CROSS-REGIME BEHAVIOR OF REAL EXCHANGE RATES: EVIDENCE FROM THE EUROPEAN MONETARY SYSTEM* ANUSHA CHARI The University of Michigan SEPTEMBER 2002 *I thank Michael Darby, Sebastian Edwards and Mark Grinblatt for providing valuable comments. This paper was completed when I was an Summer Intern in the Monetary and Exchange Affairs Department of the International Monetary Fund. I am grateful for the hospitality of the IMF and the financial support of the Swiss Institute of Banking and Finance, St.Gallen. This paper reflects the author's views and not those of the IMF. Any errors and omissions are my sole responsibility. Correspondence to: Anusha Chari, University of Michigan Business School, 701 Tappan Street, MI 48109 U.S.A. Internet: achari@umich.edu

CROSS-REGIME BEHAVIOR OF REAL EXCHANGE RATES: EVIDENCE FROM THE EUROPEAN MONETARY SYSTEM This paper examines the pattern of real exchange rates across three distinct nominal exchange rate regimes in Europe within a framework of changing trade regimes. Panel data analysis reveals strong evidence for a decrease in real exchange rate variability when nominal rates are managed rather than freely floating. Spectral density estimates show that although we cannot reject the null of a unit root using traditional tests of non-stationarity, real exchange rates display a substantial negative auto-correlation at later lags and hence a long term mean reverting component under the ERM arrangements. KEYWORDS: Real exchange rates, nominal exchange regimes, panel data, spectral density.

1 INTRODUCTION 2 Introduction This paper examines the impact of nominal exchange rate policies in conjunction with trade policies on real exchange rate behavior in Europe. In particular, we focus on a)the variability and b) the tendency for mean reversion in real exchange rates. Europe provides a particularly interesting setting to conduct this empirical investigation. We are presented with an opportunity to study a set of countries that have collectively adopted similar set of nominal exchange rate and trade policy regimes. We focus on real exchange rate patterns across three distinct nominal exchange rate-trade policy regimes. We consider the Bretton-Woods period followed by the period of generalized floating in the 1970s and finally turn to the Exchange Rate Mechanism (ERM) of the European Monetary System (EMS). The Bretton-Woods period can be described as a closed-fixed regime within which countries pegged their currencies to the US dollar with periodic revaluations and in comparison to later years pursued relatively inward looking trade policies. Moreover, trade policy was actively used to manage movements in the real exchange rate about its equilibrium value. (Darby (1988), Darby et al. (1983)) Exchange rates and price levels became more volatile in the 70s following the breakdown of Bretton-Woods. The increased frequency of terms of trade shocks, most notably the two oil shocks, exacerbated the situation. However, this period was characterized by a movement towards increasingly open trade policies in Europe. This period may therefore be described as an open-floating regime. The Exchange Rate Mechanism period of the European Monetary System offers a rare opportunity to study an open-fixed regime. Member countries pegged their currencies to the Deutsche Mark and were simultaneously committed to dismantling trade barriers in preparation for the completion of the Single Market in 1992. Trade barriers both in the form of quotas or tariffs on imports and exports were no longer available as policy making tools. This meant that trade policy could no longer be used to affect movements in the real exchange rate. 2

This paper evaluates whether or not managing nominal exchange rates through international cooperative monetary arrangements such as the ERM has an impact upon the tendency for mean reversion in real exchange rates. The study differs from the existing literature in that RER volatility is examined systematically against the US dollar and the German Mark. This allows a comparison of the cross regime volatility of intra-European RERs with the volatility with respect to the rest of the world. There are two theoretical views in the mainstream literature about real exchange rate movements and their relationship to nominal exchange rate regime changes. The first is a general equilibrium perfect pooling approach according to which nominal regime changes leave RER variability unchanged. This refers to the concept of "nominal exchange regime neutrality" where both exchange rates and goods prices adjust continuously and rapidly in response to shocks so that there is no direct relationship between exchange rate regimes and the behavior of real exchange rates. On the other hand, theoretical models featuring a sluggish response of goods prices to changing nominal exchange rates generally imply that that real exchange rates will be more variable under floating rather than fixed exchange rates for a given sequence of shocks.2 If RER movements are neutral to the exchange rate regime it implies that nominal exchange rate policy has no impact on real resource allocation. Yet another approach to the link between real exchange rates and nominal regimes is in terms of the Purchasing Power Parity (PPP)-PPP refers to two distinct concepts in the literature-the growth concept and the level concept. In this paper we focus on the growth concept in terms of relative purchasing power hypothesis. See Darby (1983) for a more detailed discussion. According to this strand of the literature, if PPP were to hold, price and exchange rate changes would exactly offset each other. To the extent that there are deviations from PPP-shocks affect spot rates and prices in different ways. In the European context these observations raise several issues. (1) Did the ERM introduce mean reversion in real exchange rates? (2) Does RER variability change across regimes in Europe? (3) Is there evidence of a decline in intra-European real exchange rate variability with the inception of the ERM? This paper attempts to answer these questions. Section 2.2 provides a survey of the literature in this area. The data are described in Section 2.3. A description of the preliminary statistics of RER variability is presented in 1Stockman(1979), Helpman and Razin(1982), Lucas(1982). 2Dornbusch(1976), Mussa(1982). 3

Section 2.4. The procedures undertaken to analyze real exchange rate movements and the empirical results obtained are presented in Sections 2.5 and 2.6. In Section 2.5, we conduct a panel data analysis to show that real exchange rate variability differs across regimes and in section 2.6 we utilize a spectral density method to evaluate whether the ERM is instrumental in introducing mean reversion. Section 2.7 concludes. 3 Literature Survey Two salient empirical regularities have been documented in the existing literature for the period of floating exchange with respect to the mean reverting behavior of real exchange rates: (a) log nominal exchange rates appear to be well described by unit root processes and (b) real exchange rates closely mirror nominal exchange rate movements. Taken together these observations imply that real exchange rates appear to have unit roots and several studies have reached this conclusion.3 This observation has important implications for models of exchange rate determination that follow from it. In turn there are implications for the persistence of nominal and real shocks to the real exchange rate and the tendency and time to mean reversion is affected. The greater the permanent component the greater the persistence of real shocks as nominal shocks are expected to have only a transitory effect on real variables.4 It follows that there are important implications for macro-stabilization policy if we find evidence that managing nominal exchange rates has an impact on the persistence of real shocks to the economy.5 The unit root property also has strong implications for identifying the types of shocks that drive exchange rates. If exchange rates are viewed as being in equilibrium, then the unit root property implies that all shocks have a permanent component.6 This paper finds 3See, Meese and Singleton(1982), Huizinga(1987), Kaminsky(1987), Meese and Rogoff(1985), Edison and Kole(1994). 4Stockman(1980,1983),Huizinga (1987), Campbell and Clarida,(1987). 5External shocks impact upon nominal exchange rates and prices at different lags and with different degrees of permanence across countries so that real exchange rates change through time. Moreover, movements in real exchange rates represent those changes in the nominal exchange rate that cannot be attributed to inflation differentials between different countries. This implies that if PPP arbitrage conditions are not well enforced, changes in RERs have real implications for the long run structural composition of a country's trade and output patterns. If actual changes of RERs are permanent changes they will not be reversed in the future and this is inconsistent with long run PPP holding. Thus, the mean reverting versus non-mean reverting behavior[See (Mussa(1986), Huizinga(1987)] of RERs has an impact on real resource allocation. 6Moreover, a random walk finding is used to argue against the predictability of models such as the sticky 4

