Leicester University Ec 3064 Project Template

1 This three-way voting system is not, in practice, often implemented by the Central Banks, however, it is arguably the simplest. We have examined the behaviour of a number of alternative voting schemes though the differences in outcome schemes are negligible.

2

Student No.: 119047265

TESTING FOR PURCHASING POWER PARITY BETWEEN

DENMARK, SWEDEN AND UK

Course project prepared within the EC3064 module

Applied Econometric Project

University of Leicester, 2014

Date of Submission: 15/05/2014

1 This three-way voting system is not, in practice, often implemented by the Central Banks, however, it is arguably the simplest. We have examined the behaviour of a number of alternative voting schemes though the differences in outcome schemes are negligible.

3

EXECUTIVE SUMMARY

This project concentrates on explaining the relationship between nominal exchange rates and price levels with particular focus on the relationship’s macroeconomic policy implications. Using annual data from 1975-2013, long-run models were developed to test how the price level ratio effects the bilateral nominal exchange rate. All data was taken from the OECD database and the countries investigated were Denmark, Sweden and UK with Denmark acting as the domestic country. These models failed to prove that movements in the nominal exchange rate were solely down to changes in the price ratio. Therefore it must be concluded that strong purchasing price parity doesn’t hold. However, they did indicate that the bilateral nominal exchange rates between Denmark and Sweden, and Denmark and UK were, in part, determined by the differencing price levels between the two countries. The tests indicated that some of the deviations in the nominal exchange rates were down to fluctuations in the price ratio. However, the low r squared values indicated that only a small percentage of nominal exchange movements can be explained by changes in the price level. The results might be weakened as the same time period might not have been long enough. Some of the tests used have also been criticized for their lack of strength.

1. INTRODUCTION (OR PROBLEMS ADDRESSED)

Purchasing Power Parity (PPP) is an economic theory which claims that the nominal

exchange rate between two countries should be equal to the ratio of aggregate price levels

between those two countries, so that a unit of currency of one country will have the same

purchasing power in a foreign country. While some economists argue that PPP doesn’t

hold in the short-run most intrinsically believe that real exchange rates converge to the

PPP level. PPP is based on the law of one price (LOP) which is an economic assumption

that assumes that prices should be the same across the world when adjusted for their real

exchanges rates. If this was not the case rational agents would take advantage of the

resulting arbitrage opportunities to make risk free profit until prices equalised. Much of

economic theory is based on the assumption that agents act rationally so to reject the

theory of PPP is to dispute the assumption that underpins much of economic theory.

However, empirical studies have only found limited evidence in support of the theory.

This has led economists such as Taylor and Taylor (2004) to call it the PPP puzzle1. The

existence of PPP will not only have a huge impact on macroeconomic policy making but

will also provide evidence in support of wider economic theory as a whole.

In this paper the theory of purchasing price parity will be tested using three European

countries. These countries are Denmark, Sweden and UK with the Denmark Krona acting

as the domestic currency. Strong and weak PPP was tested between Denmark and the

Sweden and between Denmark and the UK.

PPP is often used to develop economic comparisons of market conditions in different

countries. It is an essential tool for converting nominal measures into real measures. For

example, PPP is often used to equalise estimates of gross domestic product. It is also

widely used in the formulation of real exchange rates and comparing the cost of living

between countries.

The understanding of how exchange rates adjust is central to exchange rate policy. PPP is

seen as an ‘anchor’2 for long run exchange rates and hence provides an insight into the

1 Taylor, A.L and Taylor, M.P (2004). ‘The Purchasing Power Parity Debate’ Journal of Economic Perspectives 18, P135-1582 Rogoff K, “The Purchasing Power Parity Puzzle”, Journal of Economic Literature, Volume 34, 1996, pages 647

potential under and overvaluation of a country’s currency. In theory PPP allows policy

makers to extrapolate the economic impacts caused by long-term fluctuations in exchange

rates. The importance attached to predicting the movements of exchange rates and price

levels has stimulated a considerable amount of literature and the significance of the

concept of PPP to macroeconomic policy making is the inspiration for this paper.

In this paper I will use cointegration analysis and test the stationarity of real exchange

rates in order to test for the long run existence of PPP between Denmark and Sweden and

Denmark and the UK. The hypotheses will be tested using the two step Engl-Granger

cointegration test and the stationarity of the real exchange rates will be determined by

augmented Dickey-Fuller tests.

2. ECONOMIC THEORY AND PPP

Purchasing power parity (PPP) states that a unit of currency will have the same

purchasing power anywhere in the world. Ever since the term was coined in 1918 by

Cassel the theory has been the subject of much debate and empirical study. PPP is the

best known theory of the real exchange rate and understanding how exchange rates move

is an essential prerequisite to understanding exchange rate policy and ultimately

successful macroeconomic policy making. If PPP holds then exchange rates will adjust to

a level predetermined by PPP. This determines the extent to which the macroeconomic

system is self-equilibrating and as a result dictates the optimum level of macroeconomic

intervention in the financial markets3.

PPP claims that a unit of currency should be able to buy the same number of goods in one

country as it can in a different country. In other words there is parity in the purchasing

power of currency across economies. The theory of PPP is based on the law of one price.

This law states that a good must sell for the same price in all locations. If this was not the

case there would be arbitrage opportunities. The mechanism behind PPP is the idea that

differences in price of the same good in different countries will open up the prospect of

risk free profits to be made by buying the good in one country and selling it in another.

PPP states that all currencies must have the same real value in every country.

3 Rogoff K, “The Purchasing Power Parity Puzzle”, Journal of Economic Literature, Volume 34, 1996, pages 647

2

Although in its simplest form PPP is an attractive and intuitive theory there are some

complications when the theory is put into practice. The presence of transportation costs

for example can rule out a simple comparison of relative prices. While profitable

arbitrage situations might still exist, purchasing parity will no longer exist as traders will

have additional costs associated with transporting goods. Many countries also impose

trade barriers and tariffs which violate the law of one price. The border effect, first

observed by Engel and Rogers (2006), found that cities that were further away had

greater differences in prices.4 This price difference increased dramatically across

international borders. On top of this it is often hard to compare the price level across

economies. Different countries tend to produce differentiated goods which are not

perfectly substitutable. Moreover, goods in aggregate price indices will have different

weights. For example if the USA drinks more coffee than the French, then coffee will

have a heavier weight in the USA price index than in France. This makes it difficult to

compare price indices internationally. On top of this, many goods and services are not

traded between all counties.

Despite these objections it is often assumed that PPP will hold to a degree due to the

possibility of international arbitrage. There are two ways in which the PPP theory might

hold. Absolute PPP holds when the purchasing power of one unit of currency is equal in

the domestic country and in a foreign country. Relative PPP implies that the changes in

the exchange rate offset the changes in the price level of the countries concerned. If

absolute PPP holds then relative PPP should also hold. However, it is possible for relative

PPP to hold while absolute PPP is void, since common changes in nominal exchange

rates are happening at different levels of purchasing power for the two currencies. Due to

goods in different countries often being differentiated it is hard to determine whether an

identical basket of goods is available in each country. Therefore it is more common to

test for relative PPP.

PPP has been the subject of much empirical investigation. According to Sideris (2005)

many empirical studies on PPP have found little or no evidence of the theory. Most of the

early studies on PPP were based on the time-series analysis of short spans of data of 10

years or less Nusair (2003). Almost all of this analysis found no evidence in favour of

4 Charles Engel & John H. Rogers, 2006"The U.S. Current Account Deficit and the Expected Share of World Output,"NBER Working Papers 11921, National Bureau of Economic Research, Inc.

