Hence, a long-run equilibrium between consumer prices and exchange rates is believed to exist more often in the period after the start of the European Monetary Union than before

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(1)Master thesis finance. “Does purchasing power parity hold in the EU, or does the introduction of the European Monetary Union create an arbitrage opportunity?”. Bosse Zwerink s1618628 Supervisor: Ms. S. Bumann University of Groningen Faculty of Economics and Business January 17, 2013.

(2) Abstract This paper examines the effect of the introduction of the European Monetary Union on the equilibrium concept of purchasing power parity in the European Union. The treaty of Maastricht, entered into force on November 1st 1993, removed trade barriers between EU-member countries. Hence, a long-run equilibrium between consumer prices and exchange rates is believed to exist more often in the period after the start of the European Monetary Union than before. This paper finds evidence both supporting and contradicting this hypothesis. The results indicate an increase of 100% in the strong form of purchasing power parity between two non-Eurozone EU-member countries after the introduction of the monetary union. However between Eurozone and non-Eurozone EU-member countries, a long-run equilibrium between exchange rates and consumer prices holds 33.3% less often than before.. Key words: Purchasing Power Parity, European Monetary Union, Euro, Cointegration YEL codes: A23 C32 E31 E42 N24. 2.

(3) Table of contents List of figures ................................................................................................................... 6 1. Introduction ................................................................................................................. 8 2. Literature review ........................................................................................................ 10 2.1 Purchasing Power Parity ...................................................................................... 10 2.2 PPP and the EU ................................................................................................... 11 3. Methodology.............................................................................................................. 12 3.1 Step 1: Unit-root testing ....................................................................................... 13 3.2 Step 2: Johansen multivariate framework ............................................................ 14 3.3 Step 3: Restrictions .............................................................................................. 17 4. Data .......................................................................................................................... 18 4.1 Countries and time periods .................................................................................. 18 4.2 Data collection and manipulation ......................................................................... 20 4.2.1 CPI rates ....................................................................................................... 20 4.2.2 Danish exchange rates .................................................................................. 20 4.2.3 Swedish exchange rates ............................................................................... 20 4.2.4 UK exchange rates ........................................................................................ 21 4.3 Creating country pair samples ............................................................................. 21 4.4 Descriptive statistics ............................................................................................ 22 5. Results ...................................................................................................................... 25 5.1 Period 1970-1992 ................................................................................................ 25 5.1.1 Step 1: Unit root testing on real exchange rate .............................................. 25 5.1.2 Step 2: Johansen cointegration test............................................................... 25 5.1.3 Step 3: Restrictions ....................................................................................... 39 5.2 Period 1995-2012 ................................................................................................ 40 5.2.1 Step 1: Unit root testing on real exchange rate .............................................. 40 5.2.2 Step 2: The Johansen framework .................................................................. 40. 3.

(4) 5.2.3 Step 3: Restrictions ....................................................................................... 63 6. Discussion ................................................................................................................. 65 6.1 Discussion of the results ...................................................................................... 65 6.2 Remarks .............................................................................................................. 67 6.2.1 Lack of testable data ..................................................................................... 67 6.2.2 Lag-length selection ...................................................................................... 67 6.2.3 Reconsidering weak test results .................................................................... 68 6.2.4 Problems with unit root testing....................................................................... 68 6.2.5 Problems with normality of the residuals........................................................ 68 6.2.6 Remarks regarding the PPP theory ............................................................... 69 6.2.7 Economic shocks .......................................................................................... 69 6.2.8 Determinants of the real exchange rate ......................................................... 70 7. Conclusion ................................................................................................................ 70 7.1 Possibilities for further research ........................................................................... 71 References.................................................................................................................... 72 Appendix ....................................................................................................................... 75 A. Descriptive statistics .............................................................................................. 75 B. Unit root tests ........................................................................................................ 82 C. Unit root tests Johansen framework ...................................................................... 88. List of tables Table 1: A summary of all EU countries from 1970-2012 ............................................... 18 Table 1: Unit root tests of the CPIs of Non-Euro Countries (first time period) ................ 27 Table 0.2: Unit root tests of the CPIs of the sample Denmark (first time period) ............ 28 Table 0.3: Unit root tests of the exchange rates of sample the Denmark (first time period) ...................................................................................................................................... 30 Table 0.4: Unit root tests of the CPIs of the sample Sweden (first time period).............. 31 Table 0.5: Unit root tests of the exchange rates of the sample Sweden (first time period) ...................................................................................................................................... 33 4.

(5) Table 0.6: Johansen test Sweden vs. Belgium (first time period) ................................... 34 Table 0.7: Johansen test Sweden vs. Denmark (first time period) ................................. 35 Table 0.8: Johansen test Sweden vs. Italy (first time period) ......................................... 36 Table 0.9: Unit root tests of the CPIs of the sample UK (first time period) ..................... 37 Table 0.10: Unit root tests exchange rates of the sample UK (first time period) ............. 38 Table 0.11: Hypothesis test Sweden: Cointegrating vector β = [1, -1] (first time period) 39 Table 0.12: Unit root tests of the CPIs of all countries (second time period) .................. 41 Table 0.13: Unit root tests exchange rates of the sample Denmark (second time period) ...................................................................................................................................... 43 Table 0.14: Johansen test Denmark vs. France (second time period) ........................... 44 Table 0.15: Johansen test Denmark vs. Italy (second time period) ................................ 45 Table 0.16: Johansen test Denmark vs. Spain (second time period) ............................. 46 Table 0.17: Unit root tests of the exchange rates of the sample Sweden (second time period) ........................................................................................................................... 47 Table 0.18: Johansen test Sweden vs. Austria (second time period) ............................. 48 Table 0.19: Johansen test Sweden vs. Belgium (second time period) ........................... 49 Table 0.20: Johansen test Sweden vs. Denmark (second time period) ......................... 50 Table 0.21: Johansen test Sweden vs. France (second time period) ............................. 51 Table 0.22: Johansen test Sweden vs. Italy (second time period) ................................. 52 Table 0.23: Johansen test Sweden vs. Spain (second time period) ............................... 53 Table 0.24: Unit root tests of the exchange rates of the sample UK (second time period) ...................................................................................................................................... 54 Table 0.25: Johansen test UK vs. Austria (second time period) ..................................... 55 Table 0.26: Johansen test UK vs. Belgium (second time period) ................................... 56 Table 0.27: Johansen test UK vs. Denmark (second time period) ................................. 57 Table 0.28: Johansen test UK vs. France (second time period) ..................................... 58 Table 0.29: Johansen test UK vs. Italy (second time period) ......................................... 59 Table 0.30: Johansen test UK vs. Luxembourg (second time period) ............................ 60 Table 0.31: Johansen test UK vs. Spain (second time period)....................................... 61 Table 0.32: Johansen test UK vs. Sweden (second time period) ................................... 62 Table 0.33: Hypothesis test Denmark: Cointegrating vector β = [1, -1] (second time period) ........................................................................................................................... 63 Table 0.34: Hypothesis test Sweden: Cointegrating vector β = [1, -1] (second time period) ........................................................................................................................... 63 5.