that although RERs show deviations from an equilibrium mean value in the short run, with managed nominal exchange rates, RERs show a long run tendency towards mean reversion so that shocks tend to be outweighed by substantial negative auto-correlation in the longer run. Finally, results from Stockman (1983) show a strong correlation between the exchange rate system and the variability of real exchange rates. The study finds that after holding fixed country specific variables and time specific variables(such as the increased variability of real disturbances affecting the international economy in the 1970s), flexible exchange-rate systems are associated with greater variability of real exchange rates. The paper considers a diverse group of 38 developed and developing countries for purposes of empirical analysis and shows that in the 1970s the return to a system of flexible exchange rates explains 40% of the increased volatility of real exchange rates. Mussa (1986) studies pooled data on different price indices and shows that relative prices appear to be more stable during periods of nominal exchange rate stability. This paper extends the existing literature in that we simultaneously examine the link between intra-European real exchange rates, nominal regime policy and account for trade policy changes.7 An understanding of the manner in which real exchange rates have changed is important to policy-makers in order to alter the competitiveness of domestic industry. It is therefore important to see if long run real exchange rate movements can be decomposed and to be able to reasonably predict the time required for real shocks to die out. The spectral density procedure and the cross-regime comparisonwe employ in this paper provides a first step in this direction. 4 The Data We examine real exchange rates for thirteen currencies from countries that have been divided into three groups. Group 1: Core ERM countries: Germany, France, Belgium, Denmark, Luxembourg and the Netherlands, Group 2: the peripheral ERM countries; Ireland, Italy price monetary model of Dornbusch(1976) that describe a major role to short run dis-equilibrium dynamics and would be expected to induce systematic or predictable movements in exchange rates. 70Overall, the period of the generalized float is characterized by increases in the volatility of real exchange rates.8 Even countries that belonged to the EMS witness this increase in volatility although Stockman provides evidence that that the magnitude of the increase in volatility is greater for countries on a pure float. We find similar evidence for cross-regime changes in RER variability for the countries in our sample. 5

and the United Kingdom and Group 3: other European countries; Austria, Norway, Sweden and Switzerland. The third group was chosen to facilitate a comparison of real exchange rate volatility across countries that did not explicitly commit to a monetary arrangement like the EMS designed with the specific goal of reducing inflation by stabilizing nominal exchange rates. Austria, Norway, Sweden and Switzerland are classified as 'other European countries' as they were member countries of the European Free Trade Agreement (EFTA) but not a part of the European Union during our sample period. This means that they were not subject to the charter of the Union and hence did not formally commit to the discipline, objectives and rules of the Union for trade and monetary policy. Therefore these countries provide an ideal 'control group' to compare and contrast developments in Union member countries. Although they are inherently 'European' in nature (culturally, historically and spatially) they did not join the cooperative institutional arrangements of the Union. Instead, they continued to be governed by EFTA rules that are far more loosely formulated and did not have overall policy objectives entailed by a unified European market. These countries also display a large degree of structural similarity to the countries within the European Union as well as having comparable levels of GDP per capita. Countries such as Spain, Portugal and Greece on the contrary are not as structurally similar. Moreover, these countries became members of the Union midway(mid-1980s) through the sample period thereby becoming subject to its rules and influences. At the same time, they were not members for a sufficiently long period in order for us to derive meaningful empirical conclusions about the implications of their membership. Analyzing the behavior of countries outside the EMS allows us to assess whether the real exchange behavior observed in EMS countries is particular to the system or is a general pattern that is seen in other European-non EU countries as well. Austria, for instance, actively shadowed the DM while Switzerland let its currency float more or less freely during the entire post Bretton Woods period. This means that there was no active management to follow the German Mark. However, Switzerland does utilize a monetary target that is exchange rate oriented in order to maintain its commitment to low inflation. This paper attempts to identify broad regularities and differences in real exchange rate behavior among these country groups. The data was collected from the International Finan 6

cial Statistics database of the International Monetary Fund and the sample period is January 1957 to December 1993. The exchange rate data are the end of month values and the price indices used to construct the bilateral real exchange rates are monthly wholesale and consumer prices not adjusted for seasonality. The sample period can be divided into three main sub-periods: January 1957-March 1973 (the Bretton Woods period); April 1973-February 1979 (the post Bretton Woods float) and March 1979-December 1993 (the ERM period). The ERM period can be further sub-divided into two periods: March 1979-December 1986; the flexible phase of the ERM that was characterized by frequent realignments and January 1987-September 1992, the tight phase of the ERM with no realignments. Nominal regimes differ across countries within a single system at a point in time and regimes change over time for a given country. For instance, Italy had moving bands and a high incidence of realignments prior to 1987 similar to the British Pound that floated until 1990. After 1987, the behavior of the Italian Lira was similar to the French Franc that belonged to the narrow band of the ERM(2.5%). Therefore, although it technically belonged to the wide band(6%) it de-facto behaved like a narrow band currency. Following Edwards (1989) two indices of bilateral real exchange rates were constructed with respect to the US and Germany as follows: El x WPt(US) BRERit(I) = W It() (1) CPhit(DOM) BRERit(I) E x WPIt(GER) (2) CP i,(DOM) Where * EI = Foreign Currency Units/US dollar for country i at time t. * EII= Foreign currency Units/DM for country i at time t. * WPIt(US)= U.S.monthly wholesale price index at time t. * WPIt(GER)= German monthly wholesale price index at time t. * CPIit(DOM)= Foreign monthly consumer price index for country i at time t. This index corresponds to a proxy for the relative price of tradables to nontradables and uses wholesale price indices to measure the foreign price level and consumer price indices to 7