3

PPP. One possible reason for this is that most studies are unable to use data that spans a

great enough time period. Before 1971 most currencies were tied to the price of gold

through the Bretton-Woods agreement and the major currencies have only been floating

against each other in since 1973. Frankel (1986) claimed that the reason many studies

failed to find evidence in favour of PPP was due to the lack of power. Even if arbitrage

corrects unbalanced exchange rates the adjustment may not be immediate. Information

about arbitrage opportunities might take time to become available. It is possible that PPP

may not hold in the short run but that it may hold in the long run. There can be short run

deviations from PPP even if there is a long run tendency for PPP to hold. Rogoff

summarized this paradox neatly with the quote ‘While few empirically literate

economists take PPP seriously as a short-term proposition, most instinctively believe in

some variant of PPP as an anchor for real exchange rates.’5 Depending on the sample

size, and type of tests employed, some evidence in the favour of long run PPP has been

found. Yet, the speed of convergence to PPP is extremely slow Nusair (2003)6.

The failure of PPP in the short run led to a series of formal tests for evidence of PPP as a

long-run phenomenon. These studies claimed that PPP is retained in the long-run but

allowed for short-run deviations from the PPP price level. If the real exchange rate

displays reversion to its mean then it will settle at a certain value. The only necessary

condition for relative PPP to hold in the long run is the presence of mean reversion. For

absolute PPP to hold the real exchange rate must revert to the PPP real exchange rate

level. Adler and Lehmann (1983) investigated whether real exchange rates converged on

a particular level or whether they followed a random walk by checking the stationarity of

the real exchange rates.7 However, this early study suffered from low power and was

unable to reject the null hypothesis of a random walk.

In the late 1980’s more sophisticated econometric methods were employed in the

investigation of long-run PPP. These new empirical studies were based on the concept of

unit roots. If a unit root is present in a time series function then shocks persist forever and

the function is described as non-stationary. If there are no unit roots present,the time

5 Rogoff K, “The Purchasing Power Parity Puzzle”, Journal of Economic Literature, Volume 34, 1996, pages 64767 Nusair, S.A 2003. "Testing The Validity Of Purchasing Power Parity For Asian Countries During The Current Float" Journal of Economic Developmentvol. 28(2), pages 129-1477 “Deviations from Purchasing Power Parity in the Long Run” Adler M and Lehmann Bruce

4

series will eventually converge on a level. In other words relative PPP holds when there

are no unit roots present. However, empirical studies applying these tests on real

exchange rates unanimously failed to reject the null hypothesis of a unit root. This

resulted in a failure to find evidence of long-run PPP.

On the one hand Frankel (1990) pointed out that not being able to find sufficient evidence

required to reject the null hypothesis does not mean that we have to accept the null

hypothesis as true.8 Frankel explained that the statistical tests used to examine the long-

run stationarity of the real exchange rate may not have enough power to reject the null

hypothesis. This would have been especially true at the time when empirical studies were

based on data covering little more than 15 years. The argument was that even if the real

exchange rate did tend to revert to its mean over long periods of time, examination of the

real exchange rate over a relatively short time period may not be enough to detect this

mean reversion (Taylor and Taylor 2004). Due to sticky prices the real exchange rates

could take a long time to revert to its mean and this makes it almost impossible to reject

the unit root hypothesis without utilising a large dataset.

One the other hand Adler and Lehmann (1983) observed fixed and floating exchange

rates and were unable to reject the null hypothesis of a random walk.9 This led them to

question cointegration and claim that real exchange rates followed a random walk. This

rejection of cointegration led many to question PPP with Dornbusch stating that even if

PPP held in the long run the mean reversion time was so long that the theory ‘was of little

or no use empirically’.

One way to glean more information about the long-run behaviour of real exchange rates

is to increase the number of years of data. However, as we have already discussed this

was not a feasible option due to the Bretton Woods agreement. Another approach which

was used was to use more countries. The more information used in the tests should

increase their power.Taylor and Sarno (1998) suggested testing the hypothesis that that at

least one real exchange rate was not mean reverting.10 If this hypothesis could be rejected 8 Frankel, Jeffrey A., 1990. "And Now won/Dollar Negotiations? Lessons from the Yen/Dollar Agreement of 1984,"Department of Economics, Working Paper Series qt851615wb

9

10 Taylor, Mark P. & Sarno, Lucio, 1998. "The behavior of real exchange rates during the post-Bretton Woods period,"Journal of International Economics, Elsevier, vol. 46(2), pages 281-312

5

then it could be claimed that all of the tested real exchange rates were mean reverting.

However, once again this test suffered from a lack of power and no conclusive

conclusions could be formed.

As time passed more advanced econometric techniques were used to combat the problem

of low statistical power. Unit root tests with improved power, and the capability to

account for possible structural breaks were used by Parkes and Savvides (1999).11

Multivariate cointegration techniques such as the Johanson Technique were also used to

analyse possible cointegrating relationships between multiple variables. These modern

econometric techniques delivered mixed results with some studies finding some evidence

in support of long-run PPP.

Since the 1970’s, the theory of PPP has undergone a large amount of empirical study and

theoretical debate. For a long time, theoretical work suggested that exchange rates should

be linked to the price level with short-run deviations while empirical analysis found little

in the way of evidence to back up the theory. However, the gap between theoretical and

empiric understanding is getting smaller due to the increased power of econometric tests

and the ever increasing time frame with which econometricians can operate.

3. DESCRIPTION OF DATA EMPLOYED

Yearly data was employed from 1975-2013 for three European Countries with no missing

observations. The observed countries are Denmark, Sweden and the United Kingdom. The

data was obtained from the Organisation for Economic Co-operation and Development

(OECD.) The OECD is internationally known for the accuracy and availability of its data. All

results are measured as natural logarithms. Since the PPP hypothesis concerns a relationship

between the nominal exchange rate and the ratio of domestic to foreign price levels in order to

test the theory we need the nominal exchange rates and the price levels of the observed

countries.

The time period of 1975-2013 was chosen due to the interesting changes in exchange rate

policy during this period. After World War II the U.S signed the Bretton Woods agreement

which tied the U.S dollar to the price of gold. At this time almost all of the World’s major

11 Parkes, A & Savvides, A 1999. "Purchasing power parity in the long run and structural breaks: evidence from real sterling exchange rates,"Applied Financial Economics, Taylor & Francis Journals, vol. 9(2), pages 117-127

6

currencies were pegged to the U.S dollar. Currencies were not free to float against each other

until the 1970’s after the agreement had been dissolved. The time period is as large as

possible to give our tests as much power as possible without mixing fixed exchange rate

systems with floating exchange rate systems. Although the data set has been made as large as

possible, exchange rates seem to take a long time to converge on the PPP determined level

and our 38 year analysis might not be long enough to find evidence of long run PPP. Yearly

data was chosen for simplicity and because increasing the frequency of the observations won’t

increase the power for long-run testing because increasing the amount of detail regarding

short-run movements will not give any extra information on long-run movements.

A key concern was the choice of the price index with the CPI (Consumer Price Index) and the

PPI (producer price index) being the most popular indexes. ‘PPI places a heavier weight on

tradable goods than the CPI and tend to yield more favourable test results to PPP’ Cheung and

Lai (1993). However, it could be argued that the relationship between traded goods, prices

and exchange rates comes close to a truism. The CPI was chosen, firstly due to its availability

and consistency and secondly because the CPI was used in the actual formulation of the PPP

hypothesis by Casel. The CPI figures used in this study were obtained from the ‘Consumer

Prices (MEI)’ dataset made available by the OECD. The dataset is a subset of the Main

Economic Indicators (MEI) database. The database consists mainly of monthly data for the 34

OECD member countries. The MEI database contains a wide variety of Short-term Economic

Statistics. The CPI data series measures changes in the price level of a market basket of goods

and services purchased by consumers. When comparing the CPI it is very hard to determine

whether the goods and services available in each country is exactly the same. However, using

some sort of price index is essential to testing absolute PPP and according to the OECD ‘a lot

of effort has been made to ensure that the data are internationally comparable across all

countries.’12 It could be argued that the nominal exchange rate is the unadjusted weighted

average value of a country's currency relative to all major currencies being traded within an

index or pool of currencies. The exchange rates used in this analysis are a geometric average

of the rates against the US dollar. The nominal exchange rate is defined as the amount of

domestic currency required to purchase one unit of foreign currency.

