A Long-run View of the European Monetary System

International Finance Discussion Papers Number 339

January 1989

A LONG-RUN VIEW OF THE EUROPEAN MONETARY SYSTEM

Hali J. Edison and Eric Fisher

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

Abstract

This paper analyzes the exchange rates and consumer price indices of the six largest countries of the European Monetary System (EMS). The analysis covers the entire period of floating exchange rates. This paper shows that many of the implied real exchange rates have unit roots, even when ‘one allows for the possibility of a structural break occurring at the time of the formation of the EMS. Further, prices and exchange rates are not co-integrated during the EMS period. There is strong evidence that there is a quadratic time trend in these price indices and weak evidence that exchange rates and prices were more highly co-integrated before the advent of the EMS. The data suggest that the eleven realignments of the EMS between 1979 and 1988 have not served fully to offset the member countries’

inflation differentials.

A Long-Run View of the European Monetary System

Hali J. Edison

Eric Fisher?

I. Introduction

The European Monetary System was founded on March 13, 1979. At that time, it was seen as another step in the unification of the economic policies of the countries of the European Community. It established the European “Currency Unit (ECU) in an effort to replace the dollar as a reserve currency, in Europe at least. Nearly ten years have lapsed since the EMS’ inception; it should now be possible to assess whether the EMS has satisfied a more modest goal: that: of providing enough stability in European prices so that intra- European t:rade can be conducted according to real, not monetary, forces. This paper assesses how the EMS exchange rate arrangement has influenced real exchange irates and relative prices by comparing regimes before and after the advent of the EMS. These issues are fundamentally empirical.

The EMS is a system of quasi-fixed exchange rates. There are ten currencies that participate in the arrangement; these are: the Belgian franc, 1 The authors would like to thank Joon Park for extremely helpful discussions. The authors are grateful for the comments of seminar participants at the September 1988 meetings of the European Economic Association and the October 1988 Midwest International Economics Conference. Fisher would like to thank the Institute for International Economic Studies at the University of Stockholm for providing him with a fine research environment in which to begin this study, and Edison would like to thank the Norwegian Central Bank for providing her the opportunity to begin this research. This paper represents the views of the authors and should not be interpreted as

representing those of the Board of Governors of the Federal Reserve System or any other members of its staff.

Hali J. Edison is a staff economist in the Division of International

Finance. Eric Fisher is an assistant professor in the Economics Department at Cornell University.

2 Italian lira, the Luxembourg franc, the Dutch guilder, the pound sterling, and the Greek drachma. The currencies are allowed to fluctuate within bands of 2.25% around an ECU central rate,” and the central banks of a pair of member countries are obliged to intervene in the case that their currencies are at the limits of the divergence bands. Although the drachma and the British pound are used to define the ECU, neither the British nor the Greek government has agreed to participate in the intervention mechanism. There have been eleven realignments of the system.° When a realignment occurs, a currency’s ECU central rate is redefined, and the revaluations or devaluations of the currencies are designed to offset some or all of the changes in relative price levels.‘ ° The purpose of this paper is to examine the long-run trends of the real exchange rates of the major currencies participating in this system. Movements in real exchange rates are due either to changes in relative prices or to realignments of the EMS, which have been relatively infrequent. This paper proposes to test the proposition that EMS countries with high inflation have lost competitiveness to low inflation countries. We measure the level of competitiveness by the real exchange rate; thus, a loss of competitiveness is 2 The lira is allowed to fluctuate within 6% bands, but in practice the Italian central bank intervenes to keep its currency within the narrower divergence limits. The earlier Snake arrangement operated in a similar fashion but without having the ECU as a way of defining the central ‘ates. The following countries participated in the Snake: Belgium, Denmark, France, Germany, Italy, Netherlands, Norway, Sweden and the United Kingdom. Not all of these countries, however, participated continuously in the Snake.

3 The Appendix lists the dates of the initial formation and all realiignments of the EMS.

4 We do not intend in this paper to enter into the details of the EMS exchange rate mechanism; for a good treatment of these points, see Grabbe (1936).

5 A re-composition of the ECU is different from a realignment; a recomposition involves changing the actual number of units of each cur:rency in defining the ECU. A re-composition of the ECU occurred on 14 September 1984, the date at which the Greek drachma was added to the definition of the ECU.

3 an appreciation of the real exchange rate. If each realignment compensated high inflation countries for losses of competitiveness, then the real exchange rate would tend to exhibit no long-run trend. Giavazzi and Pagano (1987) argue that: real appreciation of high inflation members is characteristic of the EMS and suggest that this helps to discipline the high inflation countries, The implication of this view is that realignments only partially offset inflation differentials.

To test this idea, we consider three hypotheses. First, we test whether the exchange rates and the relevant price indices are co-integrated. Second, we test whether long-run real exchange rates are stationary when one allows for a structural change in these series at the advent of the EMS; this is the first application in international finance of a unit root test that allows for a structural break. Third, we test if the rate of depreciation of these real exchange rates is different after the advent of the EMS.

Since the dissolution of the Bretton Woods agreement, exchange rates of the major industrial countries have exhibited behavior indistinguishable from that of random walks.® Because the EMS is akin to a system of fixed exchange rates, it is perhaps surprising that the fifteen bilateral exchange

“rates we analyze are also essentially random walks. This fact is plausible, however if one considers that there have been frequent enough realignments of the EMS so that bilateral rates are not sufficiently rigid as to appear

7

stationary to the statistician.

Several other economists have used the co-integration approach in the

recent literature on exchange rates. Corbae and Ouliaris (1986) propose a

6 See Meese and Singleton (1982) for an early discussion of unit roots in exchange rate data and Meese and Rogoff (1983) for an analysis of the out-ofsample forecasting properties of several exchange rate models.