measure domestic price level. This index is in contrast to to the more traditional measure of the real exchange rate that uses consumer price indices for both the domestic and foreign price levels. (See Edwards (1989) pp. 88-89 for a complete discussion). An increase in the index indicates a depreciation of the foreign country's real exchange rate. Section 2.4 examines the preliminary statistics of real exchange rates for the set of ERM and non-ERM countries under consideration. In particular, we conduct a primary evaluation of the the pattern of volatility using short and long run tests. 5 Preliminary Statistics Tables 2.1 and 2.2 report the variability of the bilateral rates defined above. Variability is defined as the standard deviation of monthly changes in the log of the real exchange rate. The first table shows the variability against the US dollar. One result that becomes immediately apparent is that variability jumped after the Bretton Woods period and it did not decrease following the inception of the ERM. Thus there is no evidence that the ERM served to anchor European currencies in general and the German Mark in particular against the dollar. An explanation that may be put forth is that the early eighties witnessed twin opposing forces acting upon the exchange rate system: the dollar appreciation following the oil shock increased inflation in Europe and undermined the exchange rate cohesion while the real appreciation of non-ERM currencies against the ERM and the strong recovery in the US led to sustained economic growth and contributed to the stability of the exchange rate system. The late eighties saw a reversal of these trends: a depreciating US dollar and a slowdown of the US economy. In sharp contrast, variability vis a vis the DM declined after 1979. The results are even more dramatic for the later 'hard" period of the ERM (1987-1992). While Austria and Switzerland display the same pattern of falling variability against the DM in the 1980s, Norway and Sweden do not reflect this decline. The United Kingdom also does not display this decline in volatility. The evidence suggests that although intra-ERM real exchange rates became more stable, this effect did not spill over to dollar exchange rates. The reduction of intra-ERM variability 8

can be explained in part by the policies followed by the EMS countries, in particular, the interest rate and intervention policies followed by their central banks. In summary, intra-European real exchange rates can be seen as having been fairly stable during the Bretton Woods period and becoming more volatile during the 70s. The 1980s show real exchange rates becoming more tranquil within the ERM against the DM but the opposite result is consistently observed with respect to the US dollar. The above measure of volatility uses month to month changes-an essentially short run measure. It says nothing about long run variability or misalignment which is of interest when assessing competitiveness. These issues assume substantial economic significant when the real side of the economy is considered. A persistently undervalued or overvalued real exchange rate could lead to a significant restructuring of the industrial composition of output between traded and non-traded goods. These shifts cause the real sector to bear sizable adjustment costs. However it has not been possible to agree upon a statistical measure to capture the value of an equilibrium real exchange rate in the existing literature. Instead, we resort to unit root tests to obtain a first pass indication of real exchange rate mean-reversion. An important issue is whether the ERM or managed exchange rate policies affect the likelihood of mean reversion. In other words, do short-term mis-alignments in the real exchange rate tend to eliminate themselves in the long run or do shocks to the real exchange rate tend to be permanent. As a first step to examining the time series properties of real exchange rates in the long run we perform the Augmented Dickey Fuller unit root tests using a drift, a trend and a lagged dependent variable term. Table 2.3 presents the results for real exchange rates based on the US dollar. The results show that in all but one case it is not possible to reject the unit root hypothesis-the exception being the Swiss Franc in the Bretton Woods period. The results differ slightly when we consider the real exchange rates using the DM specification (Table 2.5). The unit root hypothesis can be rejected for Denmark, France and Ireland for the entire period. It can be rejected for Austria, Norway and Switzerland for the Bretton Woods period and for Ireland and Italy for there generalized float in the 70s. For the ERM period, evidence from Austria, Denmark, France, Ireland and the Netherlands suggests that the unit root hypothesis may be rejected. 9

We also tested for the presence of a unit root in the log differenced data for RERs both against the US dollar and the DM. It was possible to reject a unit root in all cases. In the interests of brevity we do not report these statistics. Thus, augmented Dickey-Fuller tests for non-stationarity cannot rule out the null of the presence of a unit root in the real exchange rate except in a limited number of cases as shown in the discussion above. I also conducted the Phillips-Perron test which gave similar resultsthese statistics were not reported in the interest of brevity and to avoid duplication. Now, a unit root (note, that I am not saying random walk) implies the presence of a temporary and permanent component in the time series concerned-in my case the real exchange rate. The reader should be warned that these tests have a serious shortcoming in that they have low power and are unable to distinguish between stochastic processes that are close to a unit root and those that actually contain a unit root. Nevertheless, it is a useful exercise to conduct these tests as a first pass indication of the nature of the underlying stochastic process. Edison and Kole (1994) suggest that the testing procedure used above does not consider the effect of realignments on non-stationarity tests and that this may well account for the support of the unit root hypothesis. They examine the deviation of ERM members' nominal exchange rates in DM terms from their DM central rates. They report results from unit root tests of the deviations of the log of the spot rate from the log of the central parity and show that the deviations within the band are mean reverting. This procedure makes it possible to reject the unit root hypothesis for the ERM period for Belgium, Denmark, France and the Netherlands-all narrow band countries. It is unclear as to how this particular procedure may be applied to real exchange rates and deviations from an equilibrium value since there exists no agreed upon empirical equilibrium value series for the real exchange rate. While central parity levels for nominal exchange rates are clearly defined, thereby making it possible for us to construct a series for deviations from this value, the same does not hold for real exchange rates. This equilibrium value is an underlying unobservable of the real economy and some long run equilibrium towards which it is heading. Several models exist in the theoretical literature to determine the equilibrium real exchange rate but there is no agreed upon empirical measure for the same. Thus, it is not possible for us to determine deviations of the actual real exchange 10

rate from this underlying value. We conclude that it is not possible to construct an equilibrium value for the real exchange rate adjusting the central parity levels for the nominal exchange rate for inflation differentials and then conduct unit root tests for deviations of the real exchange rate from the equilibrium value. This is also because we do not know explicitly that this is the value that policy makers target while formulating real exchange rate policy. This would require an explicit model of real exchange rate determination. Instead, we propose the use of a spectral density procedure following Huizinga (1987) in the Section 2.6. We use the spectral density method to decompose and study deviations from and movement towards an equilibrium. This allows us to conduct the same exercise implicitly and we allow the data to reveal whether or not mean reversion takes place. Therefore, these results are obtained endogenously and not imposed exogenously like deviations from a central parity level or some equilibrium value of the real exchange rate that is obtained from a specific formulation of real exchange rate determination. Further, since we cannot rule out the null of a unit root, the spectral density method, shows that in the short run, shocks to the real exchange rate via shocks to the nominal exchange rate or prices move it away from some long run equilibrium mean value. However, in the longer run (in this paper about 36 lags or three years) with managed exchange rates as is the case under the ERM arrangements, negative auto-correlations tend to dominate and pull the real exchange rate back to its equilibrium value. This implies that in the short run we observe deviations away from equilibrium which is restored at a later date. These results are consistent with the hypothesis that long run PPP holds. 6 Evidence of Regime Changes from Panel Data Analysis We employ a fixed-effects model to analyze regime changes in the European context. The procedure is similar to the one used in Stockman (1983). The separate effects of changes in the exchange rate system and of the increased importance of real disturbances in the world economy are isolated econometrically with a variance component model on pooled cross section-time series data. The methodology differs from that of Stockman (1983) in that the paper focuses on countries within Europe instead of including a set of 38 highly 11