12 http://stats.oecd.org/Index.aspx?DataSetCode=MEI_PRICES

7

Not all of the nominal bilateral exchange rates were available and some of the exchange rates

had to be created. The nominal exchange rates between Denmark and Sweden and Sweden

and the UK were calculated using the following equation:

Domestic CurrencyDollar

/Foreign Currency

Dollar= DomesticCurrency

ForeignCurrency(1)

I am aware that some slight inaccuracies might be present in this methodology but this was

the only available method for the less popular currency pairs.

Additionally, the logarithmic expressions of all series were calculated. Formally, the absolute

version of PPP is defined as:

∑i=1

N

αi Pi ,t=Et∑i=1

N

αi P¿i ,t (2)

Where the summed geometric weights sum to unity. If the price indices are constructed using

a geometric index then we must form the weighted sum after taking logs:

∑i=1

N

δi p i ,t=Et∑i=1

N

δi P¿i ,t(3)

Again the sum of the geometric weights add up to 1. If the national price levels and the

nominal exchange rates are logarithmically transformed then the popular absolute PPP

condition that is used in the literature takes the form.13

e t=p t−p i¿(4)

Equation 4 is less complicated and more intuitive than equation 2 making it more convenient

to use in terms of estimation. Therefore all variables were estimated in log form.

The exchange rates used in this study are all European exchange rates. In 1979 all of the

countries observed in this study adopted the European Exchange Rate Mechanism. The aim of

this mechanism was to reduce the exchange rate variability and achieve monetary stability in

Europe ahead of the introduction of the Euro. One of the central problems with empirical

13 Prof Peter J. Hammond (2008) Long-Run PPP: The Case of Greece: Towards the Transition to the Euro: A Maximum Likelihood Cointegration Approach

8

studies on PPP is the lack of power arising from the inability to use data from fixed exchange

rate systems. However, under the European exchange rate system currencies were still

allowed to float freely against each other. The European exchange rate mechanism was a

semi-pegged system based on the concept of fixed exchange rate margins, but with the

exchange rates variable within those margins. So while sudden, substantial fluctuations in the

values of the currencies were restricted, the currencies under investigation were still allowed

to depreciate and appreciate freely. This mechanism was designed to prevent the large

fluctuations in currency values associated with the euro. This should not prevent the exchange

rate from returning to the PPP value. Whilst these currencies might not be perfectly free,

exchange rate policy has been an important part of macroeconomic policy for the last 40 years

and it is almost impossible to find a group of currencies that is completely free of government

intervention.

Static and dynamic properties of the data:

Consumer Price Indexes:

Figure 1 shows the price levels for a basket of

goods in Denmark, Sweden and the UK. From

the graph it is possible to see that the base year

was in 2010. The graph shows that all of the

consumer prices are trending upwards over time.

This could be due to the expansionary monetary

policy that was popular during this time period.

This trend could also have resulted from a rise in

real wages caused by technological advances.

However, the graph shows that the rate at which the CPI is increasing is falling. This will be

due to increased emphasis on economic stability that central banks have focused on for the

last 20 years.

Figure 1 clearly shows that all three countries have similar price level trends. All of our

countries have similar price levels which follow a similar pattern, this could be because all

three of the sample countries have similar economic structures. They are all developed

countries with similar access to technology.

33.

54

4.5

5

1970 1980 1990 2000 2010Time

CPI Denmark CPI SwedenCPI UK

Price Levels for Denmark, Sweden and the UK

Figure 1Figure 1

9

There appears to be a slight structural break in Sweden’s CPI between the dates of 2008-2009.

Sweden’s CPI doesn’t increase by as much as it has done in recent years. This is confirmed by

Figure 2 which shows a sharp reduction in Sweden’s inflation rate in 2008. Figure 2 shows a

similar but smaller dip in the inflation rates for the UK and Denmark for this time period.

The upward trend present in the time series shows that the CPI rates are not stationary. They

are trending upwards over time and do not appear to revert to a particular mean. It is very

unlikely that they have a constant mean.

To confirm the non-stationarity of the CPIs, autocorrelations graphs of the price indexes were

used. Autocorrelation graphs are a tool commonly used to check the randomness in a data set.

If the time series is stationarity, the lags will oscillate around 0 for all time-lag separations. If

the variable is non-stationary there will be one or more autocorrelations which will be

significantly non-zero. The autocorrelation graphs in Appendix Figure 1 and 2 show that there

are lags significantly different from 0 for all three CPI values confirming that the time series

are probably not stationary. The autocorrelation graphs don’t appear to be stationary until the

second difference this is shown in Appendix Figure 2. The second differenced time series

appear to be much more stationary. The autocorrelation graphs of these variables quickly fall

to zero implying stationarity. The graphical analysis of the CPI rates implies that they are all

integrated to I(2).

Yearly Inflation Rates:

Figure 2 shows the inflation rates for

Denmark, Sweden and the UK. All three

countries have very similar average

inflation rates as previously suggested by

Figure 1.

The inflation rate is the annual change in

the CPI. Like Figure 1, Figure 2 shows

that the price levels in all three countries

are increasing with time. Sweden is the only country that has experienced deflation in the last

0.00

000.

0500

0.10

000.

1500

Infla

tion

Rat

e (%

)

1970 1980 1990 2000 2010Time

Denmark Inflation Rate Sweden Inflation RateUnited Kingdom Inflation rate

Yearly Rates of Inflation for Denmark, Sweden and the UK

Figure 2

10

40 years. One of these times was in 2008 during the great recession. All three countries

experienced lower inflation in this year probably due to the reduction in demand caused by

lower demand caused by the depression. However, the inflation rates of all three sample

countries spiked after the initial 2008 dip pushing inflation to the highest level since the mid

1990’s. This will be due to the loose monetary policy adopted by central banks in an attempt

to boost demand and offset the negative effects of the recession. An increase in fuel and food

prices also pushed inflation higher.

Exchange Rates:

.6.8

11.

21.

4

1970 1980 1990 2000 2010Time

NER Denmark-Sweden Den-Swe priceratio

Denmark:Sweden

0.2

.4.6

.81

1970 1980 1990 2000 2010Time

NERDenmark-Sweden Den-UK priceratio

Denmark:UK

Figure 3

Figure 3 shows the bilateral nominal exchange rates where foreign currency is expressed in

units of domestic currency. The CPI ratio between the home and domestic countries is also

plotted on the same graphs. The motive behind this is that if relative PPP is to hold between

the two countries then there should be a parallel movement in the nominal exchange rate and

the price ratio between the two countries. As each exchange rate has been defined as the

domestic cost of buying a unit of foreign currency, an upward movement in the graph depicts

a depreciation in the nominal exchange rate i.e. the cost of obtaining a unit of foreign

currency has increased. Similarly a downward movement represents an appreciating in the

nominal exchange rate. Over the sample period the Denmark Kroner has generally

depreciated against the Swedish Kroner and the British pound. However, the price level ratio

has stayed relatively constant over this time period suggesting that strong PPP may not hold.