7 If there had been no realignments of the EMS, then it would be surprising to find exchange rates and prices co-integrated except in the degenerate case where the relevant price indices themselves were stationary.

4

robust test for unit roots in the foreign exchange market; they show that weekly spot and forward rates for six currencies have a unit root, whereas the implied risk premia are stationary. Patel (1986) examines quarterly data for currencies and price indices of Canada, Germany, the Netherlands, the United Kingdom, and the United States; he shows that the currencies of Canada, Germany and the United States were co-integrated with their respective price indices. Mark (1986) investigates monthly data covering the currencies and price indices of Belgium, Canada, France, Germany, Italy, Japan, the United Kingdom, and the United States from June 1973 through June 1985. He concludes that the null hypothesis of no co-integration cannot be rejected at standard significance levels. We find similar results for several of these currencies during our entire sample, but there is some contrast in the behavior of the European currencies before and after the advent of the EMS.

Huizinga (1986) examines the spectral properties of ten different exchange rates, using monthly data for the thirteen years between 1974 and 1986. He studies the low frequency properties of many of the implied real exchange rates and argues that these series exhibit mean reversion. He states that he finds no difference in the long-run behavior of the European exchange rates from the exchange rates of other countries. We find some evidence to the contrary simply by breaking the sample into two periods. Kaminsky (1987) analyzes data on the U.S. dollar, yen, pound sterling, mark, and Swiss franc covering the period from April 1973 through April 1986. She finds that the implied real exchange rates exhibit mean reverting behavior; hence they are not random walks.

There have been several other empirical studies of the EMS; Rogoff (1985), Giavazzi and Giovannini (1985), Ungerer, Evans, Mayer, and Young

(1986), Collins (1987, 1987a) and Giavazzi and Pagano (1987) are recent

5 examples. None of these papers studies the co-integrative properties of exchange rates.

We structure the rest of the paper as follows. In Section II, we present a simple description of a relationship between price indices and exchange. rates. Section III presents a preliminary analysis of the data, analyzing whether these time series have unit roots; we break the sample into two periods, one covering the period before the advent of the EMS and the other covering the time since then. Section IV presents the results of our tests for co-integration between the nominal exchange rates and the relevant consume: price indices. Section V tests whether these European real exchange rates have unit roots, even when one allows for a structural break at the advent of the EMS; we test also whether the real exchange rates show a

significantly different rate of depreciation during the EMS period. Section VI

presents our conclusions.

II. Models of the Time Series

The usual empirical analyses of the absolute version of purchasing power parity involve running a regression of the logarithm of an exchange rate index on a constant and the difference of the logarithm of two relevant price indices; one traditionally tests the null hypothesis that the constant is zero and the coefficient on the difference of the price indices is unity. Of course, this kind of analysis is not a test of a model of exchange rate determination; it is perhaps best interpreted as the estimate of a reduced

8

form equation relating an asset price and two price levels. We too must

8 See Levich (1985) for a discussion of empirical studies of exchange rates in the traditional genre. The new wave of this literature discusses some of these issues within the framework of an error correction model; see Edison (1985) and Edison and Klovland (1987), for early examples of this work.

6 admit at the outset that we are not presenting a model of exchange rate determination. Instead, we analyze the statistical properties of consumer prices and exchange rates among the major European economies.

For an arbitrary time series (x,}, consider the model (1) x7 B, + B, t + B, X17 U-

If x, represents the logarithm of a consumer price index at time t and if we assume that B, is unity, then equation (1) states that the logarithm oi? the price level can be modeled as a random walk with drift and a systematic time component. Using logarithms allows simple economic interpretations of the ‘model's parameters; in particular, £, is the rate of consumer price inflation and B, is a systematic change in the inflation rate. If x, represents the logarithm of an index of the number of units of domestic currency necessary to purchase one unit of foreign currency, then assuming that B, is unity implies that By is the rate of depreciation of domestic currency and B, is a systematic acceleration in that depreciation.

We assume that the errors {u,} in equation (1) satisfy the following

statistical properties.

Assumption: (i) E ul = O Vt; (ii) sup, E Ju, |?" < © for some f > 2 and some ¢ > 0; (iii) let S| = 2 u,; then o” = lim, E(S,/T) exists and o” > 0; and

(iv) {u,} is a strong mixing with coefficients 6, satisfying

a6 17/8 < w, m

These are the assumptions that Phillips and Perron (1988) have made standard

for much of the literature testing for unit roots where the error generating

7

process {u,) is heterogeneous.® Much of the current applied work using unit roots in international finance has not imposed this assumption; it assumes an innovation process that is independently and identically distributed. This is particularly inappropriate for price indices because they display strong seasonal components. For example, several of the European countries have annual or biannual administered price increases for basic foodstuffs and housing; these prices, of course, have a strong influence on consumer price indices. Allowing for heterogeneity of the error process is also important for exchange rates because, in a regime of floating exchange rates, these are simply asset prices. There is strong evidence that first differences of these prices seem to be drawn from heteroscedastic distributions.

Let an exchange rate and two relevant price indices be generated by

(1). Consider now a generalization of the notion of the real exchange rate ry

defined by

(2) r= ae +a, p*, +a, Py where e, is the logarithm of the exchange rate index, p*, is logarithm of the foreign price level, and p, is that of the domestic price level, all taken at time t. If we assume that (a,, a, @,) = (1, 1, -1), then un is simply an index of the real exchange rate at time t. An increase in r, is a real depreciation. A decrease in r, is a real appreciation; this is often called a loss of competitiveness. If we assume that exchange rates and prices are not themselves. stationary but that r, is a stationary stochastic process, then the

arbitrary triple (a,, a, a,) has an interpretation as constants of co-

integraticn.