(6) Table 0.35: Hypothesis test the UK: Cointegrating vector β = [1, -1] (second time period) ...................................................................................................................................... 64 Table 0.1: Conclusions of cointegration tests in the first time period.............................. 65 Table 0.2: Conclusions of cointegration tests in the second time period ........................ 66 Table A.1: Descriptive statistics, Consumer price indices per country (1970-1992)..…. 75 Table A.2: Descriptive statistics, Danish exchange rates per country (1970-1992) ……76 Table A.3: Descriptive statistics, Swedish exchange rates per country (1970-1992)...…76 Table A.4: Descriptive statistics, UK Exchange rates per country (1970-1992)…………77 Table A.5: Descriptive statistics, Consumer price indices per country (1995-2012)…….78 Table A.6: Descriptive statistics, UK Exchange rates per country (1995-2012)…….......79 Table A.7: Descriptive statistics, Swedish exchange rates per country (1995-2012)…...80 Table A.8: Descriptive statistics, Danish exchange rates per country (1995-2012)….....80 Table B.1: Unit root tests real exchange rates (first time period)…………………….……82 Table B.2: Unit root tests real exchange rates (first time period)………………..………..85 Table C.1: Unit root tests of the CPIs of Non-Euro Countries (first time period)…..…....88 Table C.2: Unit root tests CPI tests sample Denmark (first time period)…………….......89 Table C.3: Unit root tests Exchange rates Denmark (first time period)……………….….92 Table C.4: Unit root tests CPI tests sample Sweden (first time period)……………….….94 Table C.5: Unit root tests exchange rates tests sample Sweden (first time period)….…96 Table C.6: Unit root tests CPI tests sample UK (first time period)…………………...…...98 Table C.7: Unit root tests exchange rates tests sample UK (first time period )…….……99 Table C.8: Unit root tests CPI tests (second time period)………………………..….…..101 Table C.9: Unit root tests Exchange rates Denmark (second time period)……….……104 Table C.10: Unit root tests Exchange rates Sweden (second time period)…….…….. 106 Table C.11: Unit root tests Exchange rates UK (second time period)………….………108. List of figures Figure 1: Denmark versus Portugal from 1-1987 until 12-1992...................................... 22 Figure 2: Sweden versus Belgium from 1-1970 until 12-1992........................................ 23 Figure 3: Denmark versus Spain from 1-1995 until 03-2012 .......................................... 23 Figure 4: Sweden versus Spain from 1-1995 until 03-2012 ........................................... 24. 6.

(7) List of abbreviations ADF. Augmented Dickey-Fuller. AIK. Aikake criterion. CPI. Consumer price index. EMU. European Monetary Union. ERM II. Exchange rate mechanism. EU. European Union. FPE. Final prediction error criterion. Ger. Germany. HQ. Hannan-Quinn criterion. IMF. International monetary fund. Ire. Ireland. KPSS. Kwiatkowski-Phillips-Schmidt-Shin. Log. Logarithm. LR. Likelihood ratio. Max. Maximum. Min. Minimum. OECD. Organization for Economic Co-operation and Development. PPP. Purchasing power parity. SC. Schwarz criterion. St. Dev.. Standard deviation. Swe. Sweden. UK. United Kingdom. US. United States. VAR. Vector auto regression. VECM. Vector error correction model. Interpretation of a variable in a table or figure L_E_SPA. Log of the exchange rate of Spain. L_CPI_DEN. Logarithm of the consumer price index of Denmark. 7.

(8) 1. Introduction Purchasing power parity, henceforth PPP, is an important instrument in macroeconomic models, because it represents a constant long-run equilibrium for real exchange rates (Koedijk et al., 2004). In short, the PPP theory states that similar goods must sell for the same price in different countries, also known as the Law of One Price (Cassel, 1918). Fluctuating exchange rates are an important concern for policy makers, requiring thorough understanding about what drives real exchange rates. Hence, PPP theory states that. a long-run equilibrium exists between the nominal exchange rate and. consumer prices of two countries (Christidou et al., 2010).Since the introduction of the Euro in 1999 the Euro exchange rates have fluctuated widely and a financial crisis has taken place in the recent past. Therefore it is important for policy makers to know whether the exchange rates are moving from or towards their long run equilibrium (Zhou et al., 2011). The European Monetary Union, henceforth EMU, obliges countries to meet four criteria in order to adopt their single currency, the Euro. The four requirements are: (1) a target range for inflation rates, (2) government debt and deficit target ratios, (3) a long-term interest rate target range and (4) adoption of the Exchange Rate Mechanism II, henceforth ERM II, for at least two consecutive years1. These prerequisites, established in the treaty of Maastricht, should help maintain price stability in the Eurozone. Candidate-member countries that fulfill the four criteria for at least two years may enter the European Monetary Union. By adopting the Euro, the countries effectively exit the ERM II. So countries in the European Union, henceforth EU, face a tradeoff between retaining their exchange rate policy and becoming a Eurozone country. Before entering the ERM II program, countries are able to appreciate/depreciate their currency in order to stimulate their national economy. Of course, this worsens the economy of EU member countries as outsider countries are able to favorably influence the value of their currency. In order to preserve price stability in the Eurozone, candidate-member countries give up their monetary policy equipment. As it is argued that adopting a common currency facilitates trade between countries, the effect of adopting the Euro on the national economy is ambiguous (Egert et al., 2005). As mentioned, these admission criteria are designed to maintain price stability in the Eurozone. Hence, these criteria should dampen the variability in real exchange rates when introducing the Euro. Consequently, a long-run PPP equilibrium should exist. As a 1. http://eur-lex.europa.eu/en/treaties/dat/11992M/htm/11992M.html. 8.

(9) result there have been several empirical studies testing the validity of PPP for Eurozone countries recently (Koedijk et al., 2004; Christidou et al., 2010; Kasman et al., 2010; Borsic et al., 2012; Liu et al., 2012). These studies indicate that there is no conclusive result whether PPP holds for Eurozone countries. One of the flaws of PPP is that transactional and transportation costs are not coped with (Sercu et al., 1995). However all the researches focus on the validity of PPP when the national currency is compared to the US Dollar or the Euro. However, in this situation transactional and transportation costs, which might cause the PPP equilibrium not to hold, exist. Since lots of EU countries are adjacent, transportation costs are low, and since the EU has an act in free movements of goods2, PPP should hold more often between EU countries after the enforcing of the treaty of Maastricht. So by examining country pairs that are both in the EU, but are not both Eurozone countries, an interesting situation can be tested. By comparing the time period before the enforcing of the treaty of Maastricht with the time period afterwards, the effect of removing trade barriers and thus the introduction of the European Monetary Union can be tested. The tested hypothesis in this paper is that removing trade barriers increases the PPP to hold. Therefore, the main research question is proposed: Does the introduction of the European Monetary Union cause the equilibrium concept of PPP to hold more often between EU member countries? This main research question is split up into two sub questions. Firstly, the time period before the enforcing of the treaty of Maastricht is tested. Hence, the first sub question is proposed: Does the PPP theory hold between EU member countries before the enforcing of the treaty of Maastricht in November 1993? Secondly, after the enforcing of the treaty of Maastricht trade barriers in the EU have disappeared, hence PPP is intuitively believed to hold more often. Therefore the second research question is proposed:. 2. http://eur-lex.europa.eu/en/treaties/dat/11992M/htm/11992M.html. 9.

(10) Does the PPP theory hold between EU member countries after the enforcing of the treaty of Maastricht? In both time periods a distinction is made between Eurozone- and non-Eurozone EU countries. Answering these research questions will give us better insight what effects joining the Eurozone has on exchange rates and purchasing power. The conclusions may add relevant information to the debate whether the introduction of the Euro actually increased financial stability in the EU. Furthermore, it might help future country policy makers in decision making. on whether to join the Eurozone or not. This paper. contributes to the literature on PPP, by examining PPP in the EU and comparing the time period before the enforcing of the treaty of Maastricht with the period afterwards. Furthermore, the used data in this research also contribute to previous literature since no other research has looked at exchange rates of Eurozone countries versus EU-member countries that did not adopt the Euro in these two periods. Lastly, by using both unit root tests and a cointegration analysis, PPP is believed to be tested properly. This paper contains the following sections. The second section discusses the relevant literature. In section 3 the methodology will be described. In section 4 a description of the data is given followed by the results in section 5. Section 6 and 7 will respectively contain the discussion and the conclusions. 2. Literature review 2.1 Purchasing Power Parity The theory of Purchasing Power Parity was first established by Cassel (1918). It states that similar goods must sell for the same price in different countries, also known as the Law of One Price. As goods are subjected to arbitrage, price differences should cease to exist. Otherwise, agents would be able to earn a riskless profit by transferring goods from one market to another. This paper makes a distinction between the weak and the strong form of PPP. The weak from of PPP will implicate a long-run equilibrium between consumer prices and the exchange rate of two countries. Whereas the strong form of PPP will implicate a long run equilibrium between consumer prices and the exchange rate of two countries and that these variables move one-on-one. The theory of PPP suffers from some real-world restrictions, which causes the Law of One Price not to hold. First, there is the consideration of transaction costs, such as transportation costs and trade barriers, which will violate the law (Koukouritakis, 2009). Second, the theory 10.