The price ratio does not seem to follow the nominal exchange rate very well indicating that

PPP doesn’t hold. In both cases there is no tendency for the series to revert to a constant

11

mean. The visual impression suggests that the nominal exchange rates are consistent with

random walk and hence an I(1) process.

This impression is backed up by Appendix Figures 3 and 4 which show that the bilateral

exchange rates don’t appear to be stationary until they are first differenced.

Nominal Exchange Rates:

-10

12

3

1970 1980 1990 2000 2010Time

ERDenmark ERSwedenERUK

Nominal Exchange Rates

Figure 4

Figure 4 plots the nominal exchange rates of the three economies in dollar terms. As shown

the UK nominal exchange rate is very stable and doesn’t appreciate or depreciate much at all.

The Swedish Krona and the Danish Krona depreciated against the dollar in the mid to late

1970’s as the currencies were allowed to float freely against the dollar. The graph shows that

all three of the currencies experienced fluctuations in their exchange rates during the

European Exchange rate mechanism (EERM). The Swedish Krona suddenly devalued in

1993 when the Swedish Government announced that it would be leaving the European

monetary union. Informal graphical analysis seems to suggest that the Danish Krona and the

Swedish Krona fluctuate together despite these currencies not being pegged to each other. In

all three cases there appears to be no tendency for the series to revert to a constant mean. The

visual impression given off by the graphs is that, in each case, the nominal exchange rate is

consistent with random walk and hence appears to be a non-stationary I(1) process.

Appendix Figure 5 shows the autocorrelation graphs of the nominal exchange rates at levels.

The three nominal exchange rates do show a tendency to die out, but only at very long lags.

Appendix Figure 6 shows the autocorrelation graph of the first difference of the bilateral

12

exchange rate. In general these approach the zero axis quickly. These autocorrelation graphs

indicate that the first difference of the nominal exchange rates do not have any significant lags

and therefore appear to be stationary.

Stationarity of the Data:

A time-series variable that has a mean and variance that don’t change over time are described

as stationary. A weakly stationary timer series satisfies the following criteria:14

1. E (Y t )=μ (constant mean)

2. Var (Y t )=σ2(constant variance)

3. Cov (Y t−Y t−1 )=γs(covariance stationarity)

Augmented Dickey-Fuller test:

The unit root test is the formal way to check the stationarity of a time series variable. In this

paper the augmented Dickey-Fuller test was used to check the variables for unit roots. Dickey

and Fuller (1979) developed a procedure to formally test for non-stationarity based on a

stimple AR(1) model. The test used in this paper took the following form:

∆ Y t=β1+β2t+δ Y t−1+∑i=1

m

αi ∆ Y t−1+εt (5)

The augmented Dickey-Fuller test allows for the addition of lagged lengths. The number of

lagged difference terms that were included was chosen so that the error term is serially

uncorrelated. The number of lags selected were based on the number of significant lags in the

AC graph.

The null and alternative hypothesise of the augmented Dickey-Fuller test can be written as:

H 0 :∅=0 the variable is non-stationary

H 1:∅ <0 the variable is stationary

14 Voinea L.G THE PURCHASING POWER PARITY: EVIDENCE FROM THE GREAT FINANCIAL CRISIS

13

Under the null hypothesis of unit root, the z-ratio is not normal distributed and has a

nonstandard density function known as the Dickey-Fuller distribution.15The distribution will

not be normal and the exchange rate will fail to converge on a particular level. As PPP

requires real exchange rates to converge on the PPP level, if the augmented Dickey-Fuller test

fails to reject the null hypothesis of a unit root the theory of PPP is violated. If the tests found

a variable to be non-stationary another unit root rest was performed on the first difference of

the variable.

Phillips-Perron Test:

The Phillips-Perron test, is arguably more powerful than the ADF test as it does not lose

observations through lags, takes the form:

Z (t a )=~S

σ TWt a−

T 3

4√3 Ex0.5~σTw

(~σ Tw2−~S2)(6)

Here again the null hypothesis is the presence of a unit root and the alternative hypothesis is

stationaity.

Unit Root Test:

Augmented Dickey-Fuller test

results

Phillips-Perron test results

Variable

Name

t-value 5%

Critical

Level

Hypothesis

result

t-value 5%

Critical

Level

Hypothesis

result

lCPIDenmark

(3)

-2.374 -2.972 Fail to

Reject

-2.635 -12.916 Fail to

Reject

lCPISweden

(3)

-3.110 -2.969 Reject -2.959 -12.916 Fail to

Reject

lCPIUK(3) -2.268 -2.972 Fail to

Reject

-2.635 -12.916 Fail to

Reject

ERDenSwe -1.206 -2.972 Fail to -2.417 -12.916 Fail to

15 The Purchasing Power Parity: Evidence from the Great Financial Crisis

14

Reject Reject

ERDenUK -1.411 -2.969 Fail to

Reject

-6.839 -12.916 Fail to

RejectTable 1

Table 1 contains the results of the unit root tests on the CPI and nominal exchange rates at

levels. As expected the null hypothesis of a unit root was not rejected meaning that the

variables are non-stationary. These unit root results were backed up by the autocorrelation

graphs, analysed in the data description section, which show several lags that are significantly

different from zero. However, the augmented Dickey-Fuller test did manage to reject the null

hypothesis for the consumer price index of Sweden concluding that this series was stationary.

The Phillips-Perron test on the other hand failed to reject the presence of a unit root. Arguably

the Phillips-Perron test has more power than the augmented Dickey-Fuller test. The non-

stationarity result is also backed up by the graphical analysis of the trend and the

autocorrelation graphs. Therefore it is possible to assume that all variables are non-stationary

at levels.


results


Variable Name t-value 5%

Critical

Level

Hypothesis

result

t-value 5%

Critical

Level

Hypothesis

result

dlCPIDenmark

(2)

-1.760 -2.972 Fail to

Reject

-2.487 -12.884 Fail to

Reject

dlCPISweden

(3)

-1.138 -2.975 Fail to

Reject

-2.639 -12.916 Fail to

Reject

dlCPIUK(3) -3.400 -2.975 Reject -6.523 -12.884 Fail to

Reject

dERDenSwe(0

)

-5.941 -2.966 Reject -32.079 -12.884 Reject

dERDenUK(0) -4.900 -2.966 Reject -32.079 -12.916 RejectTable 2

Table 2 shows the results of the unit root test of the first differenced values of the CPI and

bilateral nominal exchange rates. The unit root tests performed on the two bilarteral nominal

15

exchange rates found enough evidence to reject the null hypothesis of a unit root. The first

difference of the bilateral nominal exchange rates are stationary and integrated to order I(1).

However, the unit root tests failed to reject the null hypothesis for the first deference of the

CPI series. The only test that managed to reject the presence of a unit root was the ADF test

on the UK’s CPI. The Phillips-Perron test and the AC graphical analysis.

4. EMPIRICAL MODEL(S) AND ITS (THEIR) ESTIMATION

Methodology:

This econometrics project aims to test weak and strong relative PPP in three countries.