9 See Corkae and Ouliaris (1986, p. 376) for a good discussion of the restrictions that this assumption imposes on the stochastic process.

8 In the Section III, we test certain restrictions on the parameters in equation (1) for data on European exchange rates and prices. In Section IV, we examine the time series uy defined by setting (a,, @,, @,) = (1, a,» a,)

: ‘ 10 where a, and a, are the ordinary least squares estimates of a, and a,,

and in Section .V, we examine the time series u defined by setting (a,, @,, @,) =

(1, 1, -1).

III. Preliminary Analysis of the Data

We examine the currencies of the six largest countries participating in the European Monetary System: the Belgian franc, the French franc, the German mark, the Italian lira, the Dutch guilder, and the pound sterling. The data are observations representing the value on the last business day of the month of these six currencies’ noon quotes on the New York foreign exchange market. These six currencies implicitly define fifteen European bilateral exchange rates, only six of which are independent.’ The price indices are monthly consumer prices, not adjusted for seasonality, whose sources are the six countries in our sample. These indices are typically announced during the third week of the month, but they generally involve sampling a basket of commodities in different cities during the course of the month in which the data are reported. See the appendix for a full description of the data.

For sake of comparison throughout this paper, two sub-samples are

considered: the six years of the Snake and the nine years of the EMS.'* A

10 Stock (1987) has shown that these are consistent estimates of the cointegrating constants.

11 During the rest of this paper, we shall use the terms "exchange rates" and "exchange rate indices" to mean the logarithms of the exchange rate indices, appropriately normalized. The traditional literature testing purchasing power parity almost always uses an exchange rate index; this allows the interpretation of the error in a typical regression as the percentage deviation from a base year relationship.

12 We have normalized each time series so that its initial logarithmiz value is zero; this occurs in March 1973. Each time we run a regression involving a sub-sample from the EMS period, we re-normalize so that each series has a

9 central question we want to address is whether exchange rate behavior has changed bet:ween the two arrangements. It may not be entirely proper to draw a sharp distinction between periods before and after the advent of the EMS because the Snake was quite similar in practice to the EMS arrangement. On the other hand, it has been argued that there has been much more coordination of policy between countries during the EMS than during the Snake.

Figure 1 shows the plots of the logarithms of the fifteen EMS bilateral nominal exchange rates over the entire sample. Consider the model expressed by (1). For each series in each sub-sample, we test first the null hypothesis H,: 8, = 1 against the general alternative. We use the test statistic z(t (@)) described by Park and Choi (1988) because of its

13

computational elegance. The critical values for this test are given in

Fuller (1976, Table 8.5.2). The first sub-samples for each exchange rate covers the months from April 1973 through February 1979. The test statistics are reported in Table 1.

Table 1 shows that the null hypothesis that these bilateral exchange rates have a unit root can be rejected in only two cases: those of the Belgian franc-mark and Belgian franc-guilder bilateral rates. This is evidence that the Belgian monetary authorities may have used the Snake to control the rates of depreciation of their currency against the mark and the guilder.

We have also run the same test for these currencies in the period from

March 1979 through May 1988. Table 2 reports these results. During the

logarithmic value of zero in March 1979. None of the test statistics used in this paper depend upon this re-normalization.

13 All the tests based upon the work of Phillips (1987) and Phillips and Perron (1988) use an estimate of the ratio of the short-run variance to the long-run variance of the random variable S, described in the Assumption above; throughout this paper have we have used estimates of the first four autocorrelations of the processes generating the data in constructing this ratio. The values of the test statistics seem not to vary much with the inclusion of more auto-correlations. Corbae and Ouliaris (1986) report a similar finding.

10 period of the European Monetary System, we could reject the null that these nominal exchange rates have unit roots in only two cases. These were the Belgian franc-French franc rate and the mark-guilder rate. Many observers of the EMS have noted that its realignments tend to maintain rough parity between the German.and Dutch currencies; this sample also shows that these realignments maintain a systematic relationship between the Belgian and French currencies.

We performed the same tests on first differences of these time series, and in every case it was possible to reject soundly the null that these differenced time series had unit roots. For the sake of brevity, we do not report all thirty statistics. These tests present very strong evidence for the conclusion that none of the exchange rates is integrated of an order higher than one.

Figure 2 depicts the six consumer price indices. These series trend upward; moreover, there seems to be a systematic change in the rate of inflation in each of these countries over the entire sample period. This reduction in the rate of inflation has to do with the coincidence of the advent of the regime of floating exchange rates with the first oil price shock. Further, the EMS was started about six months before the second oil price shock. We show below that it is important to include a time trend in analyzing first differences of these series.’ The economic interpretation of this is that the decline in inflation is an integral part of the data.

Again, we model the time series according to the process in equation

(1), and we test the null hypothesis H,: B, = 1 against the general

14 Patel (1986) conjectured that several of these consumer price indices were integrated of order two for the period he was examining. He did not ‘pursue this insight by including a time trend in his unit root tests.

11 alternative. We used again the statistic given by Park and Choi (1988). This statistic is very useful for price indices because they have seasonal componerits, and the Parzen window of four lags seemed to be able to capture the process generating the data quite adequately.*> The test statistics for the consumer price indices are presented in table 3. In only one case can we reject the null for these time series. The value of the test statistic for the case of the United Kingdom during the EMS period is strong evidence of the monetary policy of the Thatcher government. We ran the same tests on first differerices of the series; to keep the number of tables manageable, we do not report these statistics. They allow us to reject soundly the hypothesis that the differenced price series have a unit root. We conclude that the price indices are integrated of order at most one.

