Some New Empirical Evidence
on the Relative PPP Hypothesis
in new EU Member States
WORKING PAPER No. 21/2010
Václav Žďárek
December 2010
Řada studií Working Papers Centra výzkumu konkurenční schopnosti
české ekonomiky je vydávána s podporou projektu MŠMT výzkumná
centra 1M0524.
ISSN 1801-4496
Vedoucí: prof. Ing. Antonín Slaný, CSc., Lipová 41a, 602 00 Brno,
e-mail: slany@econ.muni.cz, tel.: +420 549491111
SOME NEW EMPIRICAL EVIDENCE ON
THE RELATIVE PPP HYPOTHESIS IN
NEW EU MEMBER STATES
Abstract:
The paper focuses on testing the relative version of purchasing power
parity (PPP) on data for new EU Member States over the time period
1995 to 2009. Three definitions of exchange rates (the Euro, the US
Dollar and REER) are employed to test the relative version of the PPP
hypothesis. Given a large number of potential problems with verifying
PPP hypotheses, univariate (linear and non-linear). Our results are not
unambiguous; however, for robust univariate non-linear unit root tests
indicate that the relative version of PPP holds for the majority of new
EU Member States for the Euro currency pairs. In the case of other
currency pairs are results less robust. Our results are robust even after
shortening the time span to eliminate effects of the ongoing financial
crisis.
Abstrakt:
Text se zaměřil na testování relativní verze parity kupních sil (PPP)
v nových členských zemích Evropské unie. Pro empirickou analýzu
byly využity tři definice měnového kurzu: jednotlivé měnové páry byly
ve vztahu k euru, k USD a dále byl testován i reálný efektivní měnový
kurz na bázi indexu spotřebitelských cen (CPI). Protože empirická
verifikace relativní verze PPP je spojena s řadou problémů, byly
využity jak jednoduché (lineární), tak nelineární testy jednotkového
kořene v časových řadách a rovněž testy určené pro testování v rámci
panelu (panelové testy jednotkového kořene). Výsledky unilaterálních
testů nejsou zcela jednoznačné, kromě eurových měnových párů.
Robustnost výsledků je ověřena i zkrácením časového období tak, aby
nezahrnovalo období počátku stále ještě probíhající světové finanční
krize.
Recenzoval:
Ing. Bořek Vašíček, PhD., PhD. (Universidad de Barcelona)
4
1. INTRODUCTION
The exchange rate economics and empirical studies attempting to
verify the related hypotheses have attracted much attention of both
empirical and theoretical economists. The reason for that may be very
simple; this particular field has experienced rapid theoretical
development recently, or it is particularly attractive for empirical
economists due to ambiguous results.
One of the most frequently empirically tested hypotheses is the
purchasing power parity (PPP). There are two versions of the PPP.
The absolute version of the PPP is based on the law of one price
(LOP) that is usually tested for individual commodities or baskets of
commodities. The relative version of the PPP is a simplification, as it
approximates the changes in individual prices by changes in price
indices. Particular attention has been devoted to the latter as it is not
so difficult to test that and some associated implications.
There has been a large number of studies focusing on the PPP, both in
developed and developing countries. Empirical results seem to have
been in favour of supporting PPP in developed countries. Therefore,
recent articles have focused on developed countries such as selected
OECD countries (e.g. Chortareas and Kapetanios, 2009) or EU15
countries (e.g. Christidou and Panagiotidis, 2010). However, the
findings have been mixed for the developing and transition countries,
depending on the set of countries, time period, price indices and
applied econometric techniques. Some studies have even rejected the
PPP hypothesis using univariate unit root tests (hereinafter referred to
as URTs) and more recently panel unit root tests (hereinafter referred
to as pURTs).
1
While the former are exposed to criticism mainly due to
their low power, the latter have solved some problems but
simultaneously led to new ones (see e.g. Bahmani-Oskooee et al.,
2008). Some authors even cast doubts on the PPP theory, and its
empirical testing, as PPP is a long run concept of exchange rate
determination (in the horizon of decades for instance), which may span
different exchange rate regimes and monetary policy environments.
2
Various definitions of exchange rates have been used throughout this
text. The Euro, the US Dollar (US $) and the CPI-based real effective
exchange rate (REER). As REER are available only for some of NMS
countries,
3
and we want to use various specifications, we test the PPP
hypothesis only on via employing URTs .
1
LLC and IPS tests have been extensively used in the literature to test PPP
hypothesis as a response to problems of URTs, see e.g. Alba and Papell
(2007).
2
For a brief discussion see e.g. Alba and Papell (2007).
3
In the IMF IFS database that is the main source of the underlying data used
in this paper. REER's are missing for the Baltic States, and Slovenia.
5
Why have the transition countries in Europe not seen as much
attention so far? This might be for a number of reasons. For example,
the availability of data has been limited and the radical and deep
structural changes during the 1990s make any analysis difficult.
4
Additionally, some countries did not exist before 1993,
5
which puts
limits on available time series. Several studies have tried to overcome
this problem by using data for the black market. However, given
characteristics of the former regime in most of the new EU member
states (hereinafter referred to as NMS),
6
it is not certain how valid
these data and their results are. There have also been studies
covering selected NMS countries, which focused on issues related to
the process of joining the EU (see e.g. Rahn, 2003) or discussed
selected problems associated with the adoption of the euro (Frait et al.,
2006).
It is a well-known fact that at several points in history, the PPP concept
has been used as a guidance for restoring exchange rate parities.
7
The
reasons why it is relevant to study PPP for transition countries and in
Europe in particular (see (e.g. Alba and Park, 2005); Chortareas and
Kapetanios, 2009) may be summarised as follows:
1. The adoption of the euro – if PPP is not a `yardstick' for a
country, then it is much more difficult to think about the right
level for fixing an exchange rate.
2. Income convergence – PPP values are used for international
comparisons and conversion of domestic aggregates to one
artificial currency that is not biased by exchange rate
fluctuations.
8
3. Misalignment of a currency – if the PPP does not hold – with
impact on current account and competitiveness of a country.
4
The same does hold true for emerging (transition) countries in general, for an
overview see e.g. Bahmani-Oskooee et al. (2008).
5
The Czech Republic and Slovakia or 1990 in the case of the Baltic States.
6
Throughout the text, we will use either NMS12 or simply NMS as synonyms
for all the NMS countries. NMS10 consists of countries from the 5th (2004)
wave of enlargement (i.e. without Bulgaria and Romania); NMS8 encompasses
only Central and Eastern European transition countries (i.e.
without Cyprus and Malta) and NMS5 is the Visegrad group of countries (the
so-called core of the NMS countries): the Czech Republic, Hungary, Poland,
Slovakia and Slovenia.
7
The most prominent case seems to be in the 1920s, when some countries
restored their pre-war exchange rate regimes (gold parities), following
recommendation of Gustav Cassel (see Cassel, 1922).
8
The PPP works as a double convertor: it converts domestic prices to
international prices and it converts currencies.
6
4. Effects of devaluation or revaluation of a currency (i.e. effects
on competitiveness) – they are expected to vanish in the long
run if PPP does hold.
As shown above, there are a number of reasons for having a look at
PPP. In this paper, we test the relative version of PPP for the NMS
countries, using two approaches: firstly, simple univariate cases
(URTs) and secondly, the whole group of countries in panel settings
(pURTs). In order to do that, we will use real exchange rate (RER in
two definitions following two main world currencies and REER). Even
though our results are in many cases inconclusive (mainly for
univariate cases), only the more robust non-linear KSS test gives
support to PPP. The same does hold for other non-linear URTs (the
Bierens (1997) test). Our results for a panel of countries show some
evidence in favour of the PPP concept (for the Pesaran's CADF test).
In particular, PPP holds for countries that are more open, less
regulated or growing faster.
To date there has been no empirical study that would use both
approaches and the complete set of NMS countries as far as we are
aware of. The main contributions of this study can be summarised as
follows: PPP is tested vis-à-vis the euro currency (followed by tests
using the US Dollar and REER)
9
and selected URTs are employed,
including high power ones compared to standard ADF (the non-linear
KSS and the Bierens (1997) tests), while focusing on quarterly instead
of monthly data for all NMS countries. This allows us to test PPP over
a longer period of time as many time series are available for this
particular frequency, but not as monthly time series.
The paper is structured as follows. The second section aims at
summarizing the literature in the field and explaining the main
problems and our empirical strategy. The third section describes briefly
the main tests employed. The fourth mentiones main aspects related to
the used data. The next section presents and discusses the results of
our empirical analysis. The last section concludes and offers possible
extensions of this study.
2. THEORETICAL FOUNDATIONS
The determination of exchange rates and their changes is one of the
most questionable parts of modern international economics. Even
though there has been a large number of studies that have dealt with
this subject, it is not certain whether our current knowledge is better
than few years (or even decades) ago, for brief discussion see (e.g.