All results were obtained and graphed using the Stata program. Relative PPP holds when

the ratio between the nominal exchange rate and the domestic price levels (this doesn’t

make sense or is incomplete). If Et is equal to the domestic price of a unit of foreign

currency, or the nominal exchange rate, Ptis the domestic price level and Pt¿is the

overseas price level then PPP can be expressed by this equation:

Et=Pt /Pt¿ (7)

Taking logs of both sides gives us:

ln Et=α0+α 1 pt−α 2 pt¿ (8)

The left hand side of this equation is the logarithm of the real exchange rate. This implies

that if PPP holds then the real exchange rate must be constant. As we have already

discussed it is likely that the real exchange rate does fluctuate over the short term. To

allow for these random deviations a stochastic shock ε t can be added to the equation. The

stochastic shock should be stationary with a mean value of 0 to ensure that the real

exchange rate doesn’t depend on t. The disturbance term must also not exhibit random

walk behaviour. The equation can now be written as:

ln Et=α0+α 1 pt−α 2 pt¿+ε t (9)

Strong PPP:

16

The empirical analysis starts with the strictest version of PPP which assumes that α 0=0,

α 1=1 and α 2=−1. If these values hold then a change in the ratio of consumer price

indexes triggers an automatic change in the nominal exchange rate of the same

magnitude. In other words all of changes in the nominal exchange rates between

countries are explained by their respective price indexes. Thus, real exchange rates

should be constant and stationary over the long-run. If there is a unit root in the data,

PPP requires the nominal exchange rate and the consumer price indices to be cointegrated

so that ε t is stationary.

The real exchange rates are a function of nominal exchange rates and price indexes.

R Et=Et (Pt

¿

Pt) (10)

Where R Et is the real exchange rate, Et is the nominal exchange rate, Pt is the price level

in the domestic country, Pt¿ is the price level in the foreign country. By taking logs of

equation 4 we can express the real exchange rate as:

R Et=et+ pt¿−pt (11)

Equation 12 was used to graph the real exchange rate for the three economies. The graph

of a stationary time series is not supposed to show a time trend so informal graphical

analysis was used to observe the real exchange rates stationarity.

To formally test the stationarity of the real exchange rate the augmented Dickey-Fuller

and the Phillips-Perron tests was used. The tests took the same form as in equations 6 and

7. Where we test the null hypothesis H 0 :δ=0, if the null hypothesis holds there is a unit

root present and shocks persist forever. For the strictest form of PPP to hold we must

reject this null hypothesis.

Weak PPP:

A weak form of PPP is when β1and β2 are neither equal to 1 or each other. Weak PPP

assumes there is a stationary linear combination of e t, pt and pt¿. All restraints in equation

(10) are relaxed. In this weak case the nominal exchange rate and domestic and foreign

price levels are related in the long-run but with the assumption that a 1% increase in

domestic and foreign prices does not completely offset the nominal exchange rate. The

17

requirement for weak form PPP is an existence of any linear relationship among the

variable that has stationary properties.

ln Et=β0+β1 pt−β2 pt¿+εt (12)

For the weakest form of PPP we are looking for a linear relationship among the observed

variables which means that cointegration analysis should be used.

To investigate if weak long-run PPP holds, the relationship between the nominal

exchange rate and the price indexes needs to be examined. To examine the link between

the variables, ordinary least squares regression analysis was used. The main motivation

for using cointegration analysis is to identify meaningful long-run relationships among

non-stationary variables. As previously discussed the PPP relationship is likely to be a

long run one, it is also likely that the most of our variables are non-stationary. This is

because although our variables measure different aspects of the economy, they are closely

related.

The cointegration test employed in this paper is the Engle-Granger test which follows two

steps. The first test is to conduct a unit root test in order to ensure that all variables are

integrated to the same order. Non-stationary variables that become stationary after being

n times become integrated to the nth order. If all the variables are integrated to the same

order, the next step is to estimate the model and test whether the residuals of the model

are stationary.

PPP holds in the long run if the sum of the nominal exchange rate and the foreign

country’s CPI are cointegrated with the CPI of the domestic country. Thus the PPP

relation for the Engle-Granger test is:

log (e i )=log ( p )+ log ( p¿) (13)

To allow for short run deviations from the PPP exchange rate value an error term is

added.

18

log (e i )=β0+β1 log ( p )+ β2 log ( p¿)+εt(14 )

The resulting residuals from equation 8 are then tested for a unit root. If these residuals

are found to be stationary it can be concluded that weak PPP holds.

However, before we apply this test we must make sure that all of the observed variables

are stationary. If all of the observed variables were not stationary there would be a risk of

spurious regression. We would be unable to tell whether our conclusions were based on

economic relationships or simply the randomness in our data. Thus augmented Dickey-

Fuller tests were performed for individual CPIs and nominal exchange rates following the

same method as described in the previous section. If we are unable to reject this null

hypothesis at a 5% confidence interval that variable is non-stationary and could therefore

suffer from spurious regression.

When we have non-stationary variables we can try to difference them until they become

stationary and then using the differenced variables in our analysis. However, differencing

to achieve stationary requires the mean to be stochastic. Differenced variables are also

often not statistically significant and have no economic interpretation.

The error correction model:

As noted earlier, there are non-stationary variables in our regression model which could

result in our estimates being spurious. So if we regress equation 15 the estimated

parameters might not be accurate.

One way of resolving this problem is to difference the variables until they are stationary

and then run the regression. In this case the regression will produce correct estimates of

the parameters and the problem of spurious regression is resolved. However, this

regression only measures the short-run relationship between the variables. As PPP is

generally seen as a long-run phenomenon this would be an inappropriate regression.

19

The error correction model is a convenient model that measures the correction from

disequilibrium of the previous period. If β1 and β2 from equation 14 are cointegrated

with lnE t then the ECM specification can be written as:

∆ ln E t=¿ α+∈t−1+∆ ln pt❑+∆ ln pt

¿ ¿+μt (15)

Results:Real exchange rate Stationarity:

As discussed one way to test for strong PPP is to test the stationarity of the real exchange

rates. This paper uses graphical analysis and employs the augmented Dickey-Fuller and

Phillips-Perron tests for unit roots in order to test the stationarity of the real exchange

rates.

Graphical Analysis:

The first step in assessing the empirical evidence is to graph the data. Figure 5 plots the

real exchange rates and the bilateral nominal exchange rates between the three sample

countries.

-.4-.2

0.2

.4

1970 1980 1990 2000 2010Time

REDenSw ldenmarksweden

Nominal and Real ER Between Denmark and Sweden

-2.8

-2.6

-2.4

-2.2

-2

1970 1980 1990 2000 2010Time

REDenuk ldenmarkuk

Nominal and Real ER between Denmark and UK

Figure 5 and 6

Figures 5 and 6 plot the real and the nominal bilateral exchange rates for Denmark,

Sweden and the UK. The real exchange rate for the Denmark and Sweden does not look

like it is stationary. There does not appear to be a constant mean and the time series

appears to be integrated to order I(1). The real exchange rate for Denmark and Sweden

appears to be more stationary with values appearing to oscillate around a constant mean.

This implies that strong PPP might hold between Denmark and the UK. This hypothesis

20

is backed up by the AC graphs in Appendix Figure 7 and 8 which shows significant lags.

The first differenced AC graphs, in Appendix Figure 8 and 9, show that the real exchange

rates are stationary when they are first differenced.

Unit root testing:

To formally test for stationarity in the real exchange rates unit root tests were performed

on the two variables.


results


Variable Name t-

value

5%

Critica

l

Hypothesis

result

t-

value

5%

Critica

l

Hypothesis

result

REldenswe(3) -1.335 -2.972 Fail to

Reject

-2.543 -12.916 Fail to

Reject

REldenuk(2) -0.907 -2.969 Fail to

Reject

-5.796 -12.916 Fail to

RejectTable 3

Table 3 contains the results of applying the augmented Dickey-Fuller and Phillips-Perron

unit root tests to the real exchange rate series at levels. All of the tests have failed to find

evidence of stationarity in the real exchange rates. Therefore it must be assumed that the

variables are non-stationary and that strong PPP doesn’t hold between the sample

countries.


results


Variable Name t-

value

5%

Critica

l

Hypothesis

result

t-

value

5%

Critica

l

Hypothesis

result

REldenswe(0) -5.461 -3.668 Reject -34.229 -12.916 Reject

REldenuk(0) -5.057 -3.668 Reject -27.911 -12.916 Reject

21

Table 4

Table 4 confirms the AC graphs in Appendix 7 and 8. The unit root test were able to

reject the null hypothesis concluding that the real exchange rates were stationary when

difference. It is therefore possible to conclude that the real exchange rates are integrated

to I(1). This implies that the real exchange rates do not converge on a mean value and

therefore there is no evidence to suggest that strong PPP exists between any of the

countries.