diverse countries in the sample set. Also, by including the German Mark in addition to the U.S.$ we were able to study intra-European developments more specifically since the Mark was utilized as the anchor currency within the Exchange Rate Mechanism (ERM). Last, focusing on European countries allowed us to study real exchange rate behavior across three distinct set of nominal exchange rate regimes in conjunction with changing trade policies. Following the construction of the bilateral exchange rates against both the US dollar and the DM, an average annualized variability measure, Vij, was constructed from monthly data for each country as follows: 1=12 i=12 Vij = 12 E ((lnBRERit)2- ( lnBRERit))2 (3) i= i= where: Vij is the annual variance for which we obtain 38 observations (1957-92) for each country i. Since we are interested in the relationship between the exchange rate system and the variability of the real exchange rate it is important that the characteristics of a particular country be held fixed. The share of non-traded goods in the price indices differs across countries and this share affects the the magnitude of Vij for any given variation of traded and non-traded goods. This problem is corrected by estimating a different mean Vij for each country. Further, the degree of openness is a variable that strongly influences the extent to which a country is exposed to external shocks. A relatively closed economy is likely to be affected in a somewhat different manner to changes in nominal exchange rate regimes as opposed to a more open one. In order to account for this, the exchange rate regime variable was interacted with an openness measure to obtain a continuous dummy variable.9 A direct implication of dismantling trade barriers is that the trade share of GDP(i.e., the ratio of exports plus imports to GDP) should rise as freer trade ensues. As trade controls were 9The case for a unified European market rests on premises largely identical to the case for universal free trade and factor movements. It is argued that the completion of a single European market would result in the exploitation of economies of scale while stimulating competitiveness and promoting greater specialization between member countries of the Union. This would allow a wider range of choices for consumers, raise living standards and lead to increased gains from the free movement of both goods and factors of production. To facilitate the free movement of goods and factors it was imperative that trade barriers be gradually dismantled and the Single Market plan for the European Union envisaged that this goal would be achieved by 1992. A direct result of this "commitment" to dismantling trade barriers is that active trade policy (both quantitative(quotas) and price(tariffs) controls) is not available as a discretionary "policy tool" for member governments. This implies that it is no longer possible for governments to alter the real exchange rate(and hence competitiveness) by utilizing trade policy(e.g., the imposition of import tariffs) to change the relative price of traded to non traded goods. We use this argument to construct a continuous measure of "openness" in the paper. 12

gradually dismantled over the 1970s and 1980s we should expect a steady change in this ratio over time. Hence, this variable accounts for changing trade policies or the movement towards greater openness in trade within the Union. The model that is obtained is as follows: Vit = ai + 0 x ERit x OPENit + (it (4) where * ai is a (fixed) country effect, * ERit is a nominal regime dummy variable that takes the value of zero for country pairs characterized by fixed exchange rates and one for country pairs characterized by flexible exchange rates, * OPENit measures openness as the ratio of exports plus imports to GDP and * (it is the disturbance term assumed to be iid(0, a2). The ER dummy thus takes the value of zero for the Bretton Woods period and is equal to one after 1973 for the real exchange rates against the dollar indicating the shift to a freely floating regime. The value of the same dummy is zero for Bretton Woods, one between 1973-1979 and zero again after 1979 for the real exchange rates against the DM to account for the ERM membership. Months where realignments took place are dropped from the sample. Rates were realigned 11 times during the eight years after the formation of the ERM. The currencies involved and the magnitude of exchange rate changes resulting from nominal realignments are shown in Table 2.7. The results from the panel data analysis are presented in Table 2.11-2.17. For the US dollar rates the coefficient on the exchange rate regime dummy is highly significant indicating that the post-Bretton Woods period has witnessed a distinct rise in real exchange rate volatility. This observation confirms the results contained in Stockman (1983). The results for the DM specification for the period 1974-93 highlight some interesting details. When the complete sample of countries is considered, the size and significance of the coefficient on the exchange rate dummy variable interacted with the openness measure suggests that volatility decreases with the adoption of managed exchange rates. When the 13

sample is divided into two subsets-countries that were members of the EMS and EFTA countries that were not, show that while the exchange rate regime variable remains highly significant for the former group, while the coefficient for the latter group loses all significance. This result provides further evidence that attempts to stabilize exchange rates through the creation of monetary arrangements such as the ERM serves to reduce the volatility of real exchange rates substantially. On average, the shift to the ERM served to reduce intraEuropean RER volatility with respect to the DM by 23% over the previous period. 7 Empirical Evidence from Spectral Density Analysis Before proceeding to analyze the long run statistical properties of real exchange rate behavior let us encapsulate the stationarity properties of short-run movements in real exchange rates. Table 2.8 presents results DM real exchange rates vis a vis the countries under consideration. The only preliminary evidence to indicate mean reversion to be found in these auto-correlations comes from the French Franc-German Mark real exchange rate, which shows negative auto-correlations at lags one, two and three. Table 2.8 also reports the estimated slope coefficient from the regression of the level of the real exchange rate with one lag and a constant as well as the t-statistic to test the hypothesis that the value of this coefficient is significantly different from one. It is interesting to note that the t-stats more or less confirm the suggestion conveyed by the auto-correlations of the first differences that the short run behavior of real exchange rates is not easily distinguishable from a unit root. In this section we examine the long run properties of real exchange rates in order to see if the unit root explanation continues to hold. The method used to measure this is the spectral procedure. S(O) is a summary statistic for the ratio of the variance of the change in the permanent component of the real exchange rate to the variance of the actual change.10 It is estimated as follows: N S(0) = + 2 E pj X (5) j=1 where N is the number of estimated auto-correlations used for different time horizons. WN = N+lj. pj is a measure of the auto-correlation at lag j. This formulation implies 10For a complete discussion see Huizinga(1987) 14