Alba and Papell, 2007). It is not obvious why this so; however, it may
9
The standard approach is to test the PPP against the US dollar or a set of
currencies (real effective exchange rate, REER), see e.g. Bahmani-Oskooee
et al. (2008) or Telatar and Hasanov (2009). However, it seems to be a natural
choice to start testing the PPP against the euro for NMS countries.
7
be due to the fact that an exchange rate is one of the prices in an
economy. Such a price is determined by a great number of factors and
since their influences may be pushing the price (the exchange rate) in
both directions, the results remain uncertain. In addition, a significant
factor may be the role of psychological factors that are related to
participants acting in foreign markets.
There are several approaches and concepts that put emphasis on the
role of various factors (determinants) that may be at play in
determining the value of an exchange rate. It is possible to classify
them, e.g. with respect to the time dimension. Some of them are
important in the short run, others in the long run. While the main theory
for the short run seems to be the uncovered interest rate parity, there
are several classification schemes used for exchange rate
determination and its determinants in the long run (equilibrium
concepts):
10
• Firstly, the concept of purchasing power parity (PPP) that
emphasises the role of changes in price levels between countries
11
;
• Secondly, an approach that is based on having macroeconomic
balance (both internal and external) and macroeconomic identities
without explicitly stating any theoretical grounds for exchange rate
determination (Clark and MacDonald, 1998) – the fundamental
equilibrium exchange rate (FEER). In this approach, the key
variables determining the equilibrium exchange rate are the
national income and the current account balance;
• Thirdly, the last approach is based on a set of economic indicators
that help to explain behaviour of exchange rate – the behavioural
equilibrium exchange rate (BEER). The key distincition between
FEER and BEER is that the BEER includes a part that can be
described as `behavioural' Gandolfo (2001). The inclusion of
individual (fundamental) variables rests upon theoretical underpinnings.
Clark and MacDonald (1998)'s study includes the ratio
of domestic consumer price index to the producer price index (a
10
A recent study written by Bussiére et al. (2010) distinguishes between:
• the macroeconomic balance approach,
• the external sustainability approach and
• the reduced form equilibrium real exchange rate.
The approaches nos. 1 and 2 can be classified as the FEER concept (following
Williamson, 1994) as they rely on calculations of an exchange rate that closes
gaps between a selected balance (various definitions -- broader or narrower)
of balance of payments and its 'normal' value. In the former case they are
estimated, in the latter, they are derived so that external debt is stable. The
approach no. 3 consists of the PPP concept and its extensions.
11
However, there have been discussions associated with price indices that
may be used and mainly, theoretical assumptions that are not satisfied in
reality.
8
proxy for the Balassa-Samuelson effect (B-S effect)
12
), the stock of
net foreign assets, terms of trade, and the fraction of the supply of
domestic to foreign government debt (a risk premium factor).
However, the list of potential variables is longer (see e.g. BénassyQuéré
et al., 2009.)
However, there are various approaches to the classifications of
exchange rates. For example, the study of Kanamori and Zhao (2006)
distinguishes among (all approaches can be also divided into three
groups as far as the time dimension is considered, see below)
13
• partial equilibrium models (absolute and relative PPP and covered
and uncovered interest rate parity models) – only one 'relevant'
market in an economy is considered;
• general equilibrium models (the Mundell-Fleming model, the
Balassa-Samuelson model, the Redux model (Obstfeld and Rogoff
(1995), Obstfeld and Rogoff (1996)) and the Pricing to Market (PT
or PTM) model) and
• disequilibrium (hybrid) models – simple monetary models and the
Dornbush (overshooting) model.
2.1. The issue of time horizon
The time dimension that is used seems to be the crucial factor for the
exchange rate determination and discussions of equilibrium concepts.
Bénassy-Quéré et al. (2009) distinguish between among possibilities:
• The medium run – only prices of goods and services are flexible
and therefore, they will drive an exchange rate towards the level
that will result in adjusting trade balance and net foreign assets
(NFA) to their 'equilibrium levels'. This case is equivalent to the
definition of FEER.
• The long run – prices and stocks can change, an exchange rate is
driven by these variables (differences in NFA positions and productivity
gaps). This case is consistent with the definition of BEER.
• The very long run – all variables can change as all adjustment
processes have been completed. This case reflects the PPP
definition.
Figure 1.1: Exchange rate determination
12
For details regarding the Balassa-Samuelson effect see e.g. Égert et al.
(2005).
13
Among other approaches to the exchange rate determination, we can
distinguish between monetaristic and Keynesian models, i.e. exchange rate
determination explained via money (monetary models where an exchange rate
is the relative price of two monies) and asset markets (portfolio models) where
an exchange rate is the relative price of bonds) see MacDonald (2007) or
Gandolfo (2001).
9
Note: RER – level of the real exchange rate.
Source: Égert, B. et al. (2005), p. 26, own adaptation.
Figure 1.1 shows how one can interpret the link between individual
approaches to exchange rate determination (with respect to one
classification scheme – time dimension). The PPP concept with its
assumptions can be viewed as guidance for the development of an
exchange rate in the long run, in the horizon of decades (see [Wu et al.
(2010)]). The FEER can be used for medium run assessments (given
its construction), the BEER for short and medium run. PPP is not
indicated as one possible level (equalling to one) but rather as a band
( ).
14
The PPP does stand for the values of ERER (equilibrium
real exchange rate) that are compatible with the PPP definition.
Under past political regimes, exchange rates oscillated within a band (if
they oscillated at all) and they were reset at the outset of the
14
Due a number of problems ranging from different tax policies to various
combinations of exchange rate occur in individual countries.
10
transformation process in the NMS countries. In some countries it may
have been close to the PPP value (given productivity, price and wage
levels), while in others below or above this parity (i.e. between and
in the 1). This deviation may have occurred unintentionally owing to
a great deal of uncertainty at that time in NMS countries. However, the
RER was generally higher than one. Since then, the trend may have
been following fundamental factors of an economy, i.e. showing trend
appreciation.
15
There are two other things to mention: firstly, exchange rate tends to
converge towards its equilibrium level (PPP) at rather fast pace (an
estimated half life is about 3–5 years, Rogoff (1996) even after
allowing for heterogeneity and small sample bias, see Chen and Engel
(2004). A faster pace has been found for transition countries, see
Solakoglu (2006); however, secondly, RER does fluctuate within a
band around this equilibrium level even during the transition period
(see the figure 1). As Égert et al. (2005) mentions, a trend in ERER
behaviour as long as 15–30 years may be observed due to changes in
structural characteristics of transition economies.
16
3. LITERATURE REVIEW
There have been several studies that focused both on individual
countries (for example an early study by Thacker (1995), rejecting PPP
for Poland and Hungary) and on groups of countries. However, they
differ in many aspects: Bahmani-Oskooee et al. (2008) test PPP inter
alia for 25 European countries (24 post-communistic European
countries and Turkey). Two univariate URTs (ADF and Kapetanios et
al. (2003)'s test, the KSS test) are applied to the REER. They signal
non-linear mean reversion to a constant trend for Bulgaria, Slovak
Republic, Slovenia, and to a trend for the Czech Republic and
Romania.
Twelve CEE countries (the NMS without Cyprus and Malta, but with
Croatia and Macedonia) are analysed by Telatar and Hasanov (2009).
They apply two standard URTs (ADF, KPSS) and also two URTs
accounting for non-linearities (KSS) and asymmetric adjustment (the
Sollis' test). They use monthly time series of REER from 1990 to 2007
(with different starting points). They find that PPP holds for five
countries with standard URTs, for seven countries when nonlinear
URTs are employed and for all countries if asymmetric adjustment is
allowed. Bilateral PPPs (CPI based) between the Czech Republic,
15
Based on productivity differentials and increase in price levels reflecting
usually faster economic growth in transition countries than in developed ones.
16
The ERER can fluctuate too as it is based on level of net foreign assets
(NFA) reflecting current account sustainability. It may also exhibit a kind of
overshooting behaviour -- lower values in the medium run adjusting the current
account so that it strengthens in the long run.
11
Hungary and Slovenia and their main trading partners (Austria,
Germany, France and Italy) were analysed by Bekö and Boršič (2007).
They employ univariate URTs (ADF and KPSS) and the Johansen
cointegration approach, using monthly data on individual currency
pairs for this set of countries over the period of 1992–2006. They do
not find any significant evidence for PPP. Sideris (2006) focuses on the
PPP for 17 CEE countries (without Cyprus and Malta but with selected
CIS
17
and Balkan countries) against the US dollar. He makes use of
cointegration approaches (Johansen for individual countries and
Larson's for a panel). He finds support for both weak and strong
versions of PPP.
Cuestas (2009) applies non-linear URTs to data (KSS and Bierens test
– a generalisation of the ADF test) to REER calculated by the IMF and
RER for the US dollar and the euro/ECU (monthly data 1992/1993–
2006/2007) for eight CEE countries (without Cyprus and Malta and the
Baltic States). While standard URTs reject PPP, KSS and Bierens test
do the same for most countries and currency pairs (exceptions are
Bulgaria, Croatia and Romania). Koukouritakis (2009) focuses on all
NMS countries over the period mid-1990s to 2006 (monthly data and
the euro) and uses the Johansen cointegration method. He finds that
PPP holds for Bulgaria, Cyprus, Romania and Slovenia.