Cointegration Analysis:

Denmark and Sweden:

To assess whether there is a purchasing power parity relationship between Denmark and

Sweden equation 15 is estimated by ordinary least squares.

Figure 7

Using the results expressed in Figure 13 our model becomes:

ldenmarksweden=1.394−.438lCPIDenmark +.778 lCPISweden(16)

The model shown in equation (16) shows that as the price level in Sweden increases the

nominal exchange rate between Denmark and Sweden appreciates. It also shows that if

there is an increase in the price level in Denmark the nominal exchange rate between

Denmark and Sweden will depreciate. β1≠−β2 holds implying that there might be weak

PPP between Denmark and Sweden. The r-squared value has a relatively high value of

0.843 which suggests that cointegration exists.

22

The next step is to check the residuals for stationarity, using the augmented Dickey-Fuller

test, to check for the existence of a cointergrating relationship. If the residuals are

stationary we can conclude that a cointegrating relationship exists and weak PPP holds.

Augmented Dickey-Fuller test results

Variable Name t-value 5% Critical

Level

Hypothesis

result

Res -2.811 2.966 Reject (10%)

Table 4

-0.5

00.

000.

501.

00A

utoc

orre

latio

ns o

f res

2

0 5 10 15 20Lag

Bartlett's formula for MA(q) 95% confidence bands

-.4-.2

0.2

.4

1970 1980 1990 2000 2010Time

Residuals ldenmarksweden

Figure 8 and 9

The results of the ADF (Table 4) show that there is evidence to suggest that the residuals

are stationary. The null hypothesis of unit root can be rejected by the ADF test. This

implies that there is evidence in the data that the spot exchange rate and the price levels

are cointegrated. The conclusion is backed up by the relatively strong fit of the model and

the AC graph of the residuals looks stationary.

There is weak evidence of weak PPP between Sweden and Denmark but a problem with

running a linear regression between Denmark and Sweden is the variables are integrated

to a different order. The CPI variable for Denmark and Sweden are integrated to I(2)

whereas the bilateral nominal exchange rate between the two countries is integrated to

I(1). This could result in spurious regression. To check whether our regression suffers

from spurious results the error correction model was constructed.

23

Figure 10

The error correction model becomes:

∆ ln DenmarkSweden t=+.015−.048 ∆ ln CPIDenmark t+.001 ∆ lnCPISwedent−.389∈t−1

(17)

The negative coefficient on the lagged residuals supports the theory of purchasing price

parity. The coefficient suggests that if the nominal exchange rate differs from the

predetermined PPP level by 1% in one period it will move 0.39% closer to the PPP level

in the next term. This shows that the nominal exchange rate is mean reverting and

converging on a particular level. This supports the theory of weak long-run PPP.

However, the error correction model is not without faults. The R-squared value only 0.26

which is shows that the model does not explain much of the nominal exchange rate

deviations. The d . ln CPIDenmark t and d . ln CPISwedent are also not statistically

significant. When these variables were removed from the model the error correction

model becomes:

24

Figure 11

∆ ln DenmarkSweden t=.013−.391∈t−1(17)

In this new error correction model the R squared value has not fallen much at all

suggesting that the new model is still relevant. All the variables are significant and the

coefficient of the residuals is still negative implying a weak PPP relationship.

The regression and the error correction model provide weak evidence to suggest that a

weak PPP relationship exists between Denmark and Sweden despite the model not fitting

very well.

Denmark and UK:

To assess whether there is a purchasing power parity relationship between Denmark and

UK equation 14 is estimated by ordinary least squares. A problem with running a linear

regression between Denmark and UK is the variables are integrated to a different order.

The CPI variable for Denmark and UK are integrated to I(2) whereas the bilateral

nominal exchange rate between the two countries is integrated to I(1). This could result in

spurious regression.

Figure 12

25

-0.5

00.

000.

501.

00A

utoc

orre

latio

ns o

f res

0 5 10 15 20Lag


-3-2

-10

1970 1980 1990 2000 2010Time

Residuals ldenmarkuk

Figure 13 and 14

ldenmarkuk=2.575+.884 lCPIDenmark−.937 lCPI UK (18)

The model shown in equation (18) shows that as the price level in Sweden increases the

nominal exchange rate between Denmark and UK appreciates. It also shows that if there

is an increase in the price level in Denmark the nominal exchange rate between Denmark

and Sweden will depreciate. β1≠−β2 holds implying that there might be weak PPP

between Denmark and UK.

Augmented Dickey-Fuller test results

Variable Name t-value 5% Critical

Level

Hypothesis

result

Res2 -2.651 -2.966 Reject (10%)

Table 5

Once again the results of the ADF test (Table 5) show that there is evidence to suggest

that the residuals aren’t stationary. The null hypothesis of unit root can be rejected by the

ADF test. This implies that there is evidence in the data that the spot exchange rate and

the price levels are cointegrated. However, the stronger Phillips-Perron test fails to reject

the null hypothesis at the 5% critical level. The AC graph looks more stationary between

Denmark and the UK than it does between Denmark and Sweden although the residuals

still don’t fit very well.

There is weak evidence of weak PPP between Sweden and UK but a problem with

running a linear regression between Denmark and Sweden is the variables are integrated

26

to a different order. The CPI variable for Denmark and UK are integrated to I(2) whereas

the bilateral nominal exchange rate between the two countries is integrated to I(1). This

could result in spurious regression. To check whether our regression suffers from

spurious results the error correction model was constructed.

Figure 15

The error correction model becomes:

∆ ln DenmarkUK t=−0.03+1.90 ∆ ln CPIDenmark t−1.21∆ lnCPIuk t−0.21∈t−1(19)

The negative coefficient on the lagged residuals supports the theory of purchasing price

parity. This again suggests that weak long-run PPP applies to Denmark and UK.

However, once again the R-squared values are very low meaning that our model doesn’t

fit very well.

The regression and the error correction model provide weak evidence to suggest that a

weak PPP relationship exists between Denmark and UK.

Policy Conclusion:

The theory of PPP has many uses in macroeconomic theory. Weak PPP can explain why

the exchange rate moves in certain ways. PPP can indicate the desirable exchange rate,

when the actual nominal exchange rate differs from the PPP determined level. The central

bank may try to narrow the gap between the actual nominal exchange rate and the

preferable nominal exchange rate by expanding or contracting monetary policy. Weak

PPP between Denmark and Sweden and Denmark and the UK allows the government of

27

those countries to set an appropriate target level nominal exchange rate which the

Government can use to stabilise their exchange rates.

Finding weak PPP between the sample countries indicates that those countries have a

similar level of competitiveness. The real exchange rate is a frequently used measure of

international competitiveness. When the real exchange rate rises, the home country gains

competitiveness because domestic prices are lower. The tests employed in this paper

found evidence of weak PPP. This indicates that domestic prices are relatively similar

between the Denmark, Sweden and UK. However, when the strong PPP relationship was

analysed using real exchange rates it was found that Denmark appeared to loose

competitiveness when compared to Sweden and the UK. The lack of strong PPP could

imply that Denmark’s Government needs to concentrate on policies designed to boost

international competitiveness. Denmark could for example devalue its nominal exchange

rate or reduce the amount of red tape to boost the competitiveness of its domestic

companies.