(11) requires perfect substitute goods which in reality might not be available, such that one can reasonably argue price differentials are based on product differentiation. Third, another objection for the theory of PPP to hold perfectly is that not all goods are (physically) traded (Krugman et al., 2009). For example, service goods can only be consumed at a certain location whereas tangible goods can be transported cross-border. As arbitrage forces are more significant on traded goods, the theory of PPP is expected more likely to hold for tradable goods (Krugman et al., 2009). In order to cope with the comparability problems regarding prices of goods, researchers commonly use a country’s Consumer Price Index, henceforth CPI. CPIs are designed to cover the whole set of goods and services consumed within a country by the population.3 2.2 PPP and the EU Countries that want to enter the EMU have to meet various criteria, known as the treaty of Maastricht. This treaty provides convergence criteria regarding monetary and exchange rate policy (Kasman et al., 2010). Therefore, PPP in the EU is frequently tested. Kasman et al. (2010) test the theory of PPP for new members and candidate countries of the European Union. The authors find mixed results. With regards to the exchange rate with the United States, henceforth US, Dollar, PPP is invalid. With the Deutsche Mark, the authors find support for the theory. The paper outlines how countries transform their economic policy in order to align it with European economic policy. Along the lines of this paper, Christidou et al. (2010) study the effect of the introduction of the Euro on PPP for fifteen European Union (EU) countries, vis a vis the US Dollar, before and after adoption of the Euro. They find inconclusive results as the panel data stationarity tests fail to support PPP whereas panel unit root tests fail to reject PPP for the whole sample and for the period before the adoption of the Euro. Koedijk et al. (2004) studies the impact of the introduction of the Euro on the behavior of real exchange rates of domestic currencies, vis a vis the Euro, of Eurozone countries. They use data from 1973 until 2003 and present evidence in favor of PPP for the full panel real exchange rates, but remark that accounting for cross-country differences in the Euro area is essential. Hence, they conclude that the process of economic integration in Europe has accelerated the convergence toward PPP within the Euro area. Wu et al. (2011) find that PPP holds before the introduction of the Euro, whereas it fails to hold after 1999. Their results are consistent with Engel and Rogers (2004) and Rogers 3. http://epp.eurostat.ec.europa.eu/statistics_explained/index.php/Glossary:Consumer_price_index. 11.

(12) (2007) that there is no evidence that supports the law of one price after the introduction of the Euro. Borsic et al. (2012) looked at twelve Central and Eastern European economies from 1994 until 2008 and found some support for the validity of PPP, using the currency- US Dollar exchange rates in a panel unit root test. Liu et al. (2012) investigate the real exchange rate for seven Central and Eastern European countries, vis a vis the US Dollar, with a nonlinear unit-root test. They find robust evidence that PPP holds true for Slovakia, Romania and Bulgaria from a nonlinear point of view. Their findings indicate that exchange rates are reverting to their equilibrium values in a nonlinear way. Thacker (1995) studied the validity of PPP for Poland and Hungary. Whereas prior research mainly focuses on industrialized countries, the author sets out to test to what extent the PPP theory holds for transition economies. Thacker recognizes that in the short run, deviations from PPP can be expected as money supply shocks and variable inflation shocks are experienced. This however does not prevent the PPP theory to hold in the long run. Forces which might jeopardize short-run PPP are real shocks to the economy. Thacker concludes that PPP does not hold for Poland and Hungary, both vis-a-vis the Dollar as well as the British Pound and the German’s Deutsche Mark. None of the paper, mentioned above, test the PPP relation between Eurozone and EU member countries that have not adopted the Euro and what effect the introduction of a monetary union had on this relationship. Therefore, this paper is considered a good addition to previous literature on PPP in the EU. The next section discusses the methodology used in this paper. 3. Methodology4 Purchasing power parity states that there is a long-run equilibrium between the exchange rate of two countries and the ratio of their relative price levels. It implies that the real exchange rate, Qt, is stationary (Koedijk et al., 2004). Hence the real exchange rate can be defined as follows:. . 4. ∗ 1. . Eviews 7.2 is used to perform every statistical analysis in this paper. 12.

(13) where is the nominal exchange rate in domestic currency per unit of the foreign currency, is the domestic consumer price index and ∗ is the foreign consumer price. index. By taking logarithms of formula 1 we obtain the following equation:

(14) ∗ 2. where the lower case letters denote the logarithmic transformations of the corresponding uppercase letters in formula 1. Long-run PPP is said to hold if the qt sequence is stationary. A popular way to test this is by using a unit root test (Enders, 2010). 3.1 Step 1: Unit-root testing The stationarity, or non-stationarity, of a series can strongly influence its behavior and properties. A ’shock’ is the word that is commonly used to denote a change or an unexpected change in a variable or simply the error term ( ) during a particular time period (Brooks, 2008). In a stationary series a ‘shock’ to the system will gradually die away (Brooks, 2008). Hence, a shock during time t will have a smaller effect in time t+1. In a non-stationary series the effect of a shock is infinite (Brooks, 2008). Hence, the effect of a shock during time t will not have a smaller effect on time t+1. In other words, the series contains a unit root. Unit-root testing is used to test for non-stationarity in order to prevent a spurious regression. (Brooks, 2008). Because the shock is believed to never die away the following formula is obtained: . → ∞ 3. . where the value of the non-stationary variable is simply an infinite sum of previous. shocks plus the starting value (Brooks, 2008). To test the real exchange rate (qt) for. unit roots the Augmented Dickey-Fuller, henceforth ADF, test is used. Formula 3 is rewritten and augmented to prevent the test from becoming oversized. Hence, p lags of the dependent variable are used to make sure that the test does not proportionally incorrectly reject a null hypothesis more often than the nominal size used (e.g. 5%) (Brooks, 2008). The following formula is tested:. 13.

(15) #. ∆ !" ∆ " 4. ". where the lags of ∆ ‘soak up’ any dynamic structure present in the dependent variable to ensure that the residuals are not autocorrelated. p is based on minimizing the Schwarz criterion as proposed by Christidou et al. (2010) and Koehler et al. (1988). The maximum lag length is chosen to be p=12, because monthly data are used (Christidou et al., 2010 and Brooks, 2008). It is very important to choose the optimal lag length in the unit root tests. Including too many lags reduces the power of the test to reject the null hypotheses since including more lags reduces the degrees of freedom. On the other hand when including too few, the actual error process might not be captured (Brooks, 2008). The null hypothesis H0: 0, meaning that the series contains a unit root and hence is non-stationary, is evaluated using the t-ratio:. & . . 5.

(16) . where E( is the expected value of and se(E( ) is the standard deviation of the. expected value of . If the test statistic is higher than the 5% critical value, H0 cannot be rejected, and it will be concluded that there is a unit root. To increase the robustness of the test, a stationary test will be conducted. In stationarity tests the null hypothesis is. reversed, so the null hypothesis is that the series is stationary by default. The Kwiatkowski-Phillips-Schmidt-Shin, henceforth KPSS5, test is used to see whether it confirms the results from the ADF tests. If it is not possible to reject the hypothesis of non-stationarity the ADF- and the KPSS test, higher orders of integration are tested in order to make sure that H0 is not rejected invalidly. 3.2 Step 2: Johansen multivariate framework If the unit root tests implicate that qt is non-stationary, cointegration offers an alternative to test if PPP holds. The sequence formed by the sum of {

(17) + ∗ } should be cointegrated with the { } sequence. Long run PPP asserts that there exists a linear. combination of the form {

(18) + ∗ } = β0 + β1 + µt such that {µt} is stationary and the 5. In the KPSS test, Bartlett Kernel is used as the spectral estimation method with the Newey-West Bandwith.. 14.