Yearly data from 1992–2003 for 21 post-communistic countries
(unbalanced data) and pURTs used by Solakoglu (2006). It finds that
PPP holds, even for subgroups of less and more open countries
(based on an EBRD classification). Estimated half-lives for his group of
countries are around 1.1 year, faster (slower) for more (less) open
countries. Another panel data study was conducted by Matei (2009).
She focuses on selected NMS countries over the years 1995–2008
(with subdivision before and after EU accession) and uses monthly
data. Selected URTs and pURTs have been used to check the
presence of unit roots in the data. Matei (2009) finds evidence that
PPP does not hold for NMS countries (ambiguous results). However,
no robustness test was applied and it is unclear why the countries
were selected, as the main focus of the paper is on nominal (price)
convergence.
3.1. Methodology
The purchasing power parity (PPP) is one of the most empirically
tested hypotheses is. There are two versions of the PPP. The absolute
version of the PPP is based upon the law of one price (LOP) that is
usually tested for individual commodities or baskets of commodities.
The relative version of the PPP is a simplification, as it approximates
17
The Commonwealth of Independent States (CIS) is a group of new
independent states established after the break-up of the former Soviet union.
12
the changes in individual prices by the changes in price indices. PPP
can be tested in two forms: an absolute or a relative version.
18
The absolute PPP is a generalization of the 'law of one price'. The LOP
can be written as
(1)
where is the domestic price level, is the foreign price level
both for a good , expressed in the domestic and the foreign currency
respectively and is the spot exchange rate.
The absolute PPP can be formally written (assuming inter alia that
price baskets in both countries are the same, for discussion see below)
as
(2)
where is the domestic price level, is the foreign price level,
expressed in the domestic and the foreign currency respectively and
is the spot exchange rate. The subscript t may be dropped as it is
assumed that this relationship holds over time.
The PPP is based on several theoretical assumptions that must be
satisfied for it to hold perfectly: no transaction costs, no trade barriers
and no non-tradable goods in the strict form (see e.g. Kanamori and
Zhao, 2006). However, this is not the case in reality. Apart from these
prerequisites that are usually not satisfied, there are other explanations
why it does not hold: measurement errors, non-economical factors
different from trade barriers, imperfect information and information
costs leading to existence of non-equalised prices, various market
participants (volume of currency trade associated with trade flows is
only a tiny fraction of total transactions in foreign markets). That means
that the exchange rate may be driven by other factors such as interest
rate differentials (capital flows) and the power of empirical methods
used for testing PPP (for details and review of studies see e.g. Sarno
and Taylor (2003); MacDonald (2007). If that were the case, it would
hold that changes in an exchange rate would fully reflect the price
differentials between domestic and foreign country over a period of
time and real exchange rate ( ) would equal to one. That means (if
18
Sometimes these forms are referred to as to the 'weak' and 'strong' version
of the PPP hypothesis, see Taylor and Taylor (2004).
13
absolute PPP holds and the real exchange rate is given by the ratio of
price levels)
19
(3)
(4)
A log-linearised form of the relative version of the PPP (hereinafter
referred to as simple PPP unless indicated otherwise) can be written
as
20
(5)
where the lower case letters indicate the values in natural logarithms,
are the individual price indices for the country and time (for
details see data descriptions),
21
is the nominal exchange rate for
country against the euro expressed as units of domestic currency
against one unit of the euro (i.e. direct quotation of the exchange rate).
For countries that joined the Euro area, the exchange rate is calculated
as , where is the Euro area member's national
currency conversion rate of one euro. For the US Dollar (US $), the
indices are in relation to the US $ and also price indices are calculated
agains the US price index ( ).
22
In the case of the real effective exchange rate (REER) the same
definition as the equation 5 states is used. However, due to data
unavailability, REER time series based on CPI (the IMF definition) are
available only for eight out of twelve NMS countries.
19
The same can be shown for relative PPP if inflation rates replace price
levels and cross term stemming from multiplication is omitted.
20
Some studies have used one of the approaches, e.g. Juvenal and Taylor
(2008) takes the US economy as the benchmark country.
21
CPI indices are usually used in tests of PPP. However, CPI is a proxy for
changes in national price level. Therefore broad price indices such as the GDP
deflator may be preferred, for quarterly or yearly time series in particular. Here
problems such as availability, methodological changes of such a time series
come into the fore.
22
As it would be possible to argue that fixing conversion rates and applying
them to data prior 1998 is artificial, the same set of tests is applied to
exchange rates against the US $.
14
3.2. Estimation strategy
The relative version of the PPP theory in the equation (3.1) can be
tested by checking the properties of . If followed a non-stationary
process (e.g. I(1)), then the PPP would not hold in the long run due to
non-stationary properties.
23
On the other hand, if a unit root is not
present in a time series, it means that a deviation from equilibrium is
only of a temporary nature and the PPP does hold in the long run.
As there are many potential factors influencing exchange rates, pURTs
are also applied to subgroups of the NMS countries (NMS10, NMS8,
and NMS5). The reason is that some countries may be viewed as one
group (block) by international investors using the same rule for each of
them. In addition, some criteria may be used used to check robustness
of our results (panel data URTs, see Zdarek, 2011).
3.3. Available methods
A wide variety of methods may be applied in this context. They range
from pure time series to combinations of time and panel data
techniques. As there are two dimensions, the natural step is to decide
whether to use an individual country approach or a panel. This leads to
the use of URTs and pURTs. Empirical studies usually work with one
of two possibilities:
• time series analysis based on individual country data – the most
commonly used approach (univariate URTs), but there are some
problems (see below);
• panel data approach – which enables the researcher to make use
of information from both dimensions (pURTs).
However, estimations of exchange rates may be a difficult task in the
case of transition countries in particular, as there is a large number of
potential problems (ranging from data availability, its consistency, to
short time span, etc., see discussion above). For example, MaesoFernandez
et al. (2005) point out that using data from the period before
regimes changed does not make much sense, given a large number of
differences between centrally planned economies and standard market
economies. This reduces the time span that can be used. Some NMS
countries created new currencies during the first years of the 1990s,
which further reduces the possible time span.
A discussion of the possible data problems in the context of transition
countries can be found e.g. in Kim and Korhonen (2005). One of the
major problems seems to be the fact that all of these countries
changed (devaluated) the exchange rates at the outset of
23
A shock influencing this time series would lead to disequilibrium that would
not be restored due to increasing variance and non-existence of unconditional
mean of this time series, see Fan and Yao (2003) or Tong (1990).
15
transformation processes. The magnitude varied but usually was in
terms of dozens of percentage points rather than several percentage
points. Additionally, as some external shocks were expected,
24
some
of the NMS countries kept changing the official level of exchange rates
during the 1990s. All these factors turn the estimations of exchange
rate models into a challenging task.
Further methodological notes
There is no agreement among empirical economists which of the
expanding set of unit root tests is appropriate for testing PPP. If the
relative version of PPP is tested, it is verified that exchange rate
osciallates within a `certain band' around `1'. That is the very long-term
level of an exchange rate in an economy if strict assumptions of the
PPP theory are satisfied:
(6)
where is a time series (e.g. an exchange rate), is an
autoregressive parameter and is the error term.
Due to difficulties with the time series that can be used and their
sensitivity to a large number of factors, `standard' and non-linear
URTs are applied to our data. Additionally, pURTs are employed too.
If a unit root is not found, the next step can be done, which is the
calculation of half-lives.
25
Some studies have shown that unit root tests and cointegration tests
may have very low power if the number of observations ( ) is low (for
an application associated with transition countries and yearly data see
e.g. Solakoglu (2006). However, it may also be argued that long time
series may include (multiple) structural breaks in the case of transition
(developing) countries in particular.
26
Additionally, using higher
frequency data may not help to increase variability, as the power of a
unit root test when the length of time series remains unchanged.
It is a well-known fact that panel data techniques have a large number
of advantages compared to cross-section or time series analyses
(pooling cross-sections and time dimensions for analyzing the null
hypothesis of unit roots in each time series against the hypotheses of
stationarity), see e.g. Baltagi (2008). The variation of individual time
series is assumed to improve efficiency and therefore to enhance the
24
The break-up of the former Soviet Union, the 1992–1993 ERM crisis to
mention at least the most important ones.
25
Half-life means a period of time necessary to halve the existing gap of one
(economic) variable. A decay rate and a decay constant is necessary to
calculate a half-life.
26
An example can be a change of a policy regime that is very likely in those
countries.
16
power of unit root tests even for shorter time series when used in a
panel data analysis.