Consider equation (1) again. For all series in each sub-sample, we now test: the joint hypothesis H,: (8,8, +B.) - (B,,0,1) against the general alternative. We are interested in determining whether the exchange rates or price indices show systematic changes in the rates of depreciation or inflation respectively. Again, we use a statistic developed by Park and Choi (1988) because it is robust with respect to the process generating the innovations in (1) and because of its computational elegance. This statistic is esseritially an adjustment to the standard Wald statistic for H, that takes into account the heterogeneity of the innovation process for the series. Its critical values are given in Dickey and Fuller (1981, Table VI). Table 4

presents the values of the test statistics for the nominal exchange rates in

SS

15 In an earlier draft of this paper, we used the Augmented Dickey Fuller Statistic in performing these tests. That statistic was quite sensitive to the filter applied to the data, and we had to apply complicated filters in

order to make the errors in the estimates of equation (1) appear to be white noise.

© 12 the earlier period, and Table 5 presents those in the later period. ‘Neither of these tables is very surprising. They confirm essentially the evidence given in tables 1 and 2 that these exchange rates have unit roots; there is some marginal evidence that Italy's rate of depreciation against Germany and the Netherlands accelerated during the first sub-sample. Italy experienced high inflation after the first oil price shock, and the other two countries had relatively low inflation during the last decade.

Tables 6 presents these test statistics for the price indices in the two sub-samples. Here the evidence is strikingly different from that of table 3. We can reject the null for two of the six indices in the first sub-sample and for every index in the later sub-sample. This is very strong evidence of the systematic decline in inflation of this decade; price indices have showed significant decelerations over much of the regime of floating exchange rates. The earlier tests seemed to indicate that most of these price indices had unit roots; we interpret the values in table 6 as indicating that the deterministic part of the time series has much explanatory power. Co-integration has to do, of course, with the stochastic element of the time series involved. This has strong implications for the kinds of co-integration tests one might run. In particular, it is probably necessary to include a quadratic time trenc to capture the systematic changes in inflation if one hopes not to mis-specify the reduced form between exchange rates and prices in the last two decades.

No applied work in international finance has noticed this fact.

IV. The Co-integrating Regressions

We now continue the analysis by examining whether the bilateral exchange rates are co-integrated with the appropriate pairs of price indices.

If an exchange rate and a pair of price indices are co-integrated, then we

13

interpret this as a loose form of purchasing power parity.*® In particular, although all three time series have unit roots, there is a long-run equilitrium relationship among them. Consider equation (2) again; a traditional test of purchasing power parity constrains this relationship to be given by the triple (1, 1, -1), but a test of cointegration allows for the arbitrary triple (1, a; @,), where we have imposed an implicit normalization. Hence, we are not constraining the relationship to the traditional view of purchasing power parity, but we are looking for empirical evidence of the notion that the three series cannot drift infinitely far apart in time.

There are two kinds of tests for co-integration: those that are not based upon analyses regressions residuals and those that are. We conduct one test of each kind in this section. The first is a test proposed by Park,

Ouliaris, and Choi (1988). Consider running a regression based upon the model 2 (3) e,7~ 8, +A, t+ At + B, Pp, + B, p*,+ u,

where the variables are defined as above. If these exchange rate and price indices are not stationary but the error process is, then the reduced form given by (3) has the simple interpretation that these series are cointegrated, with the coefficients of co-integration defined up to the normalization factor that we have imposed implicitly on the term e,. This test uses the J(p,q) statistic proposed by Park, Ouliaris, and Choi; the null hypothesis is that the three series are not co-integrated. This test is based upon the simple intuition that if exchange rates and two price series are

indeed co-integrated, then adding higher order polynomial time trends in

16 See Mark (1986), Patel (1986), and Corbae and Ouliaris (1988) about testing purchasing power parity in both the traditional and co-integrative framework.

14 estimating (3) will not reduce this regression’s residual sum of squares drastically.*” We have good evidence indicating that it is necessary to include a quadratic time trend in (3); hence, we include four extra polynomial time trends in our test. Park, Ouliaris, and Choi do not give critical values

18

for J(2,6); we had to estimate them from Monte Carlo simulations. The test

statistics are reported in tables 7 and 8. These tables seem to indicate that there is little co-integration of the exchange rates and relevant prices in either of the periods. We notice, however, that the J(p,q) statistics seem to be lower in general in the earlier period; this is weak evidence that: there may be a higher degree of co-integration between the series in the first sub-

sample.

The second test is based upon the residuals from the regressi.on

implied by

(4) ec B, + B, P, + B, p*,+ u,-

This test uses the Dickey-Fuller statistic on the residuals from this regression; we follow the two step procedure outlined in Engle and Yoo

(1987).*° For these data, this test may be unsatisfactory because it ignores

17 One way of illustrating this intuition is to note that one can fit: estimates of a time series arbitrarily well by adding increasingly higher order polynomial time trends as regressors. If the addition of seveiral such trends does not give rise to a large relative reduction in the residual sum of squares, then the parsimonious specification of the regression given by (3) is indeed an adequate representation of the relationship between exchange rates and price indices.

18 No other work in applied econometrics has included a quadratic time trend. Hence, these test statistics are the first reported which include a second degree polynomial and heterogeneously distributed innovations as the null hypothesis.

19 This procedure is an extension of the seminal work of Engle and Granger (1987).

. 3S

the deterministic time trends that seem to be an important part of many of the price ssries. We include it to illustrate the possibility of finding spurious co-integration if the data generating process is mis-specified. This test uses the residuals from the regression based on (4); the null hypothesis is that the exchange rate and the two price indices are not co-integrated. Table 9 reports the Dickey Fuller Statistic for the residuals of the regression based on (4) for the period before the EMS. The critical values for this test are given by Engle and Yoo (1987, Table 2). Table 10 presents the test statistics for the period of the EMS. We cannot reject the null of no cointegration for any regressions in either sub-sample. Many other empirical analyses of exchange rates have had difficulty in finding evidence of cointegration; it is perhaps surprising that even European exchange rates do not seem to satisfy the weak form of purchasing power parity that a co-integrative relationship entails. We see, again, that the test statistics generally seem

to have slightly higher significance levels in the early period.