(19) cointegrating vector is such that β1 = 1 (Enders, 1995). The Johansen methodology is a commonly used method to test for cointegration (Brooks, 2008, Enders, 1995). Before testing for cointegration all the variables need to be tested for unit roots to make sure that a variable contains the same number of unit roots. Therefore step 1 is repeated for the logarithms of the exchange rate (

(20) ) and both CPIs ( and ∗ ). These variables are tested to see: if series is stationary (I(0)); if a series needs to be differenced once to induce stationarity, hence it contains one unit root (I(1)); and if a series needs to be differenced twice to induce stationarity, hence it contains two unit roots (I(2)) (Brooks, 2008). If the same number of unit roots in all the variables cannot be rejected for the logarithms of both the consumer price indices as the exchange rates, the cointegration analysis can proceed. Suppose a country pair has g variables that are all I(1) and which may be cointegrated. A vector auto regression (VAR) with k lags containing these variables could be set up (Brooks, 2008): ( () ) ⋯ (+ + 6. - . 1 - . - - . 1 - . - - . 1 - . - - . 1 - . 1. In order to use the Johansen multivariate test, formula (6) needs to be turned into a vector error correction model (VECM) of the form: +. ∆ /+ 0 ∆" 7. ". ". where ∏ and 2" are matrices with the coefficients: ∏ = (∑+" (" ) - 45 and 2" = (∑"6 (6 ) - 45. and is an error term with mean zero (Brooks, 2008).This VAR contains g variables in the first differenced form on the left hand side and k-1 lags of the dependent variables on the right hand side, each with a V coefficient matrix attached to it (Brooks, 2008). It is important to choose the optimal lag length in the cointegration tests. As in unit root tests, including too many lags reduces the power of the test to reject the null hypotheses since including more lags reduces the degrees of freedom. On the other hand when including too few, the actual error process might not be captured (Brooks, 2008). To select the optimal lag length, the VAR in equation (6) is estimated without caring for an optimal lag length. The optimal lag length is then chosen based on minimizing the value of various. 15.

(21) information criterions: the Likelihood Ratio, henceforth, LR, -statistic, Final prediction, henceforth FPE, error and the Aikake-, henceforth AIK, Schwarz-, henceforth SC, and the Hannan-Quinn, henceforth HQ, information criterion starting from k=12, because monthly data are used (Brooks, 2008). The lag length that is appropriate according to most of the information criterions is selected, if the results are inconsistent the LRstatistic is used (Brooks 2008, Enders 1995). The Johansen test focuses on examining the ∏ matrix. ∏ can be interpreted as a long-run coefficient matrix, because in equilibrium, all the ∆" will be zero, and when the error terms, , are set to their. expected value of zero will leave ∏ + 0 (Brooks, 2008). The test for cointegration. between the y’s is calculated by looking at the rank of the ∏ matrix via its eigenvalues. The rank of a matrix is equal to the sum of the eigenvalues that are different from zero. If the variables are not cointegrated, the rank of ∏ will not be significantly different from zero (Brooks, 2008). There are two test-statistics under the Johansen approach: #. 89:;< = > lnA1 8" B 8. "9D. And λF:G =, = 1 > lnA1 λ9D B 9. where r is the number of cointegration vectors, E(λi) is the estimated value for the i-th ordered eigenvalue from the ∏ matrix. λ9:;< is a joint test where the null hypothesis is that the number of cointegrating vectors is equal or less than r than against an alternative that there are more than r (Brooks, 2008). λF:G conducts separate tests on each eigenvalue, and has the null hypothesis that the number of cointegrating vectors is r against an alternative of r+1 (Brooks, 2008). MacKinnon et al. (1999) provide critical values for the two test statistics. The distribution of the test statistics is non-standard, and the critical values depend on the value of the number of non-stationary components and whether constants are included in the equation (g-r) (Brooks, 2008). Since there are only two variables in the system, {

(22) + ∗ } and { }, there can only exist one cointegrating vector. Hence r can by definition not be larger than r=1. Therefore, only r=0 and r=1 will be tested as a null hypothesis. If the test statistic is greater than the critical value from. 16.

(23) the Mackinnon tables, the null hypothesis that there are r cointegrating vectors in favor of the alternative that there are r+1 is rejected (Brooks, 2008). After the VECM is estimated, a multivariate normality test on the residuals is performed in the orthogonalization of Lutkepohl. Since the residuals are ought to be normally distributed white noise; the null hypothesis, of the Jarque-Bera test, that the residuals are normally distributed should not be rejected (Brooks, 2008). If for a country couple cointegration cannot be rejected, this implies that there is a long-run equilibrium relationship between nominal exchange rates and consumer prices in the domestic- and foreign country (Koukouritakis, 2009). Hence, evidence for the weak form of PPP is found. Now it would be interesting to see whether the cointegration factor [1, -1] can be found between {

(24) +. ∗ } and { }, in order to confirm the strong form of PPP. To test this, a restriction will be imposed on the regression to test for this cointegrating factor. 3.3 Step 3: Restrictions To test whether the strong form of PPP holds, a restriction will be put on ∏ matrix, in order to test if the cointegration factor β=[1,-1] can be rejected (Brooks, 2008, Enders, 2010). If there exist r cointegrating vectors, only these linear combinations or linear transformations of them, or combinations of the cointegrating vectors, will be stationary (Enders, 2010). The matrix of cointegrating factors β can be multiplied by any nonsingular conformable matrix to obtain a new set of cointegrating vectors (Enders, 2010). If the restriction is not binding, i.e. it does not affect the model much, then the eigenvectors should not change much following the position of the restriction (Enders, 2010). The test statistic to test this hypothesis is given by: 9.

(25) JJK > LMN1 λ" MN1 λ∗" O ~ χ) R 9. ". where λ∗" are the characteristic roots of the restricted model, λ" are the characteristic roots of the unrestricted model, r is the number of non-zero characteristic roots in the unrestricted model and m is the number of restrictions (Brooks, 2008, Enders, 2010). If the hypothesis of the restriction cannot be rejected, this implies that the strong form of PPP holds. Hence this indicates that the nominal exchange rates move one-by-one with the relative price levels in the long-run.. 17.

(26) 4. Data 4.1 Countries and time periods This research focuses on every EU country from January 1970 until April 2012. The year 1993 is of special importance, since it is the year of the introduction of the ‘four freedoms’. The freedom of transporting goods, services, people and money. Hence it is the year in which the Maastricht treaty is enforced. Table 1 shows all the EU countries, their year of entering the EU and the year in which they adopted the Euro. Table 1: A summary of all EU countries from 1970-2012 EU entrance (year)6. Adoption Euro (year)7. Austrian Schilling (ATS). 1995. 1999. Belgium. Belgian Franc (BEF). 1952. 1999. Bulgaria. Bulgarian Lev (BGN). 2007. NA. Cyprus. Cypriot Pound (CYS). 2004. 2008. Czech Republic. Czech Koruna (CZK). 2004. NA. Denmark. Danish Krone (DKK). 1973. NA. Estonia. Estonian Kroon (EEK). 2004. 2011. Finland. Finnish Markka (FIM). 1995. 1999. France. French Franc (FRF). 1952. 1999. Germany. German Mark (DEM). 1952. 1999. Greece. Greek Drachma (GRD). 1981. 2001. Hungary. Hungarian Forint (HUF). 2004. NA. Ireland. Irish Pound (IEP). 1973. 1999. Italy. Italian Lira (ITL). 1952. 1999. Latvia. Latvian Lats (LVL). 2004. NA. Lithuania. Lithuanian Litas (LTL). 2004. NA. Luxembourg. Luxembourg Franc (LUF). 1952. 1999. Malta. Maltese Lira (MTL). 2004. 2008. Netherlands. Dutch Guilder (NLG). 1952. 1999. Poland. Polish Złoty (PLN). 2004. NA. Portugal. Portuguese Escudo (PTE). 1986. 1999. Country. Currency. Austria. Continued. 6 7. http://europa.eu/about-eu/countries/index_en.htm http://www.ecb.europa.eu/euro/intro/html/map.en.html. 18.