Another issue related to empirical studies of the PPP hypothesis is the
so-called bivariate or trivariate approach. Some authors prove that the
results of PPP tests depend on the method used for calculations of
RER (see the equation 5) – inflaton differential of substracting and
adding changes of price indices.
27
This is particularly important for the
cointegration approach (see Al-Omar and Ghali (2009). In this text, we
rely on the trivariate approach that seems to be more robust and does
not seem to be sensitive to the method of calculating differentials.
3.4. Univariate unit root tests
In the first step, univariate URTs are applied to the data. Then we will
proceed with a variety of panel unit root tests (first and second
generation of tests, see classification below). However, due to a large
number of problems with the URTs, the pURTs seem to be preferrable
for some applications.
28
Nevertheless, we start with the univariate unit
root tests (the Augmented Dickey-Fuller test (ADF), the Phillips-Perron
test (PP) and the Kwiatkowski-Phillips-Schmidt-Shin tests, KPSS) and
their modified versions adjusted to the case of structural breaks such
as the DF-GLS test developed by Elliott et al. (1996), which is a
modified Dickey-Fuller test transformed by a GLS regression; for
details about these URTs see e.g. Harris and Sollis (2005). As our time
period does not include the early 1990s, we eliminate the problems
with possible structural breaks (at least partially).
29
However, the main
reason is the data availability for the NMS countries.
KSS test
In addition to the standard URTs, we make use of a non-linear test that
accounts for the non-linear behaviour of RERs Kapetanios et al. (2003)
– I(0) outside of a band but I(1) inside of a band – and therefore, this
test is more robust. The KSS test (a version of the standard ADF test)
is based on an ESTAR model that can be written as:
(7)
where is the demeaned or detrended (exchange rate) time series,
is the exponential transition function presenting the
27
The bivariate approach presumes symmetry between domestic and foreign
prices, i.e. instead of working with two price indices, a term expressing an
inflation differential is used.
28
Low power of these tests in presence of structural breaks (e.g. changes of
exchange rate regimes), small sample problems, existence of cross correlation
and heterogeneity in a panel see e.g. Matei (2009).
29
In the early 1990s many countries devaluated currencies, changed
exchange rate regimes, etc., which has not occurred so often since the late
1990s.
17
non-linear adjustment, if , it affects the speed of mean reversion
and is i.i.d. error term ( ).
The null hypothesis is that ( ) and the term in
brackets is zero. The alternative means that drives the
speed of a mean reverting process. As in the equation (7) cannot
be used to test the directly, the parameter is not identified,
reparametrization (a first-order Taylor series approximation) is used
instead. That leads to the following regression equation (8)
(8)
Generalisation of the equation (8) allows for serial correlation of the
error term
(9)
where the sum augments the equation (8) with lags, so that the
term is not serially correlated. The null hypothesis in the equations (8)
and (9) remains unchanged, the alternative is . As the statistics
( )
30
are not standard normally distributed, the critical
values must be tabulated via simulations. In the following text,
for the equations (8) and , (9) are the test
statistics for demeaned data and detrended data respectively. The
demeaned data are obtained from regressions of time series on a
constant and/or on a constant and a time trend (the residuals are
saved and used in next steps). If the is rejected, it means that the
time series reverses to a constant mean (demeaned data), i.e. it
supports PPP. Although linear or nonlinear reversion in time series to a
trend (detrended data) gives support for the B-S effect. The selection
on the appropriate number of lags follows the same procedure as for
the other URTs tests.
Bierens test
The Bierens (1997) test (Bierens, 1997) helps to overcome problems
with structural breaks as non-linear trends are approximated by
interrupted (broken) time trends. It assumes nonstationarity under ,
and non-linear trend stationarity under . It extends standard ADF
regression with a Chebishev polynomial term . The process
can be written down as:
30
in the expression is left out for individual variants of the KSS test.
18
(10)
where are the Chebishev polynomials
and is the order of the polynomials. Under the and last
the components of are zero.
There are three possibilities that can be tested (Bierens, 1997)):
31
1. all coefficients are tested via t-test;
2. test, or;
3. the joint hypothesis that under the and the
last components of are zero.
32
As Cuestas (2009) mentions, rejection of the left side hypothesis for
the first and second tests means linear or non-linear trend stationarity.
(It cannot be decided which of the cases is true.) Rejection of the right
side means non-linear trend stationarity. The third test is a one-sided
test that does not give us any answer regarding the trend as right side
rejection is only the rejection of the . All possibilities are
summarised in the table 1.
Table 1: Alternative hypotheses ( ) for the Bierens (1997) test
Test Left-side rejection Right-side rejection
ST, TST or NTST NTST
ST, TST or NTST NTST
- ST, TST or NTST
Note: ST – (mean) stationary, TST – (linear) trend stationary, NTST – nonlinear
(trend) stationarity. The test is only a one-sided test, the
and are specified for both sides.
Source: Cuestas, J. C. (2009), p. 92, own adaptation.
31
As the tests nos. 1 and 2 do not accommodate all information available, the
test no. 3 is added.
32
An alternative is a test proposed in Bierens (1997) with a standard null
distribution. The text also introduces three tests that are independent of the
assumed AR structure for the error term .
19
4. DATA
Empirical studies have used different sorts of data, as there is no prior
information. While some have worked with monthly data Telatar and
Hasanov (2009), others used quarterly Matei (2009) or even yearly
data Solakoglu (2006). We have decided to rely on quarterly data, as
they are sufficiently long and allow us to perform robustness tests. This
is also connected with some advantages and disadvantages. The time
span is longer for quarterly data than it would have been for monthly
data and it is a reasonable way of solving problem of low number of
yearly observations for our set of countries. On the other hand,
quarterly time series were not available for all countries and time series
used in this paper.
33
We use seasonally adjusted data for the calculations of the RER, since
seasonal patterns may affect the results of the URTs. For seasonal
adjustments, the ARIMA X-12 method is applied.
34
We do not use
dummy variables in the URTs, as they would require us to calculate
new critical values for and properties of these tests are unknown
Chortareas and Kapetanios (2009).
35
The nominal exchange rates for individual pairs of currencies (against
the Euro and US $) are obtained from database Eurostat, UNECE
Statistical Database, DataStream, and IMF IFS (quarterly periodic
averages). As the euro exchange rate is not available before 1999 Q1
(only the ECU), an implicit proxy derived from bilateral exchange rates
(UNECE) is used instead.
36
The last time series is the REER that is
CPI based and it is calculated by the IMF.
Harmonised consumer price indices (HICP) are taken from the
Eurostat and UNECE databases for individual countries, with the base
year 2005 = 100. The same data for the Euro area stem from the
Eurostat database and the ECB statistical data warehouse. The
consumer price index reflects the demand side and can be viewed as a
proxy for changes in the total price level of an economy.
33
Surprisingly even for countries such as Malta or Cyprus that can hardly be
characterised as transition countries.
34
As some time series were at monthly frequency, as the first step they were
converted into quarterly time series (following the IMF IFS methodology) and in
the next step, seasonally adjusted using the ARIMA X-12 method.
35
However, the main concern regarding seasonal fluctuations would be in the
case of monthly time series, but even for those some studies do not used
seasonally adjusted time series, see e.g. Alba and Papell (2007); Chortareas
and Kapetanios (2009). On the other hand, some studies (e.g. Christidou and
Panagiotidis (2010) use monthly seasonally adjusted values.
36
As there have been denominations and changes of individual currencies, our
data set includes comparable time series. Due to space constraints details
from author are available upon request.
20
The producer price indices (PPI) stem from the Eurostat, IMF IFS and
UNECE databases (NACE Rev. 2, 2005 = 100). However, this time
series is available for Malta only since 2005, which means that this
country could not be included in additional robustness tests. The PPI is
based on the supply side as it measures changes in prices of tradable
(partially non-tradable) commodities. Selected summary statistics for
our time series are included in the Appendix (in the section 4). The cutoff
date for the data was November 2010.
5. EMPIRICS
5.1. Univariate unit root tests
The Euro
For the univariate URTs of the PPP concept, the data for individual
countries are employed. The main specifications rest upon the RER,
based on consumer price indices. The first step is to conduct purfor our
sample of countries. Starting values for lag selection are based on
Schwert (1989) criterion
37
and confirmed by checking values
suggested by the H-QIC criterion. In the case of the PP, KPSS and
DF-GLS tests
38
, the optimum number of lags is selected automatically
if this option is allowed. As we are not sure about the character of
individual time series, models with a constant or a constant and a time
trend are employed. The results are presented in table 2.
Table 2: Univariate unit root tests
ADFa)
PPa)
KPSSb)
DF-GLS
constant trend constant trend constant trend constant trend
Bulgaria -0.239 -5.048*** -2.892** -6.383*** 0.995*** 0.178d) 1.504 -0.539
Cyprus -3.871*** -2.757 -1.781 -3.191* -1.512 0.234*** 0.787 -0.811
Czech Rep. -1.020 -2.975 -0.925 -3.088 1.070*** 0.069 0.867 -3.743***
Estonia -0.924 -1.872 -4.807*** -6.271*** 1.000*** 0.184d)
1.797 -2.174
Hungary -1.496 -2.147 -0.562 -2.671 1.050*** 0.153*** -0.077 -1.095
37
This rule rests upon a criterion that calculates the optimal number of lags ( )
as: , where is the length of a time series, and means that only the
whole part of a number is considered. In our case for is the value
lags was the starting value; see e.g. Greene (2008), p.
