Administration Interdisciplinary
Course Code
BUS 10123
Eric Von Hendrix
Study Guide

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An Application of Markov Switching Models
to the Real Exchange Rate
Purchasing power parity (PPP) theory suggests that the law of one price should always
apply in the long run such that, after converting it into a common currency, the cost of a
representative basket of goods and services is the same wherever it is purchased.
Under some assumptions, one implication of PPP is that the real exchange rate (that is,
the exchange rate divided by a general price index) should be stationary.
However, a number of studies have failed to reject the unit root null hypothesis in real
exchange rates, indicating evidence against PPP theory.
It is widely known that the power of unit root tests is low in the presence of structural
breaks as the ADF test finds it difficult to distinguish between a stationary process
subject to structural breaks and a unit root process.
In order to investigate this possibility, Bergman and Hansson (2005) estimate a Markov
switching model with an AR(1) structure for the real exchange rate, which allows for
multiple switches between two regimes.
An Application of Markov Switching Models
to the Real Exchange Rate
The specification they use is
where yt is the real exchange rate, st (t = 1,2) are the two states and
t ~ N(0,
The state variable, st, is assumed to follow a standard 2-regime Markov process.
Quarterly observations from 1973Q2 to 1997Q4 (99 data points) are used on the real
exchange rate (in units of foreign currency per US dollar) for the UK, France, Germany,
Switzerland, Canada and Japan.
The model is estimated using the first 72 observations (1973Q2 - 1990Q4) with the
remainder retained for out of sample forecast evaluation.
The authors use 100 times the log of the real exchange rate, and this is normalised to
take a value of one for 1973Q2 for all countries.
The Markov switching model estimates are obtained using maximum likelihood
Analysis of Results
As the table shows, the model is able to separate the real exchange rates into two
distinct regimes for each series, with the intercept in regime one (
1) being positive for
all countries except Japan (resulting from the phenomenal strength of the yen over the
sample period), corresponding to a rise in the log of the number of units of the foreign
currency per US dollar, i.e. a depreciation of the domestic currency against the dollar.
2, the intercept in regime 2, is negative for all countries, corresponding to a domestic
currency appreciation against the dollar.
The probabilities of remaining within the same regime during the following period (p11
and p22) are fairly low for the UK, France, Germany and Switzerland, indicating fairly
frequent switches from one regime to another for those countries' currencies.
Interestingly, after allowing for the switching intercepts across the regimes, the AR(1)
, is a considerable distance below unity, indicating that these real exchange
rates are stationary.
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