(27) Table 1, continued. Country. Currency (former). EU entrance (year). Adoption Euro (year). Romania. Romanian Leu (RON). 2007. NA. Slovakia. Slovak Koruna (SKK). 2004. 2009. Slovenia. Slovenian Tolar (SIT). 2004. 2007. Spain. Spanish Peseta (ESP). 1986. 1999. Sweden. Swedish Krona (SEK). 1995. NA. United Kingdom. Pound Sterling (GBP). 1973. NA. As can be seen in table 1, 11 of the 17 Eurozone countries adopted the Euro in 1999. However there are only three countries, henceforth “non-Euro countries”, Denmark, Sweden and the United Kingdom, henceforth UK, that where EU-member states before 1995 and haven’t adopted the Euro yet. Therefore we can only test the effect of the introduction of the monetary union on the equilibrium between these three countries and the Eurozone countries. Bulgaria, Cyprus, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Malta, Poland, Romania, Slovakia and Slovenia joined the EU after 1995 and these countries are not considered to belong to the group of major trading partners. Therefore, these countries are excluded from the rest of this research, since their implications will be less strong. Also data availability would become a bigger issue, since less data is available for these countries. Therefore we will first look at the PPP equilibrium between Denmark, Sweden and the United Kingdom versus Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain and versus each other from 01-1970 (or earliest date possible in data) until 12-1992. This will provide insight whether PPP held before the enforcing of the treaty of Maastricht. Secondly we will evaluate the PPP equilibrium between Denmark, Sweden and the United Kingdom versus Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, Portugal, Spain and versus each other from 01-1995 until 03-2012. When selecting a starting date, the writer faced a tradeoff between the time it took for the effect, of the treaty of Maastricht, to be incorporated in the data and having a sample size that is large enough to obtain significant results. The starting date of 01-1995 is considered to be a good approximation of the optimal start date for the second period by the writer. The results of the second time period can be. 19.

(28) compared to the previous period to evaluate the effect of the introduction of the Monetary Union. 4.2 Data collection and manipulation 4.2.1 CPI rates Monthly CPI rates for all countries are collected from Organization for Economic Cooperation and Development8, henceforth OECD, from 01-1970 until 03-2012. All indices are normalized on 01-2005 to the value of 100. The descriptive statistics can be found in the appendix, table A.1. 4.2.2 Danish exchange rates The monthly average exchange rates are gathered from the Danish central bank9 from 1970-2012, however not all exchange rates go back to 1970. Hence, the first date possible is used as the starting date of the dataset. Websites of the countries central banks, OECD, International monetary fund, henceforth IMF, Eurostat and Thomson Reuters DataStream are used to see whether a longer time span could be obtained, however this was not possible. Exchange rate data for Denmark versus Luxembourg is not available on websites of both the Danish and Luxembourg central bank, neither at websites of the OECD, IMF, Eurostat and Thomson Reuters DataStream. Therefore Luxembourg versus Denmark is excluded from this research. The descriptive statistics can be found in the appendix, table A.2. 4.2.3 Swedish exchange rates Swedish exchange rates are collected from the website of the Swedish central bank10 except for the Irish exchange rate which was not available. The data set runs from 19132006 but the data for Austria, Belgium, Finland, France, Germany, Italy, Luxembourg, Netherlands, Portugal and Spain is only available until 02-2002 because of the adoption of the Euro. Therefore Swedish-Euro daily exchange rates are gathered from Thomson. 8. http://www.oecd-ilibrary.org/economics/data/main-economic-indicators/main-economic-indicators-. complete-database_data-00052-en?isPartOf=/content/datacollection/mei-data-en. Accessed on May 04, 2012. 9. http://nationalbanken.statistikbank.dk/statbank5a/default.asp?w=1350. Accessed on May, 14 2012.. 10. http://www.riksbank.se/en/Interest-and-exchange-rates/Older-exchange-rates/. Accessed on May 14,. 2012.. 20.

(29) Reuters DataStream11 from 01-2000 until 04-2012 and are transformed into monthly exchange rates by calculating monthly averages. These Euro exchange rates are multiplied by the fixed Euro rates12 for Austria, Belgium, Finland, France, Germany, Italy, Luxembourg, Netherlands, Portugal and Spain in order to extend the data from 02-2002 until 04-2012. Lastly the collected data for Austria, Belgium, Denmark, Finland, France, Germany, Italy, Luxembourg, Netherlands, Portugal and Spain are in 100th of the foreign currency, hence these data sets are divided by 100 to obtain the correct exchange rate. The Irish data is gathered from the Irish central bank from 1979-2012. However the exchange rates are daily data, hence they are converted into monthly exchange rates by calculating monthly averages. The descriptive statistics can be found in the appendix, table A.3. 4.2.4 UK exchange rates Daily exchange rates are collected for 01-01-1970 until 01-04-2012 from Thomson Reuters DataStream13. Except for the UK-Danish exchange rate, this rate is available from 01-1987 until 01-04-2012. These exchange rates are converted into monthly exchange rates by calculating monthly averages from the daily data. The descriptive statistics can be found in the appendix, table A.4. 4.3 Creating country pair samples The sample size of a country pair is determined by the availability of the CPIs of both countries and the exchange rate between them. So if, for example, the CPI data of country A is available from 01-1970 until 04-2012, the CPI data of country B is available from 01-1981 until 04-2012 and the exchange rate data of A versus B is available from 01-1970 until 04-2012. All the variables are resized from 01-1981 until 04-2012, because in the cointegration analysis every variable needs to cover the same time period. The datasets are then resized again from the earliest date possible until 12-1992, the first time period, and from 01-1995 until 03-2012, the second time period. This way it’s possible to test each time period separately. Due to this data availability problem, multiple CPI variables of a country can exist. These will be denoted as follows: CPI_Country A(Country B), meaning the CPI number of country A in the sample of. 11. Thomson Reuters DataStream was accessed at the university of Groningen on May 15, 2012. 12. http://www.ecb.europa.eu/euro/intro/html/index.en.html. Accessed on May 14, 2012. Thomson Reuters DataStream was accessed at the University of Groningen on May 16, 2012. 13. 21.

(30) country pair AB. In order to create as little confusion as possible, the tables in the results section will contain as few difficult denotations as possible. Therefore separate tables for CPIs and exchange rates will be created for each non-Euro country. 4.4 Descriptive statistics In addition to the descriptive statistics that can be found in appendix A, this paragraph will provide the reader with some graphs and interpretation of the presented data. Each graph will present a country pair in a specific time period. Two figures of both the first and the second time period are presented. These figures might visually show that a longrun equilibrium is more apparent in the second time period. In the graphs the exchange rate is multiplied by (-1) to minimize the size of the plot.. 2. Logarithm of the CPI of Denmark. 1,9 1,8 1,7 Logarithm of the CPI of Portugal. 1,6 1,5 1,4 1,3 1,2. (-1) x Logarithm of the exchange rate Denmark vs. Portugal 1-10-1992. 1-7-1992. 1-4-1992. 1-1-1992. 1-10-1991. 1-7-1991. 1-4-1991. 1-1-1991. 1-10-1990. 1-7-1990. 1-4-1990. 1-1-1990. 1-10-1989. 1-7-1989. 1-4-1989. 1-1-1989. 1-10-1988. 1-7-1988. 1-4-1988. 1-1-1988. 1-10-1987. 1-7-1987. 1-4-1987. 1-1-1987. 1,1. Date. Figure 1: Denmark versus Portugal from 1-1987 until 12-1992 Figure 1 shows that both the CPIs of Denmark and Portugal are increasing invariably, but that the CPI of Portugal is increasing faster in this time period. If consumer prices and exchange rates move one-on-one as the strong form of PPP suggests, the exchange rate would be expected to show this difference in growth speed of the CPIs. However, the exchange seems quite unstable and shows only a little positive trend in the long run. Therefore, this visual representation provides very little evidence that PPP to hold for this country pair in this time period.. 22.