752. The iterative procedure follows; if the last difference is not significant, the
test is run for the same specification with one lag less until a significant lag is
found. Sometimes the numerator of the fraction is with ; however, this
does not change for large number of observations . In our case is the value
lags.
38
Optimal lag values were based on the Ng-Perron seq statistics.
21
Lithuania -5.027*** -4.025*** -3.719** -3.199* 0.880*** 0.224*** 1.295 -1.657
Latvia -2.369 -2.733 -2.268 -1.909 0.704d)
0.155** 0.174 -1.739
Malta -2.691* -1.995 -1.969 -1.472 0.525** 0.145* -0.373c)
-1.079
Poland -2.164 -2.212 -2.264 -2.408 0.714d)
0.216d)
-0.047 -1.694
Romania -1.339 -1.325 -1.295 -1.708 0.890*** 0.117 -0.548 -1.923
Slovenia -2.375 -3.739** -0.975 -2.607 0.876*** 0.107 -0.671 -3.259**
Slovakia 0.247 -2.688 0.401 -2.375 1.080*** 0.231*** 1.509 -2.213
Note:
a)
Z(t) values reported.
b)
values of the test statistics.
c)
DF-GLS suggested 0 lags.
d)
significant at
2.5% level. ***, **, and * significant at 1%, 5% and 10% respectively. Critical values for the KPSS test
(level stationary): , , and ; trend stationary: , ,
, and . Trend = a constants and a time trend included.
Source: own calculation.
The ADF test offers a mixed picture, as some of the time series are
stationary. The PP test robust against structural breaks indicates that
three exchange rates may be stationary (Bulgarian, Estonian and
Lithuanian) – while for Lithuania it does confirm the ADF results, it is
the very opposite for Estonia. The results of the KPSS test (the is
stationarity) indicate that almost all time series are non-stationary.
Ambiguous results for Cyprian, Czech, Romanian and Slovenian
currency indicate rejections of the PPP hypothesis in the long run. The
results of the DF-GLS test allows us to reject the null hypothesis of I(1)
only for the Czech and Slovenian exchange rate in one specification.
39
If the DF-GLS statistics rejects the I(1) hypothesis, PPP holds.
40
As
the results for the alternative price index (PPI) are similar, they are
shown (for individual test) in the Appendix.
Non-linear URTs may solve problems of breaks within time series due
to changes of exchange rate regimes over time. First non-linear test,
the KSS test, does reject the only for the demeaned time series for
Slovenia but for all detrended time series apart from Bulgarian,
Latvian, Lithuanian and Romanian ones. The figure is therefore
different compared to previous results based on standard pURTs. It
gives much more support to PPP and it is similar to findings of other
studies, e.g. Telatar and Hasanov (2009). It also implies that barriers to
adjustment processes exist. For example, transaction costs change the
speed of mean reversion (larger deviations will be followed by faster
gap narrowing).
39
The DF-GLS statistics is superior to the ADF statistics as its power (lower
probability of accepting wrong null hypothesis of non-stationarity) and size
properties are better (Wu et al., 2010).
40
The number of lags in augmented versions of both tests are chosen
according to the Durbin-Watson and the Durbin's alternative test for
autocorrelation. If one of them indicates presence of autocorrelation, another
lag is added unless both indicate no presence of autocorrelation.
22
Table 3: Univariate unit root test – KSS test
KSSa)
KSSa)
demeanedb)
detrendedc)
lag lag
Bulgaria -0.5459 0.0184 (3) -2.0418 0.6479 (0)
Cyprus -3.4896*** 4.7599 (6) -6.8282*** -5.8687*** (5)
Czech Rep. -0.3878 -1.1351 (1) -4.1947*** -4.2334*** (1)
Estonia -0.8791 -0.7506 (3) -6.1489*** -7.3137*** (2)
Hungary -0.9020 -2.0717 (2) -6.8154*** -6.6128*** (3)
Lithuania -0.2466 0.0666 (0) -1.5282 -3.5109** (2)
Latvia -0.5893 0.0806 (2) -3.4366*** -2.8364 (2)
Malta -2.8975* 7.7016 (1) -5.3124*** -6.0146*** (1)
Poland -2.5024 -0.3365 (1) -6.4519*** -3.3005* (1)
Romania -0.0051 0.0173 (0) -0.0428 -0.0918 (1)
Slovenia -5.6006*** -6.0313*** (1) -4.1410*** -4.2708*** (6)
Slovakia -0.0083 -0.2674 (1) -4.5413*** -4.0299*** (1)
Note: Optimal number of lags in parentheses.
a)
values of the test statistics
reported. ***, **, and *** significant at 1%, 5% and 10% respectively. Critical
values for the KSS test (Kapetanios, G. et al. (2003), p. 364, tab. 1):
b)
-3.48, -
2.93, -2.66.
c)
-3.93, -3.40, -3.13.
Source: own calculation.
The results of the other nonlinear URTs, the Bierens (1997) test, are
shown in table 4. As there are several size distortions in the case of
this test, the critical values are based on the Monte Carlo simulation
with 10000 replications (a Gaussian process for , where
is determined by the AIC or H-Q criterion from previous steps and
initial values are taken from particular time series.) If individual tests
are not concordant, more lags are included in the model. The order for
the Chebishev polynomials ( ) must be chosen long enough, as a
lack of lags compared to structural breaks might result in lower power
of the test Bierens (1997). However, there is no simple rule for its
determination. In our case, we follow the suggestion of Cuestas
(2009), i.e. the lag length is chosen so that it yields more evidence
against the null ( ).
Our results show a rejection of the left-sided hypothesis for the Czech,
Estonian and Latvian currencies, which does not allow us to conclude
whether they are (mean) stationary, stationary with a linear trend or a
stationary around a nonlinear trend. Conversely, Lithuanian and
Slovenian currencies indicate stationarity around a nonlinear trend.
There is only one significant result for the Bulgarian, Cyprian and
23
Romanian currencies, the other one are (marginally) insignificant.
Interestingly, the results for Bulgarian or Hungarian currency are found
highly significant in Cuestas (2009),
41
but similar for other countries.
Table 4: Univariate unit root test – the Bierens (1997) test
Test t. statistics P-value Test t. statistics P-value
Bulgaria -4.9998 [0.1555] Latvia -4.0550 [0.9317]
-15.9013 [0.5654] -392.6386 [0.0696]
25.2365 [0.9696] 9.7555 [0.3363]
Cyprus -0.4551 [0.1523] Malta -6.7392 [0.6305]
-16.3117 [0.0794] -610.5297 [0.3904]
15.5347 [0.6404] 9.8155 [0.7073]
Czech Rep. -10.0111 [0.0124] Poland -6.8029 [0.5217]
-69.5700 [0.8578] -159.5950 [0.3371]
13.2114 [0.9504] 6.0903 [0.6680]
Estonia -9.6901 [0.0260] Romania -8.4230 [0.1117]a)
-185.6986 [0.1606] -221.5326 [0.0683]
36.4082 [0.9878] 7.3677 [0.8527]
Hungary -0.9820 [0.8579] Slovenia -8.6992 [0.0679]
-5.2482 [0.8986]a)
-25.2222 [0.9018]
22.6888 [0.6578] 30.0060 [0.9545]
Lithuania -5.0224 [0.9667] Slovakia -7.1495 [0.3297]
-81.0954 [0.9302] -486.4810 [0.5140]
6.9682 [0.3892] 6.2722 [0.3458]
Note: p-values in brackets. Rejection of the H0 is in bold.
a)
Marginally rejected.
Source: own calculations.
Our results for the URTs are rather inconclusive, unless we check for
possible sources of nonlinearities.
42
In addition, the values of test
41
It may have been due to inclusion of the time period including the early
1990s.
42
A recent study Telatar and Hasanov (2009) does not find much support for
PPP in CEE with ADF test either.
24
statistics may be affected by the properties of time series, so the next
step of the analysis would be to employ the pURTs. Results for some
selected pURTs can be found in Zdarek (2011).
The US Dollar
Another set of results of the URTs is for the NMS exchange rates
against the US Dollar (US $). There are only a few pieces of evidence
in favour of PPP for these currency pairs and some tests. It is again
the case of Bulgaria and Lithuania that the only two countries, where
the ADF and PP and (KPSS partially) indicate that exchange rates may
be I(0) as in the case of the pairs against the Euro. However, there is
no other evidence for other currencies and tests. The possible
explanation may be in a series of structural breaks that may have
influenced the power of the univariate URTs (periods of 'weak' and
'strong' US $ in the analysed time span).