Whether or not PPP holds can provide an insight into the inflation level in a country.

Imported inflation is inflation caused by an increase in the cost of imported goods.16 If the

nominal exchange rate is below the PPP optimum level inflation is likely to increase. If a

currency is overvalued when compared to the PPP level imports will be relatively more

expensive. The Government can therefore use expansionary and monetary fiscal policy to

bring the nominal exchange rate back to its PPP optimum level without increasing

inflation.

PPP can also be used to develop comparative statistics. PPP can be used to compare

prices and wages internationally. These comparisons can then be used to analyse the

standard of living in each country.

All three of the sample countries are members of the European Union but are not part of

the euro currency area. Finding a PPP relationship between the three sample countries

insinuates that there are few barriers to trade between Denmark, Sweden and the UK.

Agents are able to correct price differentials through arbitrage. One of the main reasons

for countries giving up their monetary freedom by adopting the Euro was to eradicate

16 http://www.investorwords.com/15442/imported_inflation.html

28

currency uncertainty and by doing so increasing trade within the European Union.

However, the three countries studied have a high degree of free trade without the need to

be members of the monetary union.

5. CONCLUSIONS:

The purpose of this paper is to determine the validity of the PPP hypothesis for three

European countries. The two approaches used for the empirical analysis was the unit root test

on the stationarity of the real exchange rate and the cointegration test between price indexes

and nominal exchange rates. The empirical analysis has found some evidence of weak PPP for

Denmark and Sweden and for Denmark and the UK. However, no strong PPP was found as

the ADF tests on the real exchange rates were unable to reject the null hypothesis of a unit

root. These results are realistic. Weak PPP is likely to exist between the 3 sample countries

due to their highly correlated economies and close proximity. Strong PPP is less likely to exist

due to transportation costs and lack of information. The real exchange rate is also known to be

The Engle-Granger two step test was used to assess the cointegration between price indexes

and nominal exchange rates. This method allows us to test for the existence of a more general

cointegrating relationship between the nominal exchange rate and price levels. However, there

might be more than one cointegrating relationship between three variables. The Engle-

Granger does not allow for more than one cointegrating relationship and is often critised for

over rejecting PPP. To account for multiple cointegrating vectors the more powerful Johanson

test could have been used.

The test indicates that the nominal exchange rate between Denmark and Sweden reverts to its

mean quicker than the nominal exchange rate between Denmark and UK. This is shown by

the value of the coefficient on the lagged residuals in the error correction model. This is to be

expected due to the closer proximity of Denmark and Sweden. This reduces the transport

costs and increases the speed of information.

The data used in this paper is complete with no missing observations. It comes from the

OECD a reliable source. However, as mentioned in description of data section the bilateral

exchange rate series were manually constructed. This may have created minor errors,

although in theory the way in which exchange rates were calculated should be the same.

29

Finally, another problem encountered was the different order of integration of the variables.

The bilateral exchange rates were both intergrated to I(2) whereas all three price indexes were

only integrated to I(1). For the Engle-Granger test to different orders of integration multi-

cointegration had to be used. In this paper the trivarite system was employed were the

cointegrated relationship between the bilateral exchange rate and the price levels of the

domestic and foreign countries. In general it is possible for corresponding combination of two

I(2) variables to be cointegrated with a I(1) variable giving rise to a I(0) linear combination

among the three variables.

REFERENCE

1 Adler M and Lehmann B.F, Jeffrey A. “Deviations from Purchasing Power Parity in the Long Run”, 1990. "And Now won/Dollar Negotiations? Lessons from the Yen/Dollar Agreement of 1984,"Department of Economics, Working Paper Series qt851615wb

2.http://stats.oecd.org/Index.aspx?DataSetCode=MEI_PRICES

3.Parkes, A & Savvides, A 1999. "Purchasing power parity in the long run and structural breaks: evidence from real sterling exchange rates,"Applied Financial Economics, Taylor & Francis Journals, vol. 9(2), pages 117-1274.Prof Peter J. Hammond (2008) Long-Run PPP: The Case of Greece: Towards the Transition

5.Rogoff K, “The Purchasing Power Parity Puzzle”, Journal of Economic Literature, Volume 34, 1996, pages 647.Charles Engel & John H. Rogers, 2006"The U.S. Current Account Deficit and the Expected Share of World Output,"NBER Working Papers 11921, National Bureau of Economic Research, Inc..

6.Nusair, S.A 2003. "Testing The Validity Of Purchasing Power Parity For Asian Countries During The Current Float" Journal of Economic Development vol. 28(2), pages 129-147

7.Taylor, A.L and Taylor, M.P (2004). ‘The Purchasing Power Parity Debate’ Journal of Economic Perspectives 18, P135-158

8.Taylor, Mark P. & Sarno, Lucio, 1998. "The behavior of real exchange rates during the post-Bretton Woods period,"Journal of International Economics, Elsevier, vol. 46(2), pages 281-312

9.to the Euro: A Maximum Likelihood Cointegration Approach

10. ‘Imported Inflation’ http://www.investorwords.com/15442/imported_inflation.html

30

http://www.investorwords.com/15442/imported_inflation.html

11 Voinea L.G THE PURCHASING POWER PARITY: EVIDENCE FROM THE GREAT FINANCIAL

CRISIS

APPENDIX: RELEVANT COMPUTER OUTPUT AND FIGURES

Appendix A:

Appendix Figures 1 and 2

-0.4

0-0.2

00.0

00.2

00.4

0

0 5 10 15Lag


AC of Second Differenced lCPI Den

-0.4

0-0.2

00.0

00.2

00.4

0

0 5 10 15Lag


AC of Second Differenced lCPI Swe

-0.4

0-0.2

00.0

00.2

00.4

0

0 5 10 15Lag


AC of Second Differenced lCPI UK

-1.0

0-0

.50

0.00

0.50

1.00

0 5 10 15 20Lag


Autocorrelations of CPI Denmark

-1.0

0-0

.50

0.00

0.50

1.00

0 5 10 15 20Lag


Autocorrelations of CPI Sweden

-1.0

0-0

.50

0.00

0.50

1.00

0 5 10 15 20Lag


Autocorrelations of CPI UK

31

-1.0

0-0

.50

0.00

0.50

1.00

Aut

ocor

rela

tions

of d

enm

arku

k

0 5 10 15 20Lag


-1.0

0-0

.50

0.00

0.50

1.00

Aut

ocor

rela

tions

of d

enm

arks

wed

en

0 5 10 15 20Lag


AC Graph of Bilateral Exchange Rates

Appendix Figure 3

-0.4

0-0

.20

0.00

0.20

0.40

Auto

corr

elat

ions

of D

.lden

mar

kUK

0 5 10 15 20Lag


-0.4

0-0

.20

0.00

0.20

0.40

Auto

corr

elat

ions

of D

.lden

mar

ksw

eden

0 5 10 15 20Lag


AC Graph of Differenced Bilateral Exchange Rates

Appendix Figure 4

-1.0

0-0

.50

0.00

0.50

1.00

Auto

corr

elat

ions

of l

nER

Den

mar

k

0 5 10 15 20Lag


-0.5

00.

000.

501.

00Au

toco

rrel

atio

ns o

f lnE

RS

wed

en

0 5 10 15 20Lag


-0.5

00.

000.

501.

00Au

toco

rrel

atio

ns o

f lnE

RU

K

0 5 10 15 20Lag


AC Graph of Nominal Exchange Rates

-0.5

00.

000.

50Au

toco

rrel

atio

ns o

f D.ln

ER

Den

mar

k

0 5 10 15 20Lag


-0.4

0-0.

200.

000.

200.