(31) 2,5. Logarithm of the CPI of Belgium. 2 1,5 Logarithm of the CPI of Sweden. 1 0,5. (-1) x Logarithm of the exchange rate of Sweden vs. Belgium 1-1-1970 1-11-1970 1-9-1971 1-7-1972 1-5-1973 1-3-1974 1-1-1975 1-11-1975 1-9-1976 1-7-1977 1-5-1978 1-3-1979 1-1-1980 1-11-1980 1-9-1981 1-7-1982 1-5-1983 1-3-1984 1-1-1985 1-11-1985 1-9-1986 1-7-1987 1-5-1988 1-3-1989 1-1-1990 1-11-1990 1-9-1991 1-7-1992. 0. Date. Figure 2: Sweden versus Belgium from 1-1970 until 12-1992 Figure 2 shows that both the CPIs of Belgium and Sweden are increasing, but that the CPI of Sweden is increasing faster in this time period. A decrease in the exchange rate can be seen, which is in line with the PPP theory. But from 1-1977 until 3-1985 the exchange rate seems to behave be a bit erratic. Since PPP predicts a long-run equilibrium between exchange rates and PPP, figure 2 seems to provide some evidence in support of the theory.. 2,2 Logarithm of the CPI of Denmark. 2,1 2 1,9 1,8 1,7. Logarithm of the CPI of Spain. 1,6 1,5. Logarithm of the exchange rate of Denmark versus Spain. 1,4 1,3 1-9-2011. 1-1-2011. 1-5-2010. 1-9-2009. 1-1-2009. 1-5-2008. 1-9-2007. 1-1-2007. 1-5-2006. 1-9-2005. 1-1-2005. 1-5-2004. 1-9-2003. 1-1-2003. 1-5-2002. 1-9-2001. 1-1-2001. 1-5-2000. 1-9-1999. 1-1-1999. 1-5-1998. 1-9-1997. 1-1-1997. 1-5-1996. 1-9-1995. 1-1-1995. 1,2. Date. Figure 3: Denmark versus Spain from 1-1995 until 03-2012 23.

(32) Figure 3 shows that both the CPIs of Denmark and Spain are increasing invariably and with approximately the same speed in this time period. The exchange rate seems to be very stable over this time period, which is in line with the PPP theory. Since PPP predicts a long-run equilibrium between exchange rates and PPP, figure 3 seems to provide some evidence in support of the theory.. 2,3. Logarithm of the CPI of Sweden. 2,1 1,9 1,7 Logarithm of the CPI of Spain 1,5 1,3 1,1 0,9. Logarithm of the exchange rate of Sweden versus Spain 1-9-2011. 1-1-2011. 1-5-2010. 1-9-2009. 1-1-2009. 1-5-2008. 1-9-2007. 1-1-2007. 1-5-2006. 1-9-2005. 1-1-2005. 1-5-2004. 1-9-2003. 1-1-2003. 1-5-2002. 1-9-2001. 1-1-2001. 1-5-2000. 1-9-1999. 1-1-1999. 1-5-1998. 1-9-1997. 1-1-1997. 1-5-1996. 1-9-1995. 1-1-1995. 0,7. Date. Figure 4: Sweden versus Spain from 1-1995 until 03-2012 Figure 4 shows that both the CPIs of Sweden and Spain are increasing invariably, but the CPI of Spain seems to grow a little faster. The exchange seems stable in the long run, but is a bit erratic in the short term. Since the difference in growth speed is not captured in this visual representation, figure 4 seems to provide little to no evidence in support of the theory. The figures 1,2,3 and 4 do not present convincing evidence that PPP holds more often in the first time period than the second. The results of the unit root and cointegration tests are presented and discussed in the next section .. 24.

(33) 5. Results In this section the results of the previously described methods will be presented and discussed. The two time periods will be presented in separate paragraphs and the results are ordered to give a clear overview of each country pair. In step 1 the real exchange rates will be tested for unit roots. If a unit root in step 1 cannot be rejected, the CPIs and nominal exchange rates will be tested in the Johansen framework in step 2. Step 2 firstly presents the results of the ADF- and KPSS tests. If stationarity in the same order of integration cannot be rejected for all variables of a country pair, the Johansen cointegration test results are presented. If the variables of a country pair are believed to be cointegrated, they will be tested for the cointegrating vector [1, -1]. These results are presented in step 3. 5.1 Period 1970-1992 5.1.1 Step 1: Unit root testing on real exchange rate Firstly the ADF test- and KPSS test results of all the real exchange rates are discussed. A variable is believed to be I(0), i.e. the real exchange rate is stationary, if both the ADF test statistic can significantly reject the null hypothesis that the series contains a unit root and the KPSS test statistic cannot significantly reject the null hypothesis of stationarity. In the appendix, table B.1, the results of the regression are presented. Table B.1 shows that non-stationarity cannot be rejected for all the real exchange rates, therefore the table is not added to the main text of this paper. One reason for this is that not one of the tests is statistically significant on the 5% significance level; this could be due to a shortage of data. Other potential reasons are discussed in the discussion section of this paper. Hence, we continue with the Johansen framework. 5.1.2 Step 2: Johansen cointegration test Firstly the ADF test- and KPSS test results of the logarithms of the nominal exchange rates and both CPIs of every country pair are discussed. A variable is believed to be stationary, i.e. the series is considered I(0), firstly; if the ADF test statistic can significantly reject the null hypothesis that the series contains a unit root and the KPSS test statistic cannot significantly reject the null hypothesis of stationarity and secondly; if the ADF test statistic can significantly reject the null hypothesis that the onetime differenced series does not contain a unit root. A variable is believed to contain one unit root, i.e. the series is considered I(1), if firstly; the series is not considered to be I(0), secondly; the ADF test statistic can significantly reject the null hypothesis that the 25.

(34) onetime differenced series contains a unit root and the KPSS test statistic cannot significantly reject the null hypothesis of stationarity in the onetime differenced series, and lastly if the ADF test statistic can significantly reject the null hypothesis that the twotimes differenced series contains a unit root. A variable is believed to contain two unit roots, i.e. the series is considered I(2), if firstly; the series is not considered I(0) or I(1) and secondly; the ADF test statistic can significantly reject the null hypothesis that the two-times differenced series contains a unit root and the KPSS test statistic cannot significantly reject the null hypothesis of stationarity in the two-times differenced series. Below, the tables referring to unit root tests present the results of the regressions of equation (4). In order to reject a unit root in a series the ADF test statistic should be lower than its 5% critical value and in order to not reject the null hypothesis of stationarity in the series, the KPSS test statistic should be lower than its 5% critical value which is 0.46. The variables of a country pair are considered to be cointegrated if the trace and max test-statistic both reject the null hypothesis that r=0. Hence, the test-statistic should be significant and exceed the 5% and 10% critical values. Furthermore, the null hypothesis of the max and trace tests that r<=1 should not be rejected. Hence, the test statistics should be significant and below the 5% and 10% critical values. Tables referring to the Johansen test present the results of the regression on the VECM presented in equation (7). Little emphasis is put on the normality of the residuals, since the sample size is considered relatively large. This section is structured as follows: first the CPIs of the non-Euro countries are presented, secondly the CPIs and the exchange rates of the country pairs with respectively Denmark, Sweden and the UK are presented. After the ADF- and KPSS test results are discussed the cointegration test results will be presented as well as the results of the cointegration test restrictions will be presented.. 26.

(35) Table 2: Unit root tests of the CPIs of Non-Euro Countries (first time period) # This table presents results of the ADF test, ∆ ∑" !" ∆" , where p is the CPI of the country, and the KPSS test for the countries in the sample of Non-Euro countries in the first time period. The ADF test statistic, the 5% critical value for this statistic and the probability of the ADF test statistic are presented followed by the interpretation of these results. The last two columns present the value of the KPSS test statistic and an interpretation of this statistic.. Country (derivative) Denmark (2). N. ADF. ADF. Probability. Interpretation. KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). ADF Test. test statistic. KPSS Test. 65. -9.51. -2.91. 0.00. reject. 0.18. accept. Denmark (Ger) (0). 141. -5.37. -2.88. 0.00. reject. 1.38. reject. Denmark (Swe) (1). 269. -3.55. -2.87. 0.01. reject. 1.52. reject. Sweden (IRE) (2). 153. -9.35. -2.88. 0.00. reject. 0.19. accept. Sweden (1). 274. -14.65. -2.87. 0.00. reject. 0.58. reject. UK (DEN) (1). 70. -6.37. -2.91. 0.00. reject. 0.28. accept. UK (IRE) (1). 151. -3.92. -2.88. 0.00. reject. 0.80. reject. UK(2). 262. -7.54. -2.87. 0.00. reject. 0.16. accept. Table C.1, in the appendix, shows the extended version of table 2. That table 2 indicates that the logarithm of the CPI of UK(Den) is I(1) and that the logarithms of the CPIs of all other countries are I(2). However, tables 4,6,11 below show that over 80% of the tested exchange rates are I(1). And since is it the purpose of this research to properly test the time period 1970-1992, only UK(Den) that is I(1) is not considered to be enough. Therefore the requirements of the Unit-root test are relaxed; hence the KPSS test is left outside the requirements. This change in requirements also applies to the other Unit root tests of the CPIs of countries in this time period. Table 2 presents the key results of the Unit root tests of the logarithms of the CPIs of the Non-Euro countries. As can be seen all test statistics are highly significant. Furthermore, the ADF test statistic of all countries is lower than the 5% significance level. And KPSS. 27.