Table 5: Univariate unit root tests (US $)
ADF PPa)
KPSSb)
DF-GLS
constant trend constant trend constant trend constant Trend
Bulgaria -1.345 -4.279*** -1.862 -5.351*** 1.420*** 0.216*** 1.469 -2.138
Cyprus -0.781 -1.807 -0.746 -1.530 0.687*** 0.311*** -0.814 -0.967
Czech Rep. 0.133 -1.941 -0.046 -1.731 1.270*** 0.321*** 0.228 -1.024
Estonia -0.388 -1.804 -0.780 -1.677 1.190*** 0.283*** 0.450 -1.703
Hungary -0.304 -2.155 -0.288 -2.052 1.210*** 0.276*** -0.570 -1.261
Lithuania -0.170 -2.384 -1.214 -2.531 1.480*** 0.164** 1.799 -2.763*
Latvia 0.358 -1.346 -0.009 -1.152 1.220*** 0.317*** 1.221 -1.727
Malta -0.464 -1.700 -0.487 -1.507 0.802*** 0.323*** -0.565 -0.839
Poland -0.661 -2.196 -1.140 -2.272 1.140*** 0.284*** -0.365 -2.764
Romania -0.650 -2.197 -0.673 -2.514 1.310*** 0.231*** -0.155 -1.527
Slovenia -0.978 -1.989 -0.886 -1.524 0.595** 0.318*** -0.764 -0.839
Slovakia -0.970 -2.458 0.150 -1.640 1.290*** 0.344*** -0.433 -1.026
Note:
a)
Z(t) values reported.
b)
values of the test statistics.
c)
DF-GLS suggested 0 lags.
d)
significant
at 2.5% level. ***, **, and * significant at 1%, 5% and 10% respectively. Critical values for the KPSS
test (level stationary): , , and ; trend stationary: ,
, , and . Trend = a constants and a time trend included.
Source: own calculation.
For the case of the non-linear KSS test, some evidence in favour of the
PPP can be found (six countries for demeaned time series), indicating
that is better than for the Euro pairs. However, there is almost no
evidence for detrended time series, which is the very opposite
compared with the results for the Euro exchange rates.
Table 6: Univariate unit root test – KSS test for the US $
25
KSS
a)
KSS
a)
demeaned
b)
detrended
c)
lag lag
Bulgaria 3.24 -3.19** (1) 6.58 -5.26*** (3)
Cyprus 1.20 -2.98** (6) 1.33 -1.95 (8)
Czech Rep. 0.81 -1.96 (8) 1.79 -1.51 (9)
Estonia 1.06 -2.96** (6) 1.56 -1.49 (9)
Hungary 1.54 -3.87*** (6) 1.91 -0.87 (8)
Lithuania 2.15 0.15 (7) 2.43 -1.93 (7)
Latvia 0.25 -1.43 (8) 1.85 -1.46 (9)
Malta 1.02 -2.74* (6) 1.28 -0.75 (10)
Poland 2.12 -2.88* (5) 2.89 -2.36 (5)
Romania 1.59 -2.37 (1) 2.13 -2.01 (1)
Slovenia 1.13 -1.39 (9) 1.44 -1.22 (10)
Slovakia 0.66 -2.81 (6) 1.41 -2.24 (5)
Note: Optimal number of lags in parentheses.
a)
values of the test statistics
reported. ***, **, and *** significant at 1%, 5%, and 10% respectively. Critical
values for the KSS test (Kapetanios, G. et al. (2003), p.~364,~tab.~1): b) -3.48, -
2.93, -2.66. c) -3.93, -3.40, -3.13.
Source: own calculation.
As far as the results for the non-linear Bierens test are concerned, they
indicate that the PPP hypothesis cannot be rejected for several NMS
countries (Bulgaria, Cyprus, Estonia, Malta, Slovakia and Slovenia).
Compared with results of the same test for the Euro pairs, the Czech
exchange rate cannot be rejected to be nonstationary. There is also
more evidence in favour of the I(0) (i.e. PPP) in the case of Malta and
Slovakia. These countries can be now included into the group of I(0)
countries, conversely for Bulgaria, Cyprus, Latvia and Lithuania. No
change can be observed in the case of Romania, Hungary and Poland.
Before moving to the next series of tests, let's summarize our results
for the US Dollar. The result presented in this section showed that
there is less evidence in favour of the PPP in the case of US $
currency pairs. Apart from the fact that a certain role may be attributed
to external shocks and other influences (leading to structural breaks in
time series), it may have been also the role of price indices used in this
exercise. National price indices were used in calculating the RER,
compared with harmonized price indices in the case of the Euro pairs.
The national definition of a price index may contain more specific items
(e.g. regulated goods and services) and as a result less evidence for
PPP is found.
26
Table 7: Univariate unit root test – the Bierens (1997) test for the US $
Test t. statistics P-value Test t. statistics P-value
Bulgaria -6.7278 [0.0834] Latvia -6.6296 [0.1366]
-114.9160 [0.8376] -96.3401 [0.8104]
8.3902 [0.9837] 7.4182 [0.8801]
Cyprus -7.0561 [0.0683] Malta -7.7843 [0.0163]
-100.974 [0.1905] -114.6098 [0.1054]b)
7.3935 [0.9308] 8.0943 [0.9632]
Czech Rep. -6.2354 [0.1960] Poland -5.5389 [0.4298]
-115.4973 [0.7696] -179.9285 [0.4716]
5.5045 [0.6856] 5.2384 [0.6350]
Estonia -7.2686 [0.0458] Romania -6.0466 [0.2689]
-59.2106 [0.6872] -126.7792 [0.0588]
6.9976 [0.9122] 4.4487 [0.4890]
Hungary -6.0268 [0.2620] Slovenia -7.4196 [0.0337]
-92.8463 [0.8435] -109.1637 [0.1147]b)
6.4191 [0.8371] 8.0226 [0.9613]
Lithuania -3.9243 [0.7985] Slovakia -6.5747 [0.1265]
-61.9370 [0.7528] -1360.4636 [0.0973]
7.5029 [0.7930] 11.3572 [0.9980]
Note: p-values in brackets. Rejection of the H0 is in bold.
a)
Marginally rejected.
Source: own calculations.
REER
The last set of results for the URTs is for REER. As we mentioned, the
sample of NMS countries for the REER specification is reduced due to
the lack of comparable data (the Baltic States and Slovenia) since the
IMF does not publish REER time series for all the CEE countries. We
decided to test the time series only for a reduced set of these countries
and do not use various definitions of a REER. We prefer doing that to
27
calculating our own time series or obtaining time series of REERs from
other sources as definitions are usually not comparable (different price
indices or time frequencies that would have required either aggregation
or desaggregation of original time series).
Table 8: Univariate unit root tests (REER)
ADF PPa)
KPSSb)
DF-GLS
constant trend constant trend constant trend constant trend
Bulgaria -1.041 -3.655** -0.973 -3.291* 1.440*** 0.108 1.543 -1.664
Cyprus -0.113 -1.992 -0.233 -2.143 1.220*** 0.214d)
-0.962 -2.127
Czech Rep. -0.558 -3.048e)
-0.594 -3.182* 1.540*** 0.0964 0.958 -4.300***
Hungary -0.510 -1.341 -0.480 -3.164* 1.540*** 0.116 0.258 -1.026
Malta 0.086 -2.369 0.059 -2.389 1.460*** 0.179d)
0.941c)
-1.868c)
Poland -2.216 -2.623 -2.242 -2.707 1.130*** 0.115 -0.747 -2.558e)
Romania -1.620 -2.880 -1.268 -2.608 1.300*** 0.0794 -0.318 -3.258**
Slovakia 0.507 -2.142 0.868 -2.026 1.530*** 0.333*** 1.544 -1.501
Note:
a)
Z(t) values reported.
b)
values of the test statistics.
c)
DF-GLS suggested 0 lags.
d)
significant at 2.5% level. KPSS test (level stationary): , , and
; trend stationary: , KPSS test (level stationary): , ,
and ; trend stationary: , , , and . Trend = a constants
and a time trend included.
Source: own calculation.
To begin with, univariate URTs are used (results are in table 8). As to
the three standard tests, there is some evidence in favour of PPP in
the case of Bulgaria, the Czech Republic (the ADF test is significant at
) and Hungary (ADF, PP and KPSS).
43
The results of the
more robust test (DF-GLS) indicate that I(0) can be rejected for the
Czech Republic, Romania and marginally for Poland (at ).
Table 9: Univariate unit root test – KSS test for REER
KSSa)
KSSa)
demeanedb)
detrendedc)
lag lag
Bulgaria 2.48 -2.01 (1) 3.60 -1.99 (1)
Cyprus 1.74 -3.01** (1) 2.85 -2.74 (1)
Czech Rep. 1.02 -2.10 (5) 2.96 -3.32* (4)
Hungary 1.57 -1.23 (7) 3.76 -1.98 (8)
43
Results for KPSS and a specification with a time trend allow us to reject the
null I(0) only for Cyprus, Malta and Slovakia.