V. Analyses of the Real Exchange Rates within Europe

In this section we analyze whether the European real exchange rates are stationary time series. Recall that we define real exchange rates as r = e + p* - p, where the symbols are as above. An increase in r represents a real depreciation; this is often called a gain in competitiveness. We are interested in whether the EMS realignments of the nominal exchange rates have maintained competitiveness between European countries. Figure 3 graphs the fifteen European real exchange rates.

It is important to emphasize that the hypothesis that a real exchange rate is stationary is strictly nested within the hypothesis that the relevant

nominal exchange rate and price indices are co-integrated. We describe some

16 evidence below that several of the real exchange rates in the earlier period are stationary, but there is only weak evidence that the relevant series are cointegrated. This is may be an artifact of the testing procedure because the Engle and Yoo critical values and those of Park, Choi, and Ouliaris are quite conservative in the case of three co-integrated series. We do analyze, however, a hypothesis that is not nested within the first. We examine whether these real exchange rates can be modeled as stationary series with a single structural break occurring at the time of the formation of the EMS.

As a preliminary step in this analysis, we tested whether the real exchange rates were themselves stationary over the whole sample and in each sub-sample. We did this in exactly the same way that we analyzed the nominal exchange rates in Section III. We could reject the null of a unit: root for only one real exchange rate over the entire sample: that of Germany-Italy. We found also that we could reject the null of a unit root in only five cases in the earlier period; these were for the real exchange rates involving these pairs of countries: Belgium-Germany, Belgium-Italy, Germany-Italy, Italy- Netherlands, and Italy-United Kingdom. In the later period, we rejected the null of a unit root for the real exchange rate of this country pair only: Germany-Netherlands. This is no surprise because the EMS realignments have treated these two countries’ currencies similarly, and they are the low inflation countries of Europe. Again for the sake of brevity, we do not report all forty-five statistics.

As the last step in the analysis, we are interested in determining whether the advent of the EMS actually represents a structural break in the data generating process for these real exchange rates. The test we present below was developed by Park (1988), and Perron (1987) first noticed the

importance of distinguishing between time series with unit roots and

17 stationary time series that exhibit a structural break. Now let t, represent

the period at the end of which there is a structural break in a time series

under investigation. Further, define

0 ift<t d- b 1 otherwise and 0 iftst, Ss = t-t otherwise.

Consider this model

(5) x7 B, + B, t + B, d + B, s + B, x4 + uy where the innovation sequence {u,} satisfies the Assumption in Section II. The interpretation of the parameters B, and B, is that they model respectively a shift in the intercept and a shift in the deterministic time trend describing the series. If we consider equation (5) as a model of a real exchange rate, then B, describes a change in the rate of depreciation at the advent of a new regime and B, describes a shift in the acceleration of this depreciation.

We used Park’s H(1,1) statistic to test this null hypothesis H,: B, = ‘1 against the alternative that |B, | <1. The critical values for this statistic are given in Park (1988, Appendix B). We report the results from this test in table 11. We reject the null in six of the fifteen cases, and the test statistic is marginally significant in three other cases. This is a

reassuring finding for proponents of the notion of purchasing power parity.

18

It implies that several of these real exchange rates may actually have been stationary over the entire period of floating exchange rates if one allows for a structural change at the advent of the EMS. The evidence suggests that there are several cases where the behavior of real exchange rates in relationship to the pound sterling have undergone a structural change at the time of the advent of the EMS.*° Further, there is strong evidence that liramark and guilder-lira real rates have undergone structural breaks. This lends credence to the notion that the EMS has served to "discipline" Italy by allowing for a real appreciation against the low inflation European countries in this decade.

We conclude the analysis of these real exchange rates by testing this hypothesis directly. Consider the following model of a real exchange rate

(6) r- 6, +6, t+A,st+u,

where r, is the logarithm of the real exchange rate and the other variables are as above. Equation (6) models the notion that the rate of depreciation of the real exchange rate is systematically different after the advent of the EMS. If we assume that the innovation process {u,} is integrated of order

one, then it is natural to consider the first differences of (6) given by (7) dr, = B, + B, d + Au,

where Ar, = r, - Ty... Su, is analogous, and the dummy variable is as defined

above. Of course, the process {Au, } is integrated of order zero, bu: we still

20 The Bank of England does not participate in the EMS intervention :nechanism; since the pound sterling is used to define the ecu, the European central banks often define the par value of this currency so that there is less apparent appreciation of the mark and guilder against the other European currencies.

19 must assume that this process is not necessarily independently and identically distributed. For equation (7), we are interested in this null hypothesis H,: B, = O against the general alternative. Park and Choi propose a test statistic for models like (7) that is a modification of the Wald statistic for this hypothesis; this modification takes into account the ratio of the shortrun and long-run variances in the innovation process. This statistic is distributed x7(1) for the test based on (7). We report the test statistics in table 12. We reject the null in two cases: those involving the real exchange rates of Belgium-Italy and Italy-Netherlands. In both cases, Italy’s real exchange rate appreciated against these countries. This is evidence that

Italy actually did suffer a loss of competitiveness against Belgium and the

Netherlands under the EMS.

VI. Conclusion

This paper has explored two themes. The first has had to do with an assessment: of the European Monetary System, and the second has been an illustration of the applications of new econometric techniques to the old issue of purchasing power parity. we summarize our findings by discussing each of these themes separately.