that greater weight is placed on the auto-correlations at lags near zero and the importance of lags that are further away is minimized. The results of this procedure are presented for monthly observations of the natural logarithm of real exchange rates calculated against the Deutsche Mark during the ERM period of 1979 to 1992. This will enable us to test the hypothesis that the ERM introduces mean reversion in long run real exchange rates. Figures 2.1 through 2.4 present the results of employing the spectral procedure for the real exchange rate of the DM vis a vis the countries under consideration. A tendency to fall below the value of one indicates long run mean reversion the the real exchange rate process. These currency pairs demonstrate some interesting findings. Belgium, Denmark, France, Ireland, Luxembourg and the Netherlands all show a general uniformity in that they fall below unity at longer time horizons. A common feature that these countries share is that they all belonged to the narrow band (2.5% ) of the ERM. A striking feature of these graphs is a hump-shaped pattern- S(O) first rises and then falls below one. This pattern is evidence that positive auto-correlations at lower order lags are more than offset at higher orders. This is true even though the construction of S(O) is weighted such that that the effect of higher-order auto-correlations is minimized as was seen earlier in this section. This shape is also consistent with the findings of Huizinga (1987). Second, Italy and the United Kingdom do not demonstrate the same behavior-ie, they do not converge below one. It is pointed out that both these countries belonged to the wide band(6%) of the ERM. The third interesting piece of evidence is that Austria which was not a member of the ERM for the sample period shows a value of S(O) that is continually below one, a pattern that is observed only in the case of the Netherlands. This finding is consistent with the fact that both the Netherlands and Austria shadowed the DM very closely. This means that although Austria was not a formal member of the ERM, its exchange rate policy was such that similar results to member country real exchange rates are observed. Of the other countries that were not members of the ERM, Sweden and Switzerland also show mean reversion while Norway does not. Huizinga (1987) finds that Norway shows convergence with respect to the US dollar. This may bear some relation to the fact that the 15

Norwegian economy is predominantly based on oil proceeds and hence the close link with the US dollar. When information from the full set of covariances used here is taken into account (i.e., setting n=168), the average value of S(O) across the twelve currencies is 0.76 ( with a range from 0.1 to 2.8), while the average of the nine currencies excluding Italy, Norway and the United Kingdom is.29, with a range from 0.1 to 0.81) in Table 2.9-2.10. As described earlier, a value of 0.29 can be interpreted as indicating that the variance of the change in the permanent component of DM real exchange rates is 29% of the variance of the actual change in the real exchange rate. While interpreting these results two issues that deserve mention are that the point at which the S(0) turns downwards does not indicate the point at which the auto-correlations turn negative. This is because a higher weight is placed on the lower order lags so that S(0) can continue to rise even after the auto-correlations have turned negative. For the same reason, the point at which S(0) falls below unity is not a reliable signal of the time horizon required for mean reversion to take place. If different order lags had been equally weighted, S(0) would cut below unity earlier. Many of these issues become clear when a fixed-weight S(0) specification is used. In order to compare the mean reverting behavior across different nominal regimes when exchange rates were fixed/managed we conducted the same analysis for the Bretton-Woods period between 1957-72. The procedure was performed on the real exchange rate series constructed against the U.S. dollar. The results are presented in Tables 2.21-2.22. It is interesting to note that the mean reverting behavior of real exchange rates is unanimously observed for all the countries in our sample. Charts 2.5-2.8 show that while the aforementioned hump-shaped pattern is observed for some of the countries, Austria, France, Denmark, Ireland and the United Kingdom demonstrate immediate mean reversion suggesting stronger ties with the dollar. Moreover, the information set with the full set of covariances, i.e., n = 174 the average value for S(0) is 0.37. This value is higher than that observed for the narrow band countries of the ERM. This is a striking result as the ERM period coincides with a period of greater openness and trade liberalization in the face of the completion of the Single Market. In contrast the Bretton-Woods period coincided with a fairly closed trade policy regime and the active use 16

of trade policy to manage real exchange rates. The above evidence makes the strong suggestion that indeed the ERM had an effect in introducing mean reversion in long run real exchange rates. This indicates that nominal exchange rate policies have serious implications for the real side of the economy. In fact, these policies may play a considerable role in altering the long run competitiveness of the economy.ll 8 Conclusion This paper examines the cross-section time-series behavior of real exchange rates in Europe over the last thirty eight years. We find strong evidence supporting the idea that real exchange rate variability increases dramatically with floating nominal exchange rate regimes. This observation holds both for the US dollar and DM specification of real exchange rates. Real exchange rates were significantly less variable under the Bretton-Woods period as compared to the generalized float of the 1970s. Approximately 48% of the increase in the post Bretton Woods volatility can be explained in terms of a nominal regime change. Furthermore, our results also take into account the changing nature of trade policies over the entire period from a relatively closed inward-looking stance during Bretton-Woods period to an increasingly open outward policy emphasis as Europe has moved towards the completion of the single market. It is interesting to note that while intra-European real exchange rates become more stable with the advent of the ERM period of the EMS, the same result does not hold against the US dollar. In particular, the ERM led to reducing real exchange rate variability against the DM by 23% over the previous period. This suggests that managing nominal exchange rates through international cooperative monetary arrangements such as the EMS has strong implications for macro-stabilization policies. Given the impact of real exchange rate movements for resource allocation across the tradable and non- tradable sectors and in turn for long run competitiveness, this implies that nominal exchange rate policy has 11Throwing in other exogenous variables such as nominal and real interest rates and so on and constucting a auto-corrollelogram would require a specific model of real exchange rate determination. While this is an interesting exercise, it would be more appropriate to discuss it in a separate paper. The purpose of this paper is to conduct statistical analysis of real exchange rate movements across exchange regimes. This is accomplished in most part by letting the data speak for itself rather than committing to any specific model of real exchange rates. However, this is an interesting avenue for extending this paper. 17

important consequences for the real economy. We also find evidence that long run movements in intra-ERM real exchange rates show a strong mean reverting component. This finding is not inconsistent with the mainstream literature that suggests a strong correlation between nominal and real exchange rate movements and that nominal exchange rates can be described by a unit root process. We find corroborating evidence that tests for short run real exchange rate movements cannot rule out the presence of a unit root. However, when the long term behavior of real exchange rates is considered, negative auto-correlations dominate the process at later lags. We present results from our spectral density analysis to show that the mean reverting component is approximately 29% for the ERM period for real exchange rates vis a vis the DM. Comparing our results with a similar analysis for the Bretton-Woods period shows that the effects of the ERM lead to stronger mean reversion while a greater set of countries demonstrate immediate mean reversion for the Bretton- woods era. Once again, our results suggest that the differences in the observed behavior can in part be explained by the nominal exchange rate policies followed by the government. While all the narrow band countries show mean reversion the same does not hold for the wide band countries of the ERM. Of the countries that were not members of the ERM during this period, Austria closely shadowed the DM and shows strong mean reversion. Correspondingly, Norway was more influenced by US dollar movements and not particularly linked to the DM and in turn does not demonstrate mean reverting behavior. In conclusion, our findings suggest that there are differences in the long run behavior of real exchange rates across countries and that these differences may be attributed to government policy- in particular the move from floating to managed exchange rates in Europe. 18

