School

Kent State UniversityDepartment

Business Administration InterdisciplinaryCourse Code

BUS 10123Professor

Eric Von HendrixStudy Guide

FinalThis

**preview**shows page 1. to view the full**4 pages of the document.**• 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,

2).

• 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

estimation.

• Results

• 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)

coefficient,

, is a considerable distance below unity, indicating that these real exchange

rates are stationary.

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