Our first theme speaks to international economists interested in the European monetary affairs. We have presented very strong evidence that the realignments of the European Monetary System have not served to maintain competitiveness between its largest member countries. We have presented weaker evidence that there was a higher likelihood of co-integration between exchange rates and prices before the EMS than after it. More importantly, the evidence on real exchange rates shows that before the EMS it was more common

for countries to realign their nominal exchange rates to offset inflation

20

differentials. These observations lead us to conclude that there may be an asymmetry in the realignments of the System. Italy, the highest inflation country in the System, does seem to have lost competitiveness during the EMS period. Moreover, there seems to be a structural break in the behavior of several of the real exchange rates involving Italy. This may indicate that the EMS has treated the lira differently from the way the Snake treated it.

Our second theme is of practical importance for both applied international economists and for applied econometricians. We would like to emphasize three points that should serve to guide further applied research in this field. First, floating exchange rates are asset prices; there are good theoretical and empirical reasons to model them as stochastic processes, integrated of order one, whose innovations are heterogeneously distributed. Second, the price indices of many industrial countries in the last two decades exhibit marked declines in their rates of inflation; it is therefore necessary to include a quadratic time trend in any co-integrating regression if one hopes not to mis-specify a long-run relationship between prices and other macroeconomic variables. Third, we have provided the first application in international economics of a unit root test that allows for a structural break. Econometricians studying changes in monetary regimes, such as the advent of a hyper-inflation, would do well to apply this kind of a test in

their own research.

21

Table 1 The Nominal Exchange Rate Before the EMS

Z(t(@)) Statistic

Fr Ge It Ne | UK Be -2.005 -3.911** -2.996 -3.567%* -2.178 Fr -- -2.069 -2.925 -2.144 . -1.690 Ge , -- -- -3.016 -2.558 -2.421 It -- -- -- -3.143 -2.807

Ne -- -- -- -- -2.196

Notes to table:

The sample period is from April 1973 to February 1979 (71 observations). The critical values are given in Fuller (1976, Table 8.5.2); they are -3.18 at the 10% significance level and -3.50 at the 5% significance level.

* indicates significant at the 10% level

** indicates significant at 5% level

Table 2 The Nominal Exchange Rate During the EMS

Z(t(@)) Statistic

Fr Ge It Ne UK Be -3.441* -0.886 -2.181 -1.113 -2.309 Fr -- -1.216 -2.159 -1.582 -2.357 Ge -- -- -2.161 -3.267* -2.734 It -- -- -- -2.701 -2.405 Ne -- -- -- -- -2.784

Notes to table: The sample period is from March 1979 to May 1988 (111 observations). The critical walues are given in Fuller (1976, Table 8.5.2); they are -3.15 at the

10% significance level and -3.45 at the 5% significance level. See the notes to table 1 for an explanation of the symbols.

22

Table 3 Price Indices

Z(t(@)) Statistic

Be Fr Ge It Ne UK pre-EMS 0.314 -1.269 . -1.473 -1.558 0.748 -0.327 EMS - 1.554 -0.091 -0.841 -0.366 -0.604 -4.153%*

Notes to table:

The pre-EMS period is from April 1973 to February 1979 (71 observations). The EMS period is from March 1979 to May 1988 (111 observations). The critical values are as in tables 1 and 2 for the relevant sample sizes. See the notes to table 1 for an explanation of the symbols.

Table 4 The Nominal Exchange Rate Before the EMS

Z(a,B,) Statistic

Fr Ge It Ne UK Be 3.208 9.431%* 5.440 4.666 2.674 Fr ; -- 3.258 5.004 3.542 1.888 Ge -- -- 5.910* 3.742 3.769 It -- -- -- 5.958* 5.441 Ne -- -- -- -- 2.981

Notes to table:

The sample period is from April 1973 to February 1979 (71 observations). The critical values are given in Dickey and Fuller (1981, Table VI); they are 5.61 at the 10% significance level and 6.73 at the 5% significance level. See the notes to table 1 for an explanation of the symbols.

23

Table 5 The Nominal Exchange Rate During the EMS

Z(a,B,) Statistic

Fr Ge It Ne UK Be 6.884** 1.315 2.630 1.348 4.278 Fr -- 0.913 2.876 1.509 © 4.029 Ge -- -- 1.408 7.358%* 5.202 It -- -- -- 3.540 4.217 Ne -- -- -- -- 5.607*

Notes to table:

The sample period is from March 1979 to May 1988 (111 observations). The critical values are given in Dickey and Fuller (1981, Table VI); they are 5.47 at the 10% significance level and 6.49 at the 5% significance level. See the notes to table 1 for an explanation of the symbols.

Table 6 Price Indices

Z,(a,B,) Statistic

Be Fr Ge It Ne UK pre-EMS 6.345* 4.271 4.973 2.450 8.593%* 1.535 EMS 14.253%* 56.913%* 16.51]1** 50.109%* 24.843%* 26.779%*

Notes to table:

The pre-EMS period is from April 1973 to February 1979 (71 observations). The EMS period is from March 1979 to May 1988 (111 observations). The critical values are as in tables 4 and 5 for the relevant sample sizes. See the notes to table 1 for an explanation of the symbols.

24

Table 7 Co-integration Tests for the Period Before the EMS

J(2,6) Statistic

Fr Ge It Ne UK Be 1.878 0.317 0.529 0.243* 0.784 Fr -- 1.970 1.267 2.039 1.278 Ge -- -- 0.832 0.496 0.813 It -- -- -- 0.741 0.066** Ne -- -- -- -- 0.771

Notes to table:

The sample period is from March 1973 through February 1979 (72 observations). The critical value at the 10% level 0.254 is and that at the 5% level is 0.163. These values were estimated by Monte Carlo methods using 5000 replications. One rejects the null hypothesis of no co-integration for low

values of the statistic. See the notes to table 1 for an explanation of the symbols.