Table 1: Standard deviation %- Log difference U.S. dollar RERs Monthly 1957:1-1993:12 Time 57:1-93:12 57:1-73:3 73:4-79:3 79:4-93:12 Austria 13.0 2.7 17.3 15.6 Norway 8.3 1.3 17.3 12.2 Sweden 9.1 1.7 18.8 13.4 Switzerland 15.4 1.4 14.1 11.0 Belgium 12.5 1.4 16.4 13.2 Denmark 12.3 2.1 15.6 12.8 France 13.3 8.2 14.3 15.5 Germany 13.7 1.7 18.7 14.6 Ireland 22.08 2.3 7.85 20.01 Italy 8.0 1.8 16.8 18.8 Luxembourg 11.9 1.5 15.8 13.2 Netherlands 13.4 2.8 16.1 15.4 United Kingdom 12.6 1.7 18.7 19.5 19

Table 2: Standard deviation of log differences %: Log difference DM RERs Monthly 1957:1 - 1993:12 Time 57-93 57-73 73-79 79-93 79-86 87-93 Austria Norway Sweden Switzerland Belgium Denmark France Ireland Italy Luxembourg Netherlands United Kingdom 3.2 4.4 5.5 4.6 3.1 7.0 5.6 10.6 5.3 3.2 3.3 7.2 4.5 2.0 3.7 4.9 3.2 5.9 3.1 6.8 3.1 3.5 3.7 10.1 7.5 6.4 8.2 16.9 3.0 9.4 3.4 3.6 4.4 4.2 5.1 8.7 1.6 1.5 4.8 5.4 6.9 7.5 4.0 4.2 2.7 3.2 6.1 7.6 2.6 3.2 9.4 11.8 4.6 5.6 2.7 3.1 1.7 1.8 8.3 9.3 1.6 4.0 6.2 3.8 2.0 3.8 1.9 5.7 3.3 2.1 1.5 7.1 20

Table 3: Augmented Dickey-Fuller Tests Log U.S. Dollar Monthly RERs; 1957:1-1993:12 Lags=l1 57:1-93:12 57:1-73:3 73:4-79:3 79:4-93:12 Austria -.91 0.99 -0.55 -0.86 Norway -1.44 1.59 0.29 -1.22 Sweden -1.94 0.63 0.40 -1.23 Switzerland -.77 -3.12* 0.84 -1.01 Belgium -1.38 1.95 -1.09 -1.16 Denmark -1.24 0.73 1.18 -.99 France -1.48 -0.06 -2.05 -1.07 Germany -1.35 1.58 0.40 -1.06 Ireland -1.71 -1.08 -0.66 -1.29 Italy -1.64 -0.34 2.08 -1.15 Luxembourg -1.43 1.83 -0.75 -1.18 Netherlands -1.54 1.05 -2.03 -1.30 United Kingdom -1.79 -1.57 0.28 -1.53 Table 4: Mackinnon's critical values 1% -3.45 -3.46 -3.52 -3.46 5% -2.86 -2.87 -2.90 -2.87 10% -2.570 -2.574 -2.588 -2.575 21

Table 5: Augmented Dickey-Fuller Tests: Log DM Monthly RERs; 1957:1-1993:12 Lags=1 57:1-93:12 57:1-73:3 73:4-79:3 79:4-93:12 Austria -.84 -2.74* -1.79 -2.67** Norway -2.33 -2.92* -1.43 -1.69 Sweden -1.56 -0.66 -0.84 -2.34 Switzerland -0.81 -3.12* -1.47 -2.22 Belgium -2.32 -0.33 -1.09 -2.04 Denmark -2.69** -1.83 -2.02 -3.34* France -2.66** -1.37 -2.34 -2.62** Ireland -2.92** -1.11 -3.77* -2.96* Italy -1.58 0.06 -2.91* -2.22 Luxembourg -2.15 -0.12 -1.84 -2.11 Netherlands -1.8 -2.02 -1.68 -2.88* United Kingdom -2.18 0.08 -2.9 -2.33 Table 6: Mackinnon's critical values 1% -3.45 -3.46 -3.52 -3.46 5% -2.86 -2.87 -2.90 -2.87 10% -2.570 -2.574 -2.588 -2.575 22

Table 7: Incidence and Timing of Realignments in the ERM: Percent changes in bilateral central rates Date BLF DK DM FFR IL IP DG UKP 9-24-79 -2.86 +2.0 11/30/79 4.76 3/21/81 -6.0 10/5/81 +5.5 -3.0 -3.0 +5.5 2/22/82 -8.5 -3.0 6/14/82 +4.25 -5.75 -2.75 +4.25 3/21/83 +1.5 +2.5 +5.5 -2.5 -2.5 -3.5 +3.5 7/22/85 +2.0 +2.0 +2.0 +2.0 -6.0 +2.0 +2.0 4/7/86 +1.0 +1.0 +3.0 -3.0 +3.0 8/4/86 -8.0 1/12/87 +2.0 +3.0 +3.0 2/1/93 -10.0 Bands: All fluctuation bands are 2.25%, except the IL from 3/13/79- 1/7/90-6.0%. Effective 8/2/93, fluctuation bands were widened to 15% for all ERM currencies, except the DM and DG which remain in a 2.25% band against each other. UK became a member of the ERM on 10/8/90 and suspended its membership on 9/17/92. Key: BLF=Belgium-Luxembourg Franc,DK=Danish Krone,DM=German Mark,FFR=French Franc,IL=Italian Lira,IP=Irish Pound, DG=Dutch Guider,UKP=Pound Sterling. 23

Table 8: Summary Statistics for the Log of German Mark RERs Monthly 1979:3-1993:12 First Differences Levels X S.D., AR1 AR2 AR3 pi t-stat Austria -0.0086 0.114 0.004 0.003 -0.001 0.98 -2.04 Norway -0.0079 0.1179 0.002 0.009 0.007 0.97 -1.78 Sweden 0.0002 0.0172 0.029 -0.049 0.052 0.98 -0.84 Switzerland -0.0166 0.2304 0.007 0.007 -0.005 0.96 -1.88 Belgium -0.0078 0.1088 0.006 0.006 0.005 0.97 -2.0 Denmark -0.0072 0.0956 0.012 0.007 -0.003 0.91 -3.0 France 0.0042 0.0685 -0.028 -0.032 -0.012 0.96 -2.1 Ireland -0.0391 0.5134 -0.001 0.002 -0.004 0.92 -2.92 Italy -0.0017 0.2290 0.006 0.007 -0.004 0.97 -2.36 Luxembourg -0.0004 0.0118 0.032 -0.022 -0.067 0.96 -2.13 Netherlands 0.0045 0.0737 0.028 -0.017 0.029 0.9x -x.xx U.K. -0.0009 0.0241 0.381 0.102 0.108 0.95 -2.63 24