40Au

toco

rrel

atio

ns o

f D.ln

ER

Sw

eden

0 5 10 15 20Lag


-0.5

00.

000.

50Au

toco

rrel

atio

ns o

f D.ln

ER

UK

0 5 10 15 20Lag


AC of the Differeneced Nominal Exchange Rates


32

Appendix Firgures 6 and 7-1

.00

-0.5

00.

000.

501.

00A

utoc

orre

latio

ns o

f RE

Den

Sw

0 5 10 15 20Lag


-1.0

0-0

.50

0.00

0.50

1.00

Aut

ocor

rela

tions

of R

ED

enuk

0 5 10 15 20Lag


-0.4

0-0

.20

0.00

0.20

0.40

Aut

ocor

rela

tions

of D

.RE

Den

Sw

0 5 10 15 20Lag


-0.4

0-0

.20

0.00

0.20

0.40

Aut

ocor

rela

tions

of D

.RE

Den

uk

0 5 10 15 20Lag



Appendix B:

Stata Commands:

Generating Variables:

gen denmarksweden = ERSweden/ERDenmark. gen denmarkuk = ERUK/ERDenmark. gen ldenmarksweden=l.denmarksweden. gen ldenmarksweden= log(denmarksweden). gen ldenmarkuk= log( denmarkuk). gen lCPIDenmark= log( CPIDenmark). gen lCPISweden= log(CPISweden). gen lCPIUK=log(CPIUK). gen lCPIUnitedKingdom =log( CPIUnitedKingdom ). gen REdenswe= ldenmarksweden+ lCPISweden- lCPIDenmark

Variable Stationarity Testing:

ac lCPIDenmark

33

. dfuller lCPIDenmark, lag(3)Pperron lCPIDenmarkAc lCPISwedenPperron lCPISwedendfuller lCPISweden, lag(2)pperron lCPISwedenac lCPIUnitedKingdomdfuller lCPIUnitedKingdom (3)pperron lCPIUnitedKingdom. ac ldenmarksweden. dfuller ldenmarksweden, lag(3). pperron ldenmarksweden. ac ldenmarksweden. ac ldenmarkukDfuller ldenmarkuk, lag(2)Pperron ldenmarkukDfuller d.ldenmarkukpperron d.ldenmarkuk. ac d.ldenmarksweden. ac d.ldenmarkuk. twoway (line ldenmarksweden Time). ac d.ldenmarksweden. dfuller d.ldenmarkswedenAc d.ldenmarkukDfuller d.ldenmarkswedenPperron d.ldenmarksweden

Real Exchange Rate Generation:gen REDenSw= ldenmarksweden+ lCPISweden- lCPIDenmark. twoway (line REDenSw Time) (line ldenmarksweden Time). gen REDenuk= ldenmarkuk +lCPIUnitedKingdom- lCPIDenmark. twoway (line REDenSw Time) (line ldenmarksweden Time). twoway (line REDenuk Time) (line ldenmarkuk Time)Gen REDenUK=ldenmarkuk+lCPIUnitedKingdom-lCPIDenmark

Real Exchange Rate Stationarity:

ac REDenSw. dfuller REDenSw, lag(3). ac REDenuk. dfuller REDenuk, lag(2). pperron REDenSw. pperron REDenuk. ac REDenSw. ac REDenuk.ac d.REDenSwAc d.REDenukDfuller d.REDenukPperron d. REDenukDfuller d. REDenSw

34

Pperron d.REDenSw

Engle-Granger Cointegration:

. reg ldenmarkuk lCPIUnitedKingdom lCPIDenmark

. predict res2, resid

. ac resid1Dfuller resid, lag(1)reg ldenmarksweden lCPISweden lCPIDenmarkpredict res1, residdfuller res1, lag(1)

Error Correction Model:. reg d.ldenmarkuk d.lCPIUnitedKingdom d.lCPIDenmark l.res2. ac res2. reg d.ldenmarksweden d.lCPISweden d.lCPIDenmark l.res1. ac res2. dfuller res2, lag(2)dfuller res2, lag(2). reg d.ldenmarkuk d.lCPIUnitedKingdom d.lCPIDenmark l.res2. reg ldenmarksweden lCPISweden lCPIDenmarkgraph combine "Z:\My Documents\ac ex denuk.gph" "Z:\My Documents\ac nex denswe.gph". twoway (line REDenuk Time) (line ldenmarkuk Time). ac REDenSw. dfuller REDenSw, lag(3). ac REDenuk. dfuller REDenuk, lag(2). dfuller res1, lag(2). reg d.ldenmarksweden l.res1. twoway (line res2 Time) (line ldenmarkuk Time). twoway (line res1 Time) (line ldenmarksweden Time)reg d.ldenmarksweden d.lCPISweden d.lCPIDenmark l.res1

Appendix C:Computations:

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

Data:

Time CPIDenmark

CPISweden

CPIUnitedKingdom

ERDenmark

ERSweden

ERUK

1975 22.7 20.1 17.9 5.741258 4.150592

0.451767

1976 24.7 22.1 20.8 6.044192 4.356625

0.556683

1977 27.5 24.7 24.2 6.001142 4.48065 0.573283

1978 30.3 27.1 26.1 5.511075 4.516817

0.521408

1979 33.2 29.1 29.7 5.260533 4.286725

0.4721

1980 37.2 33.1 35 5.635792 4.2292 0.430233

1981 41.6 37.1 39.1 7.120025 5.059825

0.497733

1982 45.8 40.2 42.5 8.333233 6.28225 0.5726

57

331983 49 43.8 44.5 9.144792 7.66716

70.6597

831984 52.1 47.3 46.7 10.35522 8.27310

80.7515

671985 54.5 50.8 49.5 10.59452 8.60225 0.7793

421986 56.5 53 51.2 8.089108 7.12359

20.6821

751987 58.8 55.2 53.3 6.83835 6.34025 0.6116

081988 61.5 58.4 55.5 6.7302 6.12875

80.5621

581989 64.4 62.2 58.4 7.310083 6.44622

50.6114

081990 66.1 68.6 62.4 6.186367 5.91837

50.5630

251991 67.7 75.1 67.1 6.392792 6.04547

50.5668

831992 69.1 76.9 70 6.038375 5.82303

30.5697

251993 70 80.5 71.7 6.482183 7.78544

20.6660

421994 71.4 82.3 73.2 6.360209 7.7157 0.6532

581995 72.9 84.3 75.1 5.60375 7.13361

60.6337

1996 74.4 84.7 77 5.798242 6.707067

0.640817

1997 76 85.3 78.3 6.604075 7.634608

0.6105

1998 77.4 85.1 79.6 6.699308 7.947075

0.603567

1999 79.4 85.5 80.7 6.9799 8.26235 0.618092

2000 81.7 86.2 81.3 8.088034 9.160583

0.660575

2001 83.6 88.3 82.3 8.320808 10.33838

0.694292

2002 85.6 90.2 83.3 7.884284 9.721042

0.66655

2003 87.4 91.9 84.5 6.577 8.078217

0.612283

2004 88.4 92.3 85.6 5.987558 7.346 0.545758

2005 90 92.7 87.3 5.996092 7.473875

0.550117

2006 91.7 94 89.4 5.943008 7.373333

0.543392

2007 93.3 96 91.5 5.442759 6.757733

0.499742

2008 96.5 99.3 94.8 5.098958 6.59710 0.5457

58

8 172009 97.8 98.9 96.8 5.359408 7.65260

80.6413

332010 100 100 100 5.62175 7.20219

20.6474

672011 102.8 103 104.5 5.356925 6.48918

30.6238

172012 105.2 103.9 107.4 5.789933 6.76893

30.6310

672013 106.1 103.8 110.2 5.617767 6.51300

80.6397

42

59