(36) test statistic is lower than the 5% significance level of 0.46 for Denmark, Sweden(Ire), UK(Den) and UK. After relaxing the requirements, the variable Denmark(Ger) is considered to be I(0), the variables Denmark(Swe), Sweden, UK(Den) and UK(Ire) are considered to be I(1). And Denmark, Sweden(Ire) and UK are I(2). Since one of the Non-Euro countries, Sweden, is I(1) for almost all country pairs, this time period can properly be tested for cointegration. The country pair Denmark-Sweden is the only country pair with exclusively Non-Euro countries that has variables for which a unit root can be rejected and stationarity cannot be rejected in the same order of integration. Therefore this is the only country pair of Non-Euro countries that is tested further. Table 3: Unit root tests of the CPIs of the sample Denmark (first time period) # This table presents results of the ADF test, ∆ ∑" !" ∆" , where p is the CPI of the country, and the KPSS test for the countries in the sample of Denmark in the first time period. The ADF test statistic, the 5% critical value for this statistic and the probability of the ADF test statistic are presented followed by the interpretation of these results. The last two columns present the value of the KPSS test statistic and an interpretation of this statistic.. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Austria (2). 58. -7.73. -2.91. 0.00. reject. 0.50. reject. Belgium (1). 69. -7.11. -2.90. 0.00. reject. 0.19. accept. Finland (1). 70. -7.27. -2.90. 0.00. reject. 0.50. reject. France (1). 69. -7.71. -2.90. 0.00. reject. 0.23. accept. 140. -4.56. -2.88. 0.00. reject. 0.31. accept. Ireland(2). 65. -9.16. -2.91. 0.00. reject. 0.07. accept. Italy (1). 70. -6.07. -2.90. 0.00. reject. 0.14. accept. Germany (1). Continued.. 28.

(37) Table 3, continued. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Netherlands (1). 68. -7.25. -2.90. 0.00. reject. 0.29. accept. Portugal (1). 70. -6.05. -2.90. 0.00. reject. 0.18. accept. Spain (2). 65. -11.19. -2.91. 0.00. reject. 0.38. accept. The extended version of table 3 can be found in the appendix table C.2. Table 3 presents the key results of the Unit root test results of the logarithms of the CPIs of the sample of Denmark. As can be seen all test statistics are highly significant. Furthermore, the ADF test statistic of all countries is lower than the 5% significance level. And KPSS test statistic is higher than the 5% significance level of 0.46 for Austria and Finland. Thus the logarithms of the CPI of Belgium, Finland, France, Germany, Italy, the Netherlands and Portugal are I(1) and those of Austria, Ireland and Spain are I(2).. 29.

(38) Table 4: Unit root tests of the exchange rates of sample the Denmark (first time period) This table presents results of the ADF test, ∆

(39)

(40) ∑<" !" ∆

(41) " , where e is the exchange rate of this country pair, and the KPSS test for the countries in the sample of Denmark in the first time period. The ADF test statistic, the 5% critical value for this statistic and the probability of the ADF test statistic are presented followed by the interpretation of these results. The last two columns present the value of the KPSS test statistic and an interpretation of this statistic. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Austria (1). 69. -6.36. -2.90. 0.00. reject. 0.10. accept. Belgium (1). 69. -6.60. -2.90. 0.00. reject. 0.04. accept. Finland (2). 62. -7.36. -2.90. 0.00. reject. 0.29. accept. France (0). 70. -3.79. -2.90. 0.00. reject. 0.08. accept. 138. -11.04. -2.88. 0.00. reject. 0.13. accept. Ireland(0). 70. -3.56. -2.90. 0.01. reject. 0.25. accept. Italy (2). 68. -12.25. -2.90. 0.00. reject. 0.32. accept. Netherlands (1). 69. -6.54. -2.90. 0.00. reject. 0.07. accept. Portugal (1). 70. -5.79. -2.90. 0.00. reject. 0.10. accept. Spain (1). 70. -5.07. -2.90. 0.00. reject. 0.43. accept. Germany (2). The extended version of table 4 can be found in the appendix table C.3.Table 4 presents the key results of the Unit root test results of the logarithms of the exchange rates of the sample of Denmark. Furthermore, as can be seen all test statistics are highly significant. Furthermore, the ADF test statistic of all countries is lower than the 5% significance level. And KPSS test statistic for. 30.

(42) every country is lower than the 5% significance level of 0.46. Table 4 indicates that the logarithms of the exchange rates of France and Ireland are I(0). The logarithms of the exchange rates of Austria, Belgium, the Netherlands, Portugal and Spain are I(1) and that Finland and Germany are I(2). There are no country pairs with exclusively Non-Euro countries that have variables for which a unit root can be rejected and stationarity cannot be rejected in the same order of integration. Therefore, no country pairs with Denmark are tested further. Table 5: Unit root tests of the CPIs of the sample Sweden (first time period) # This table presents results of the ADF test, ∆ ∑" !" ∆" , where p is the CPI of the country, and the KPSS test for the countries in the sample of Sweden in the first time period. The ADF test statistic, the 5% critical value for this statistic and the probability of the ADF test statistic are presented followed by the interpretation of these results. The last two columns present the value of the KPSS test statistic and an interpretation of this statistic.. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Austria (2). 263. -15.00. -2.87. 0.00. reject. 0.21. accept. Belgium (1). 270. -3.08. -2.87. 0.03. reject. 0.85. reject. Finland (2). 263. -10.75. -2.87. 0.00. reject. 0.25. accept. France (2). 269. -13.34. -2.87. 0.00. reject. 0.20. accept. Germany (2). 263. -11.95. -2.87. 0.00. reject. 0.23. accept. Ireland(2). 156. -11.35. -2.87. 0.00. reject. 0.31. accept. Italy (1)*. 269. -2.67. -2.57. 0.08. reject. 0.28. accept. Netherlands (2). 263. -13.00. -2.87. 0.00. reject. 0.09. accept Continued.. 31.

(43) Table 5, continued. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Portugal (1). 269. -5.15. -2.87. 0.00. reject. 0.56. reject. Spain (2). 263. -9.78. -2.87. 0.00. reject. 0.19. accept. * Since the value of the ADF test statistic of Italy was very close to the 5% significance level, the 10% significance level is used in order to be able to test as many country pairs, The extended version of table 5 can be found in the appendix table C.4. Table 5 presents the key results of the Unit root test results of the logarithms of the CPIs of the sample of Sweden. As can be seen almost all test statistics are highly significant. Furthermore, the ADF test statistic of all countries is lower than the 5% significance level. And KPSS test statistic for Belgium and Portugal is higher than the 5% significance level of 0.46. Table 5 indicates that the logarithms of the CPI of Belgium, Italy and Portugal are I(1) and that Austria, Finland, France, Germany, Ireland, the Netherlands and Spain are I(2).. 32.