Table 9: Estimates for S(0):Monthly data 1979:3-1993:12 12 24 36 48 60 72 84 96 108 Austria 0.679 0.667 0.675 0.693 0.784 0.810 0.809 0.787 0.747 Norway 2.032 2.149 1.892 1.925 2.007 1.871 1.721 1.769 1.834 Sweden 2.108 2.239 1.674 1.400 1.314 1.165 1.017 0.971 0.905 Switzerland 1.066 0.700 0.427 0.354 0.341 0.310 0.280 0.249 0.192 Belgium 1.575 1.649 1.360 1.117 1.005 0.942 0.912 0.859 0.730 Denmark 0.382 0.314 0.296 0.307 0.321 0.305 0.280 0.254 0.220 France 2.063 2.246 1.625 1.044 0.902 0.961 0.953 0.888 0.793 Ireland 0.456 0.521 0.542 0.554 0.579 0.591 0.594 0.598 0.594 Italy 2.254 2.803 2.981 3.032 3.027 3.045 3.074 3.118 3.134 Luxembourg 1.365 1.322 1.043 0.799 0.715 0.716 0.722 0.705 0.622 Netherlands 0.525 0.287 0.252 0.165 0.159 0.146 0.131 U.K 1.868 1.971 1.704 1.655 1.540 1.402 1.254 1.139 1.096 Average 1.364 1.406 1.206 1.087 1.056 1.020 0.981 Std. Dev. 0.715 0.882 0.819 0.821 0.820 0.804 0.792 0.811 0.835 25

Table 10: Estimates for S(0):Monthly data 1979:3-1993:12 120 132 144 168 Austria 0.714 0.675 0.636 0.590 Norway 1.828 1.824 1.792 1.569 Sweden 0.784 0.778 0.848 0.801 Switzerland 0.205 0.185 0.136 0.129 Belgium 0.610 0.537 0.503 0.428 Denmark 0.187 0.159 0.137 0.103 France 0.748 0.758 0.788 0.728 Ireland 0.585 0.580 0.565 0.497 Italy 3.121 3.086 3.072 2.805 Luxembourg 0.548 0.495 0.466 0.398 Netherlands 0.116 01.112 0.106 0.088 U.K 1.062 1.076 1.103 0.989 Average 0.920 0.878 0.859 0.849 Std. Dev. 0.841 0.841 0.844 0.818 Table 11: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy; Whole Period, All Countries, U.S. dollar RERS 0 3.8* (9.47) AUS 0.48 (1.45) NOR 0.56 (1.80) SWE -1.18* (2.95) SWI 1.49* (4.81) BEL 0.64* (2.00) DEN 1.27* (4.09) FRA 0.25* (0.73) GER 0.75* (2.34) IRE 1.67* (5.38) ITA 0.71* (2.29) LUX 0.92* (2.96) NET 1.1* (3.54) UK 1.29* (4.16) R2=0.15; Akaike Information Criterion=-0.97 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. 26

Table 12: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy; Whole Period, All Countries, DM RERs 0 2.2* (4.92) AUS -.21 (-1.05) NOR 0.31 (1.63) SWE 0.00 (0.00) SWI 0.21 (1.10) BEL 0.19 (1.00) DEN 0.32 (1.68) FRA 0.52* (2.73) GER IRE 1.16* (6.10) ITA 0.59* (3.10) LUX 0.16 (0.84) NET 0.11 (0.57) UK 1.27* (6.68) R2=0.12; Akaike Information Criterion=-0.10 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. Table 13: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy; Whole Period, EC8 Countries, DM RERs 0 AUS NOR SWE SWI BEL DEN FRA GER IRE ITA LUX NET UK 2.9* (3.41) 0.61* 0.10 1.81* (6.46) 0.69* 0.28 0.79* 0.16 1.68* (2.1) (0.35) (2.46) (1.00) (2.82) (0.17) (4.94) R2=0.21; Akaieke Information Criterion==-0.12 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. 27

Table 14: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy;Whole Period, EFTA4 Countries, DM RERs 0 1.8* (4.58) AUS -0.09 (-0.75) NOR 0.37* (3.08) SWE 0.28 (1.75) SWI 0.31* (2.58) BEL DEN FRA GER IRE ITA LUX NET UK R2=0.19; Akaike Information Criterion=-0.12 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. Table 15: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy; Post Bretton-Woods, All Countries, DM RERs 0 2.6* (2.92) AUS -0.74* (-2.00) NOR 0.22 (0.78) SWE -.75 (-1.05) SWI 0.37 (1.37) BEL 0.07 (0.28) DEN 0.41 (1.70) FRA 0.25 (0.96) GER IRE 1.08* (4.32) ITA 0.57 (2.28) LUX 0.04 (0.16) NET 0.00 (0.00) UK 1.67* (6.18) R2=0.13; Akaike Information Criterion=-0.10 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. 28

Table 16: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy; Post Bretton-Woods, EC8 Countries, DM RERs 0 AUS NOR SWE SWI BEL DEN FRA GER IRE ITA LUX NET UK 3.13* (3.99) 0.16 0.36 0.27 0.77* 0.41 -.08 0.00 1.68* (0.61) (1.38) (1.00) (2.75) (1.51) (-0.30) (0.00) (6.22) R2=0.19; Akaike Information Criterion=-0.10 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. Table 17: Panel data regression coefficients for country specific effects and nominal exchange regime-openness dummy;Post Bretton-Woods, EFTA4 Countries, DM RERs 0 2.38 (1.1) AUS -0.60 (-0.93) NOR 0.30 (0.83) SWE -0.40 (-0.27) SWI 0.43 (1.38) BEL DEN FRA GER IRE ITA LUX NET UK R2=0.14; Akaike Information Criterion=-0.11 Notes: Whole period=1957:1-1993:12, Post Bretton-Woods period=1973:3-1993:12; T-stats reported in parentheses. * denotes significance at the 5% level. 29

Table 18: Second Moment Estimates Monthly Log RERs % U.S.Dollar German Mark 1957:1-1993:12 1957:1-1993:12 Level First Diff. Level First Diff. Austria 8.22 0.6 0.58 0.009 Norway 7.02 0.04 0.56 0.02 Sweden 4.11 0.04 0.72 0.03 Switzerland 12.31 0.07 2.30 0.08 Belgium 4.72 0.05 0.31 0.008 Denmark 8.56 0.08 0.57 0.04 France 3.19 0.06 0.88 0.03 Ireland 4.87 0.12 1.25 0.10 Italy 4.11 0.05 1.60 0.02 Luxembourg 3.43 0.05 0.79 0.01 Netherlands 8.19 0.06 0.49 0.01 United Kingdom 3.45 0.06 1.82 0.04 Germany 5.65 0.06 Table 19: Second Moment Estimates Monthly Log U.S. dollar RERs % Time 57-73 73-79 79-93 level 1st diff level 1st diff level 1st diff Austria 0.259 0.012 1.899 0.097 2.787 0.089 Norway 0.193 0.006 1.231 0.080 2.089 0.061 Sweden 0.109 0.003 1.110 0.072 2.372 0.074 Switzerland 0.283 0.005 2.518 0.117 3.599 0.109 Belgium 0.145 0.007 1.493 0.082 2.874 0.089 Denmark 0.090 0.030 1.544 0.142 3.083 0.109 France 0.343 0.035 1.334 0.084 2.814 0.085 Germany 0.257 0.012 2.253 0.105 2.778 0.088 Ireland 0.410 0.052 3.814 0.233 3.054 0.141 Italy 0.123 0.003 0.855 0.058 2.492 0.085 Luxembourg 0.142 0.007 1.418 0.085 2.876 0.091 Netherlands 0.299 0.015 1.636 0.086 2.839 0.089 United Kingdom 0.371 0.018 1.454 0.062 3.265 0.100 30