Table 8 Co-integration Tests for the Period of the EMS

J(2,6) Statistic

Fr Ge It Ne UK Be 0.149%* 1.794. 0.938 1.648 0.584 Fr -- 5.630 2.561 3.913 0.371 Ge -- 7 0.522 0.443 0.609 It -- -- -- 0.503 0.478 Ne -- -- -- -- 0.601

Notes to table:

The sample period is from March 1979 to May 1988 (111 observations) The critical values at the 10% level is 0.237 and that at the 5% level is

0.155. replications.

These values were again estimated by Monte Carlo methods with 5000

See the notes to table 1 for an explanation of the symbols.

25

Table 9 Residual-Based Co-integration Tests for the Period Before the EMS

Dickey-Fuller Statistic

Fr Ge It Ne. UK Be -1.672 -3.125 -3.150 -3.527 -2.456 Fr -- -1.971 -2.757 -1.791. -2.695 Ge -- -- -3.051 -2.457 -2.609 It -- -- -- -3.176 -3.292 Ne -- -- -- -- -2.486

Notes to t:able:

The sample period is from March 1973 through February 1979 (72 observations). The critical values are given in Engle and Yoo (1987, Table 2); they are -3.73 at the 10% level and -4.11 at the 5% level.

Table 10 Residual-Based Co-integration Tests for the Period of the EMS

Dickey-Fuller Statistic

Fr Ge It Ne UK Be -2.183 -1.758 -1.786 -1.758 -1.544 Fr -- -2.148 -1.945 -2.507 -1.987 Ge -- -- -1.716 -3.073 -3.205 It -- -- -- _ 3.313 -1.927 Ne -- -- -- -- -2.811

Notes to table: The sample period is from March 1979 to May 1988 (111 observations). The

critical values are given in Engle and Yoo (1987, Table2); they are -3.59 at the 10% and -3.93 at the 5% level.

26

Table 11 Tests for Structural Change In the Real Exchange Rates

H(1,1) Statistic

Fr Ge It Ne UK Be -3.234 -2.386 -3.466 -2.683 -3.611 Fr -- -3.144 -3.778 -3.387 -3.918* Ge -- -- -4.775** -3.512 -3.973* It -- -- -- -4.800%** -4.288** Ne ‘ -- -- -- -- -4.070*

Notes to table:

The sample period is from April 1973 to May 1988 (182 observations); the time of the structural break is March 1979 (the 72nd observation). The critical values are given in Park (1988, Appendix B); they are -3.87 at the 10% level

and -4.15 at the 5% level. See the notes to table 1 for an explanation of the symbols.

Table 12 Tests for Change in Rate of Real Depreciation

G, Statistic

Fr Ge It Ne UK Be 1.362 1.378 4.445** 0.031 0.894 Fr -- 0.109 1.547 1.129 0.108 Ge ‘se -- 1.634 2.024 0.235 It -- -- -- 4.133%* 0.178 Ne -- -- -- -- 0.777

Notes to table:

The sample period is from April 1973 to May 1988 (182 observations); =he time of the structural break is March 1979 (the 72nd observation). This is a x7(1) test; the critical values are 2.71 at the 10% level and 3.84 at the 5% level. See the notes to table 1 for an explanation of the symbols.

27

Appendix ,

Dates of Reali ents of the stem

13 March 1979

24 September 1979 30 November 1979 23 March 1981

5 October 1981 22 February 1982 14 June 1982

21 March 1983

22 July 1985

7 April 1986

4 August 1986

12 January 1987

e Data

The six currencies examined are end of month exchange rates as maintained by the Federal Reserve Board. They are the currencies’ rates at noon on the last working day of the month in New York. The implicit bilateral rates e*' have been defined so that the rates are quoted in units of currency j necessary to obtain one unit of currency i; of course, an increase in e’ is a weakening of currency j relative to currency i. The consumer price indices are raw monthly data from national sources and generally represent a sample of

consumer goods taken in geographically dispersed cities in each of the six countries.

References

[1] Collins, S. M. (1987), "“Misalignments and Realignments: Exchange Rate

Management in the European Monetary System", unpublished manuscript, Harvard University and N.B.E.R.

[2] Collins, S. M. (1987a), "PPP and the Peso Problem: Exchange Rates in the EMS", urpublished manuscript, Harvard University and N.B.E.R..

[3] Corbae, D. and S. Ouliaris (1986), "Robust Tests for Unit Roots in the Foreign Exchange Market", Economics Letters 23, 375-380.

[4] Corbae, D. and S. Ouliaris (1988), "Cointegration and Tests of Purchasing Power Perity", Review of Economics and Statistics 70, 508-511.

28

[5] Dickey, D. A. and W. A. Fuller (1981), "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root", Econometrica, 49, 1057-1072.

[6] Edison, H. J. (1985), "Purchasing Power Parity: A Quantitative

Reassessment of the 1920s Experience", Journal of International Money and Finance 4, 361-372.

[7] Edison, H. J. and J. T. Klovland (1987), "A Quantitative Reassessment of the Purchasing Power Parity Hypothesis: Some Evidence on Norway and the United Kingdom", Journal of Applied Econometrics 2, 309-334.

[8} Engle, R. and C. Granger (1987), "Co-Integration and Error Correction: Representation, Estimation, and Testing", Econometrica 55, 251-276.

[9] Engle, R. and B. S. Yoo (1987), "Forecasting and testing in co-integrated systems", Journal of Econometrics, 35, No. 1, 143-160.

[10} Fuller, W. A. (1976), Introduction to Statistical Time Series, New York: John Wiley and Sons, 373.

[11] Giavazzi, F. and A. Giovannini (1985) "The EMS and the Dollar", Economic Policy 2, 455-473.

[12] Giavazzi, F. and M. Pagano (1987), “The Advantage of Tying One’s Hands: EMS Discipline and Central Bank Credibility", forthcoming European Economic Review.