28
Malta -0.04 -1.97 (1) 1.35 -1.22 (1)
Poland -2.54 -1.18 (5) 2.82 -2.50 (5)
Romania 1.82 -1.40 (6) 3.21 -3.55** (10)
Slovakia -0.88 -2.13 (3) 2.75 -2.48 (4)
Note: Optimal number of lags in parentheses. a) values of the test statistics
reported. ***, **, and *** significant at , and respectively. Critical
values for the KSS test (Kapetanios, G. et al. (2003), p.~364,~tab.~1): b) -3.48,
-2.93, -2.66. c) -3.93, -3.40, -3.13.
Source: own calculation
.
The results for the non-linear KSS test (in the table 9) show almost no
evidence supporting the PPP hypothesis, if REER is used. On the
other hand, the results for the other non-linear test do. The results are
presented in table 10. The test results indicate that the validity of the
PPP hypothesis can be confirmed only for two countries – Bulgaria and
Romania. In the case of Cyprus and the Czech Republic, it is not
possible to decide (following recommendations in Bierens (1997) as
only one out of three test statistics indicates that PPP holds). The
results for Malta and Slovakia – significant in other cases – are
insignificant for REER. There is also no change for Hungary and
Poland (rejection of PPP). To sum up, there is even weaker evidence
for the REER exchange rate that PPP holds in the NMS countries.
Table 10: Univariate unit root test – the Bierens (1997) test for REER
Test t. statistics P-value Test t. statistics P-value
Bulgaria -4.0285 [0.9186] Malta -6.2790 [0.1826]
-46.9439 [0.9026] -103.8727 [0.1498]
2.8675 [0.0633] 6.1814 [0.8735]
Cyprus -5.3484 [0.5073] Poland -6.6419 [0.1241]a)
-100.974 [0.1905] -76.2201 [0.4927]
7.3935 [0.9308] 5.6712 [0.7454]
Czech Rep. -3.7482 [0.9229] Romania -3.7088 [0.9466]
-238.8240 [0.3113] -42.9034 [0.9213]
3.6408 [0.1585] 3.1308 [0.0638]
Hungary -4.3707 [0.8308] Slovakia -5.1902 [0.6035]
-78.0290 [0.4237] -52.2559 [0.8376]
5.0651 [0.7077] 750.9913 [0.3151]
29
Note: p-values in brackets. Rejection of the H0 is in bold.
a)
Marginally rejected.
Source: own calculations.
What conclusion can be drawn – is the 'PPP puzzle' still alive?
As we have seen, the results are rather ambiguous and do not provide
clear guidance regarding the PPP hypothesis for NMS countries. What
are the possible reasons for these findings? Wu et al. (2010) and Alba
and Papell (2007) summarize the recent studies and highlight that
there may be some country characteristics that determine whether the
PPP holds or not. These are the inflation rate, openness, volatility of
exchange rate, economic growth and distance. However, empirical
studies have not confirmed any of these determinants beyond all
doubts. The results in this study are not crystal clear, either. Possible
problems and/or reasons for the lack of clear-cut evidence in the
analysis of the PPP can be divided into three groups.
The first group includes problems and issues related to available data.
For example, some of them can be labelled as problems of transition
countries. Our time span starts in mid-1990s, which gives us enough
observations in the time dimension, but may also be teh reason why
results are rather mixed due to the changes of exchange rate regimes
in some countries. In a similar vein, the measures of inflation may have
been exposed to similar kind of shocks. Therefore, the problem may be
associated with price indices and not with exchange rates.
Another problem is well known in the literature – aggregation bias. It
can be associated either with the data used Broda and Weinstein
(2008) or linked to empirical methods Imbs et al. (2005) parameter
heterogeneity). Additionally, there may be a bias associated with small
samples in the data Chen and Engel (2004) that may have an impact
on results.
44
The second group encompasses various direct and indirect (nonmarket)
measures applied in an economy. One of them can be in the
form of exchange rate arrangements such as the ERM II. This may
have restricted the exchange rates of NMS countries and therefore the
results of URTs may be inconclusive. The euro as a benchmark for our
analysis may also influence our results, as it was an artificial currency
in the 1990s. However, this choice seems to be rational, since the US
dollar has lost its importance in the NMS countries and the euro/ECU
has gained significance due to European integration process.
Moreover, some authors argue that the RER are not I(1) but rather I(0)
process that has a nonlinear (deterministic) trend or with structural
breaks. This may give support to the notion of a 'quasi-PPP' or 'a
44
Robertson et al. (2009) surveys literature and discuss sources of these
biases in depth. It also shows how important these biases for a development
country are (Mexico compared to the US).
30
relaxed version of PPP' (for discussion see e.g. Cuestas and Regis,
2008).
Another example is mentioned in the study by Brissimis et al. (2005).
The authors claim that monetary authority's interventions in the foreign
market targeting a certain level of exchange rate may result in the
inability to confirm PPP empirically even though it holds. Additionally,
Taylor (2004) puts forward that interventions may lead to RER
displaying nonlinear behaviour, e.g. with I(1) type of behaviour within a
certain band, and I(0) outside.
45
For example, some countries have
been using inflation targeting and exchange rate is an important part of
this. An exchange rate has direct and indirect impacts on inflation.
Finally, the last group incorporates empirical problems and problems of
econometric methods. One of them may be a group of issues related
to the problem called fractional integration of time series. This means
that time series have a long memory (long range dependence).
46
This
poses a problem not only for URTs and but also for pURTs. This would
mean that standard URTs are not suitable for those cases.
It also includes more practical aspects as different specification of a
non-linear adjustment process. For example, Bahmani-Oskooee et al.
(2008) argue that assumptions for PPP are not met in many countries
and as a result, the PPP hypothesis is rejected. Additionally, some
market interventions, friction or misbeliefs may hamper market forces
from restoring equilibrium. This may lead to the necessity to account
for these by employing nonlinear methods such as threshold models.
The lag selection is a problem of non-linear tests such as the Bierens
(1997) test.
47
This is because the number of lags (k) can be
determined by various methods, but the same cannot be easily done
for the order of Chebishev polynomials m (however, the actual size of
the test depends on it). Hence, the power may be low (see Bierens,
(1997).
Even though it is not possible to list and discuss all possible problems
and issues related to the testing of the PPP, given the space limitations
of this paper, the aforementioned ones can help us to answer the
question stated in the title of this subsection. The 'PPP puzzle' is still
alive and it is not clear when we will have such (empirical) tools that
will give us a clear answer.
45
The Bierens (1997) test should account for this.
46
That is I(d) time series, where 0 < d <1. The key threshold is the value of d =
1/2 dividing time series into two groups (stationary and non-stationary).
47
This seems to be the main problem for empirical analyses of time series,
see Harris and Sollis (2005).
31
6. CONCLUSIONS
This paper focused on testing the relative version of the PPP in the
NMS countries over the time span of 15 years. It tried to shed some
light on the 'old PPP puzzle' for a set of transition countries. As there
has been a large number of studies with rather ambiguous results,
various econometrics methods were employed. We made use of
standard URTs, and additionally, more robust versions of URTs . While
standard univariate URTs do not provide a crystal-clear answer to our
question, the robust versions do for the Euro exchange rate pairs in
particular. The results for the non-linear KSS test (ESTAR model),
which gives support to PPP in eight out of 12 NMS countries and the
results for another nonlinear test (non-linear in trends, the Bierens
(1997) test), also tends to favour the existence of PPP, once the
source of non-linearities has been controlled for. In the case of other
currency pairs – the US Dollar and REER, the results are less
significant and thus, they seem to give more emphasis on the
importance of the Euro currency for the NMS countries.
There are many possibilities regarding the future research in this area.
More detailed analysis based on individual subindices of the HICP
index should be conducted as one extension going beyond the scope
of this paper.
48
Using selected price subindices that may solve
problems associated with aggregation bias. However, these subindices
are available only for a limited set of countries and/or time span is very
limited, which limits their use.
Possible extensions of this work could be done with respect to several
aspects. An extension may be based on using disaggregated price
indices (either for CPI or HICP) for our group of countries, different
indices (broad or narrow versions of REER) or different benchmark
countries (the US). Moreover, more robust univariate URTs such as
the CBL test
49
or methods based on panel smooth transition regression
models (PSTR, see González et al., 2005) that may solve some
problems of nonlinear adjustment processes or structural breaks due
to their construction. They would also allow for using longer time span.
48
Additionally, due to lack of availability consumer price subindices for some
countries and most of the 1990s, it would lead to radical reduction of our
sample and therefore, the necessity to switch from quarterly to monthly time
series so that one would gain some power for the URTs and pURTs .
49
Carrion-i-Silvestre, Barrio-Castro and Lopez-Bazo, see Carrion-i-Silvestre et
al. (2005) allowing for several structural breaks in the presence of crosssectional
dependence).