Table 20: Second Moment Estimates Monthly Log DM RERs % Time 57-73 73-79 79-93 level 1st diff level 1st diff level 1st diff Austria 0.21 0.018 0.16 0.003 0.04 0.002 Norway 0.23 0.012 0.47 0.019 0.75 0.016 Sweden 0.18 0.01 0.98 0.025 0.14 0.038 Switzerland 0.18 0.014 1.18 0.035 0.47 0.013 Belgium 0.15 0.008 0.57 0.007 0.17 0.006 Denmark 0.29 0.036 1.14 0.097 0.34 0.027 France 0.66 0.044 1.23 0.027 0.25 0.006 Ireland 0.57 0.061 3.97 0.253 0.54 0.066 Italy 0.20 0.01 1.76 0.065 0.56 0.016 Luxembourg 0.18 0.01 0.43 0.008 0.56 0.006 Netherlands 0.19 0.014 0.34 0.014 0.15 0.002 United Kingdom 0.33 0.024 2.51 0.066 2.11 0.048 Table 21: Estimates for S(0):Monthly data 1957:2-1971:7 12 24 36 48 60 72 84 96 108 Austria 1.071 1.167 1.136 1.023 0.871 0.738 0.606 0.501 0.439 Norway 0.654 0.672 0.622 0.562 0.493 0.412 0.330 0.265 0.214 Sweden 1.097 0.978 0.893 0.854 0.707 0.588 0.509 0.423 0.397 Switzerland 1.288 1.465 1.399 1.149 0.900 0.757 0.635 0.534 0.447 Belgium 1.894 2.225 1.988 1.639 1.424 1.270 1.101 0.956 0.860 Denmark 1.139 1.149 1.077 0.963 0.851 0.759 0.658 0.602 0.604 France 0.469 0.483 0.472 0.385 0.307 0.271 0.238 0.197 0.151 Germany 0.618 0.645 0.559 0.479 0.412 0.352 0.289 0.238 0.192 Ireland 0.934 1.066 1.152 1.095 0.989 0.870 0.751 0.640 0.558 Italy 0.910 0.751 0.686 0.691 0.505 0.418 0.352 0.280 0.265 Luxembourg 1.986 2.68 2.96 2.86 2.47 1.971 1.405 0.978 0.716 Netherlands 0.717 0.6714 0.584 0.522 0.467 0.403 0.341 0.309 0.296 U.K. 1.108 1.195 1.145 1.018 0.922 0.812 0.706 0.643 0.632 Mean 1.986 2.684 2.96 2.86 2.477 1.97 1.405 0.978 0.716 Std Dev 0.423 0.604 0.650 0.608 0.536 0.433 0.32 0.245 0.209 31

Table 22: Estimates for S(0):Monthly data 1957:2-1971:7 120 132 144 156 168 Austria 0.41332778 0.415147993 0.417 0.410 0.385 Norway 0.190 0.191 0.202 0.218 0.221 Sweden 0.404 0.415 0.399 0.366 0.337 Switzerland 0.401 0.406 0.399 0.395 0.361 Belgium 0.844 0.891 0.934 0.922 0.866 Denmark 0.608 0.616 0.613 0.598 0.566 France 0.128 0.129 0.145 0.153 0.153 Germany 0.154 0.142 0.149 0.163 0.159 Ireland 0.513 0.512 0.514 0.500 0.471 Italy 0.257 0.259 0.262 0.257 0.246 Luxembourg 0.620 0.594 0.583 0.578 0.545 Netherlands 0.282 0.281 0.289 0.290 0.264 U.K. 0.636 0.640 0.636 0.613 0.571 Mean 0.620 0.594 0.583 0.578 0.545 Std Dev 0.206 0.213 0.217 0.210 0.195 32

8 Figure 2.1: Spectral Density Estimates: Other European countries 1979:3-1993:12 2.5 2 " IJ 2 - Noeay 1.5 o 1. Au A 0.5 -CO)5 \___i__ 12 24 36 48 60 72 84 96 108 120 144 168 180 Number of covariances used

Figure 2.2: Spectral Density Estimates: Narrow Band ERM countries 1979:3-1993:12 2.5 -2 - NLCa) Co C 0.5 C', 0oDhr~ 12 24 36 48 60 72 84 96 108 120 144 168 180 Number of covariances used

8 Figure 2.3: Spectral Density Estimates: Narrow Band ERM countries 1979:3-1993:12 1.6 L. 1.4 0 c 1.2 - 6 W 14. 0.8 l. 0.6 C co 0.4 0.2 0 12 24 36 48 60 72 84 96 108 120 144 168 180 Number of covariances used

Figure 2.4: Spectral Density Estimates: Wide Band ERM countries 1979:3-1993:12 3.5 -I- 3 0 Italy C M 2.5 NUJ 2 ca) ~ ) 1.5 - CL co 0 12 24 36 48 60 72 84 96 108 120 144 168 180 Number of covariances used

8 Figure 2.5: Spectral Density Estimates: Austria, Luxembourg, Netherlands, Germany; 1957:2-1971-7 1.4 IU'B 1.2 c~ NIJJ >N w 0.8 c 0. 0 0. W'a) 0. c' 0 Number of Covariances used

8 Figure 2.6: Spectral Density Estimates: Norway, Sweden, Switzerland; 1957:2-1971:7 2.5 he0 c 2 0a L-D.5W 1. I-r C0. C'o 0F Number of Covariances used

8 Figure 2.7: Spectral Density Estimates: Belgium, Denmark, France; 1957:2-1971:7 1.4 Co I'B 1.2 c~ NUJ Co-" 0, >, W0.2 0%.O C',0 0 Number of Covariances used

00 Spectral Density at Frequency Zero/l Variance of First Difference (RER) 0 — ~ N) CO 6oO en -' on C o on co en -n Z0 0 o~~~~i b3~~~~~~~~~~~~o CD. CD 00 C I,LI/^ 0. 1^ // ^ /?* ^ ^~~~~~~ tLi___ i)