(44) Table 6: Unit root tests of the exchange rates of the sample Sweden (first time period) This table presents results of the ADF test, ∆

(45)

(46) ∑<" !" ∆

(47) " , where e is the exchange rate of this country pair, and the KPSS test for the countries in the sample of Denmark in the first time period. The ADF test statistic, the 5% critical value for this statistic and the probability of the ADF test statistic are presented followed by the interpretation of these results. The last two columns present the value of the KPSS test statistic and an interpretation of this statistic. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Austria (1). 274. -10.55. -2.87. 0.00. reject. 0.04. accept. Belgium (1). 274. -11.42. -2.87. 0.00. reject. 0.07. accept. Denmark (1). 274. -9.98. -2.87. 0.00. reject. 0.12. accept. Finland (1). 273. -10.53. -2.87. 0.00. reject. 0.16. accept. France (1). 274. -10.94. -2.87. 0.00. reject. 0.18. accept. Germany (1). 274. -10.48. -2.87. 0.00. reject. 0.03. accept. Ireland(1). 164. -7.12. -2.88. 0.00. reject. 0.14. accept. Italy (1). 274. -11.83. -2.87. 0.00. reject. 0.29. accept. Netherlands (1). 274. -9.95. -2.87. 0.00. reject. 0.05. accept. Portugal (2). 263. -9.71. -2.87. 0.00. reject. 0.25. accept. Spain (1). 273. -12.97. -2.87. 0.00. reject. 0.22. accept. The extended version of table 6 can be found in the appendix table C.5. Table 6 presents the key results of the Unit root test results of the logarithms of the exchange rates of the sample of Sweden. As can be seen all test statistics are highly significant. Furthermore, the ADF test statistic of all countries is lower than the 5% significance level. And KPSS test statistic for every country is. 33.

(48) lower than the 5% significance level of 0.46. Table 6 indicates that the logarithms of the exchange rates of all country pairs are I(1). The country pairs that have exclusively I(1) variables are Sweden versus Belgium, Denmark, Italy and Portugal. Since there are no other country pairs with exclusively I(2) variables, these are the only country pairs that can be tested in the Johansen framework. Table 7: Johansen test Sweden vs. Belgium (first time period) # This table presents the results of the Trace test, > ∑"9D MNA1 8" B, and the Max test, > MNA1 89D B, in the Johansen ∗ cointegration framework when the VECM, ∆ ∏+ ∑+ " ⋁"∆" , is estimated including {

(49) + } and { } of the country pair Sweden versus Belgium in the first time period. Also the 5% and 10% critical values are presented, followed by an interpretation of the results.14. Lags: 12, based on LR- test statistic Statistic. Null. Alternative. Eigen-. Test. 5% critical. 10% critical. hypothesis. hypothesis. value. statistic. value. value. Probability. Interpretation. Trace. r=0. r>0. 0.04. 9.93. 12.32. 10.47. 0.12. accept. test. r≤1. r>1. 0.00. 0.17. 4.13. 2.98. 0.73. accept. Max. r=0. r=1. 0.04. 9.75. 11.22. 9.47. 0.09. reject(10%). test. r=1. r=2. 0.00. 0.17. 4.13. 2.98. 0.73. accept. Table 7 shows that only the hypothesis r=0 for the max test can be rejected at a 10% significance level. And that we are not able to reject any the r=1 hypothesis for the max test and both trace tests. This is very weak evidence that there is one cointegrating vector. 14. Jarque-Bera test statistic is 1549.44, with the p-value: 0.00. Hence, the null hypothesis of normality of the residuals is rejected.. 34.

(50) between Sweden and Belgium. Since there are very few country pairs that can be tested, this relation will be tested in step 3 to see if the cointegrating vector [1, -1] can be rejected. Table 8: Johansen test Sweden vs. Denmark (first time period) # This table presents the results of the Trace test, > ∑"9D MNA1 8" B, and the Max test, > MNA1 89D B, in the Johansen ∗ cointegration framework when the VECM, ∆ ∏+ ∑+ " ⋁"∆" , is estimated including {

(51) + } and { } of the country pair Sweden versus Denmark in the first time period. Also the 5% and 10% critical values are presented, followed by an interpretation of the results.15. Lags: 2, based on FPE, AIC, SC, HQ test statistics Statistic. Null. Alternative. Eigen-. Test. 5% critical. 10% critical. hypothesis. hypothesis. value. statistic. value. value. Probability. Interpretation. Trace. r=0. r>0. 0.21. 66.61. 12.32. 10.47. 0.00. reject (5%). test. r≤1. r>1. 0.01. 2.83. 4.13. 2.98. 0.11. accept. Max. r=0. r=1. 0.21. 63.78. 11.22. 9.47. 0.00. reject (5%). test. r=1. r=2. 0.01. 2.83. 4.13. 2.98. 0.11. accept. Table 8 shows that the hypothesis that r=0 can be rejected at a 5% significance level for both the trace and the max test. Furthermore, it is not possible to reject the two other hypotheses that there is not more than one cointegrating vector. Therefore, this strongly indicates that there is one cointegrating vector and a long run equilibrium relation between, the CPIss and the exchange rate, of Sweden and Denmark. Hence, this relation will be tested in step 3 to see if the cointegrating vector [1, -1] can be rejected.. 15. Jarque-Bera test statistic is 6348.41, with the p-value: 0.00. Hence, the null hypothesis of normality of the residuals is rejected.. 35.

(52) Table 9: Johansen test Sweden vs. Italy (first time period) # This table presents the results of the Trace test, > ∑"9D MNA1 8" B, and the Max test, > MNA1 89D B, in the Johansen ∗ cointegration framework when the VECM, ∆ ∏+ ∑+ " ⋁"∆" , is estimated including {

(53) + } and { } of the country pair Sweden versus Italy in the first time period. Also the 5% and 10% critical values are presented, followed by an interpretation of the results.16. Lags: 2, based on FPE, AIC, SC, HQ test statistics Statistic. Null. Alternative. Eigen-. Test. 5% critical. 10% critical. hypothesis. hypothesis. value. statistic. value. value. Probability. Interpretation. Trace. r=0. r>0. 0.22. 68.88. 12.32. 10.47. 0.00. reject (5%). test. r≤1. r>1. 0.00. 0.31. 4.13. 2.98. 0.64. accept. Max. r=0. r=1. 0.22. 68.56. 11.22. 9.47. 0.00. reject (5%). test. r=1. r=2. 0.00. 0.31. 4.13. 2.98. 0.64. accept. Table 9 shows that the hypothesis that r=0 can be rejected at a 5% significance level for both the trace and the max test. Furthermore, it is not possible to reject the two other hypotheses that there is not more than one cointegrating vector. Therefore, this strongly indicates that there is one cointegrating vector and a long run equilibrium relation between, the CPIs and the exchange rate, of Sweden and Italy. Hence, this relation will be tested in step 3 to see if the cointegrating vector [1, -1] can be rejected.. 16. Jarque-Bera test statistic is 2654.74, with the p-value: 0.00. Hence, the null hypothesis of normality of the residuals is rejected.. 36.

(54) Table 10: Unit root tests of the CPIs of the sample UK (first time period) # This table presents results of the ADF test, ∆ ∑" !" ∆" , where p is the CPI of the country, and the KPSS test for the countries in the sample of the UK in the first time period. The ADF test statistic, the 5% critical value for this statistic and the probability of the ADF test statistic are presented followed by the interpretation of these results. The last two columns present the value of the KPSS test statistic and an interpretation of this statistic.. Country (derivative). N. ADF. ADF. Probability Interpretation KPSS. Interpretation. test statistic. 5% Critical value. (ADF test). KPSS Test. ADF Test. test statistic. Ireland(2). 155. -11.34. -2.87. 0.00. reject. 0.50. reject. Luxembourg (2). 266. -10.41. -2.87. 0.00. reject. 0.07. accept. All the regression results can be found in the appendix table C.6. Table 10 presents the key results of the Unit root test results of the logarithms of the CPIs of the sample of the UK, the other country pairs can be found in table 5, since their time period is equal to the UK sample. In order to not reject stationarity in a unit root, the test statistic should be lower than the 5% critical value for both the ADF- and the KPSS test. Furthermore, as can be seen all test statistics are highly significant. Lastly, the most R-squares are quite low. Hence the data doesn’t fit the test that well. Table 6 and table 10 shows that the logarithms of the CPI of Belgium, Italy and Portugal are I(1) and that Austria, Finland, France, Germany, Ireland, Luxembourg, the Netherlands and Spain are I(2).. 37.

(55) Table 11: Unit root tests exchange rates of the sample UK (first time period) This table presents results of the ADF test, ∆

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