32
OUTPUTS
Robustness check for PPI
Table 11: Univariate unit root tests
ADFa)
PPa)
KPSSb)
DF-GLS
constant trend constant trend constant trend constant trend
Bulgaria -2.139 -4.730*** -2.874** -6.830*** 1.000*** 0.190d)
1.052 -0.524
Cyprus -1.363 -2.727 -0.657 -2.316 0.663d)
0.140* 1.186 -2.633*
Czech
Rep.
-0.732 -3.368* -0.738 -3.458** 1.080*** 0.0522 0.257 -4.377***
Estonia -3.581*** -4.379*** -3.967*** -3.789** 0.792*** 0.169** 0.919 -2.145
Hungary -2.889** -3.315** -1.570 -2.568 0.893*** 0.207d) 0.461 -0.896
Lithuania -2.144 -4.025** -2.144 -2.262 0.932*** 0.165** 1.202 -1.068
Latvia -2.199 -2.481 -2.068 -2.045 0.853*** 0.130* 0.487c)
-1.727
Poland -2.164 -2.477 -2.603* -3.056 0.631d)
0.0872 -0.157 -1.757
Romania -0.633 -2.378 -0.998 -2.824 1.030*** 0.0549 1.244 -3.704**
Slovenia -2.341 -2.286 -2.106 -2.030 0.689d) 0.0883 -1.297 -2.752
Slovakia 0.187 -1.960 0.577 -1.740 1.04*** 0.251*** 1.256 -1.627
Note: a) Z(t) values reported. b) values of the test statistics. c) DF-GLS suggested 0 lags. d)
significant at 2.5% level. ***, **, and * significant at 1%, 5% and 10% respectively. Critical values for
the KPSS test (level stationary): , , and ; trend stationary:
, , , and . Trend = a constants and a time trend included.
Source: own calculation.
33
6.1. Exchange rate regimes in the NMS
countries
Table 12: The most recent exchange rate regimes – NMS
Currency regime Period
Bulgaria peg (currency board) July 5, 1997 Cyprus
free float - December 31, 2008
Czech Rep. free/managed float June 26, 1997 Estonia
peg (currency board) June 20, 1992 Hungary
managed float June 2001Lithuania
peg (currency board) April, 1 1994 Latvia
peg to the Euro January 1, 2005 Malta
free float - December 31, 2008
Poland free float April 12, 2000 Romania
managed float August 1, 2005 Slovenia
free/managed float - December 31, 2006
Slovakia peg with bands - December 31, 2008
Note: Bulgaria: till February 1, 2002 to the Deutsche Mark, to the Euro since then.
Cyprus: fluctuation margins in ERM II. From January 1, 2009 the Euro. Czech
Republic: managed float. Estonia: till February 1, 2002 to the Deutsche Mark, to the
Euro since then. Hungary: float either since June 18, 2001 when all remaining barriers
to full convertibility of HUF were removed or May 3, 2001 when band was
introduced. Lithuania: till February 1, 2002 to the US Dollar, to the Euro since then.
Latvia: with the normal fluctuation margins . Malta: fluctuation margins in
ERM II. From January 1, 2009 the Euro. Poland: free float since 2000. Romania:
inflation targeting. Slovenia: fluctuation margins in ERM II. From January 1, 2007
the Euro. Slovakia: fluctuation margins in ERM II. From January 1, 2009 the
Euro.
Source: Source: own based on [IMF (2010a)] and CB websites.
34
6.2. Exchange rates
Figure 2: Exchange Rates of the NMS countries against the Euro
35
Source: see text.
36
Figure 3: Exchange Rates of the NMS countries against the US Dollar
37
Source: see text.
38
Figure 4: Exchange Rates of the NMS countries REER
Source: see text.
39
6.3. Statistical appendix
Table 13: Summary statistics – for the EU specification
ER
a)
hicp
b)
ppi
b)
rer_hicp
c)
rer_ppi
c)
Bulgaria mean 1.071 4.091 4.057 0.798 0.808
SD 0.617 1.208 1.189 0.273 0.259
Cyprus mean 0.581 4.533 4.504 -0.517 -0.489
SD 0.006 0.120 0.120 0.039 0.064
Czech mean 31.969 4.533 4.525 3.489 3.489
Republic SD 3.787 0.160 0.117 0.152 0.139
Estonia mean 15.588 4.507 4.550 2.806 2.753
SD 0.197 0.226 0.227 0.136 0.069
Hungary mean 241.575 4.399 4.454 5.649 5.581
SD 29.819 0.347 0.355 0.155 0.069
Lithuania mean 3.900 4.584 4.493 1.319 1.413
SD 0.632 0.151 0.167 0.209 0.231
Latvia mean 0.656 4.523 4.537 -0.379 -0.402
SD 0.052 0.237 0.247 0.151 0.111
Malta mean 0.429 4.537 .. -0.835 ..
SD 0.016 0.116 .. 0.055 ..
Poland mean 3.897 4.463 4.472 1.453 1.439
SD 0.388 0.241 0.243 0.135 0.089
Romania mean 2.535 3.816 3.723 3.772 1.500
SD 1.366 1.141 1.140 2.156 0.279
Slovenia mean 213.682 4.432 4.461 5.484 5.451
SD 29.172 0.256 0.204 0.031 0.029
Slovakia mean 38.710 4.404 4.452 3.805 3.754
SD 4.154 0.271 0.218 0.257 0.207
Note: SD – standard deviation.
a)
absolute values.
b)
natural logs of seasonally
adjusted indices.
c)
natural logs of original values. `..' – not available. Values for the
Euro area – mean (SD): hicp: 4.553 (0.091), ppi: 4.573 (0.069).
Source: own calculations.
40
Table 14: Summary statistics – for the US specification
ER
a)
cpi
b)
ppi
b)
reer_cpi
c)
Bulgaria mean 1.50 4.057 4.057 4.490
SD 0.605 1.208 1.193 0.230
Cyprus mean 0.502 4.521 4.504 4.566
SD 0.076 0.120 0.149 0.059
Czech mean 27.900 4.515 4.525 4.509
Republic SD 6.630 0.160 0.116 0.181
Estonia mean 13.472 4.487 4.550 ..
SD 2.172 0.225 0.154 ..
Hungary mean 209.22 4.375 4.454 4.459
SD 44.506 0.347 0.263 0.162
Lithuania mean 3.361 4.577 4.493 ..
SD 0.674 0.151 0.189 ..
Latvia mean 0.562 4.503 4.537 ..
SD 0.044 0.237 0.218 ..
Malta mean 0.369 4.533 .. 4.555
SD 0.048 0.107 .. 0.068
Poland mean 3.370 4.448 4.471 4.535
SD 0.629 0.241 0.191 0.123
Romania mean 2.156 3.763 3.723 4.447
SD 1.105 1.140 1.189 0.208
Slovenia mean 184.096 4.418 4.461 ..
SD 34.852 0.251 0.204 ..
Slovakia mean 33.829 4.391 4.452 4.461
SD 8.382 0.273 0.218 0.250
Note: SD – standard deviation.
a)
absolute values.
b)
natural logs of
seasonally adjusted indices.
c)
natural logs of original values. `..' – not
available. Values for the US economy– mean (SD): cpi: 4.530 (0.111), ppi:
4.510 (0.138).
Source: own calculations.
41
Table 15: Data sources
Description Variable Description, base index
IMF IFS database
..RF.ZF Exchange rates (market rate, periodic average,
National Currency per US )
64H..ZF HICP 2005 = 100
64...ZF CPI 2005 = 100
..RFCZF REER
99BIPZF GDP deflator 2005 = 100
63...ZF PPI/WPI
Eurostat
GDP deflator 2005 = 100National
Accounts
ULC deflator 2005 = 100
Database
price
HICP 2005 = 100
PPI 2005 = 100
UNECE
External
economic
relations
Exchange rates
Price indices CPI 2005 = 100
Price indices PPI 2005 = 100
ECB
Statistical
Data
Warehouse
HICP 2005 = 100
PPI 2005 = 100
EBRD
Transition
Reports
Transition index
42
Lag specification
Table 16: Suggested numbers of lags – Euro based time series
country exchange rates
ER_CPI ER_PPI
BG 3 2
CY 2 2
CZ 3 3
EE 2 1
HU 3 1
LT 6 5
LV 3 2
MT 2 –
PL 4 2
RO 3 2
SI 2 4
SK 5 3
Note: '–' not available.
Source: own calculation.
43
Table 17: Suggested numbers of lags – US based time series
and REER
country exchange rates
ER_CPI ER_PPI REER
BG 1 1 2
CY 2 2 1
CZ 3 3 3
EE 2 1 –
HU 3 1 3
LT 3 5 –
LV 3 2 –
MT 2 – 1
PL 4 2 2
RO 3 3 2
SI 2 2 –
SK 5 5 1
Note: '–' not available.
Source: own calculation.
44
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