[13] Grabbe, J. 0. (1986) International Financial Markets, Elsevier: New York.

[14] Huizinga, J. (1986) "An Empirical Investigation of the Long Run Behavior of Real Exchange Rates", unpublished manuscript, the University of Chicago.

[15] Kaminsky, G. (1987) "The Real Exchange Rate in the Short and in the Long Run", unpublished manuscript, the University of California at San Diego.

[16] Levich, R. M. (1985), Empirical Studies of Exchange Rates: Price Behavior, Rate Determination and Market Efficiency", in Handbook of

International Economics: Volume 2 (R. W. Jones and P. B. Kenen, eds.), Amsterdam: North Holland, 980-1040.

[17] Mark, N. (1986), "Real and Nominal Exchange Rates in the Long Run: An Empirical Investigation", unpublished manuscript, the Ohio State University.

[18] Meese, R. and K. Singleton (1982), "On Unit Roots and the Empirical Modeling of Exchange Rates", Journal of Finance, 37, 1029-1035.

[19] Meese, R. and K. Rogoff (1983), "Empirical Exchange Rate Models of the

1970's: Do They Fit out of Sample?", Journal of International Economics 14, 3- 24.

[20] Patel, J. (1986), "Tests of Purchasing Power Parity as a Long-Run Relation", unpublished manuscript, Harvard University.

29

[21] Park, J. (1988), "Testing for Unit Roots in Models of Structural Change", Center for Analytic Economics Working Paper # 88-10, Cornell University.

[22] Park, J. and B. Choi (1988), "A New Approach to Testing for a Unit Root", Center for Analytical Economics Working Paper #88-23, Cornell University.

[23] Park, J., Ouliaris, S. and B. Choi, "Spurious Regressions and Tests for

Co-integration", Center for Analytic Economics Working Paper #88-07, Cornell University. a

{24] Perion, P. (1987), "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis", Centre de recherche et developpement en economique, Universite de Montreal.

[25] Phil.lips, P. (1987), "Time Series Regression with a Unit Root", Econometi7ica 55, 277-302.

[26] Phillips, P. and P. Perron (1988), "Testing for a unit root in times series regression", Biometrika 75, 335-46.

[27] Rogoff, K. (1985), "Can Exchange Rate Predictability be Achieved without

Monetary Convergence: Evidence from the EMS", European Economic Review 8, 93- 115.

[28] Stock, J. (1987), "The Consistency of Least Squares Estimators in Error Correction Models", Econometrica 55, 1035-1056.

[29] Ungerer, H., 0. Evans, T. Mayer, and P. Young (1986), "The European

Monetary System: Recent Developments", International Monetary Fund Occasional Paper 48.

30

Figure 1: Logarithms of the Nominal Exchange Rates

The next five pages present graphs of the fifteen bilateral nominal exchange rate indices; the series have been normalized so that their initial values are zero. The set of countries is given by (Belgium, France, Germany, Italy, Netherlands, United Kingdom} and it is identified with {1,2,3,4,5,6}.

A currency eri_j is quoted in units of currency j necessary to obtain a unit of currency i. Hence an upward movement in the graph represents a devaluation of the j-th currency.

0.0 :

74°73 76 77:78 79 80 81 82 TT

74. 75 76 77 78 79 80 81 982 83.84 85 8 FRI oY —

30c

74°75 76 77 78 79 80 81 82 8

10. -10. ~30. -30.

-70 —

-2 x1 Q 75 #77 °279°~«2=81 83. & 87

ws

74.75 76 77 78 79 80 81 82 8

oOo nM LC MD wo oO NN L

74.75 76 77 78 73 60 81 82 aT

g . “,

‘a J VW 753 77 73 8 1 83 <i —

|

74°75 76 77 78 79 80 81 82 83 6 87 ,

4 2 ER3 6 —_

- 4. -1.0- -1 2. -] 4.

31 Logarithms of the Consumer Price Indices

The next page presents a graph of the consumer price inclices. They have been normalized so that their initial values are zero.

3la

“es MTT ds —— ST SS x LIIddJ Q 4JIVIdg H4IIdJ ° JgIdJ

>

a

Ct.

£98 98 S8 h8 £8 ¢8 T8 OS 64 82 LL 9£ S4 4h rrereereerr rrr re rer ere eee ee er ee FP

L

=

CN

32

Figure 3: Logarithms of the Real Exchange Rates

The next five pages present graphs of the fifteen bilateral real exchange rate indices; the series have been normalized so that their initial values are zero. The set of countries is given by (Belgium, France, Germany, Italy, Netherlands, United Kingdom} and it is identified with (1,2,3,4,5,6}. A currency rlxi_j is quoted in units of currency j necessary to obtain a unit of currency i. Hence an upward movement in the graph represents a real devaluation of the j-th currency.

75 77 73 8 1 83

s 87 ALX | —

- | OURS poo

- 94

74.75 76 77 78 79 80 81 82 a 7 “4 - 2 RLX1 4 =

75 77 73 8 1 Sore”

73 77 73 8 1 83 85 &7

[RALxX2 3 _—

24 xl1Q<

75 77 73 81 83 s s

20. -

73 77 79 81 83 she &7 ALX2 —

30.

20.

-30

50 xLQ72

32d

\AIY i nti 75 77 #79 ~~ 81 93 more SE] Lor 75. #77 +279 ~«€8!1 93 g 87 | X3 5 — | | Ne \ fe I ; _ 75 77 +279 ~~ «8! 83 Z RLX — |

x10 72

xL072

75 77 73 8 1 83 87

IFDP NUMBER

339

338

337

336

335

334

333

332

331

330

329

328

327

- 33 -

International Finance Discussion Papers

TITLES 1989

A Long-Run View of the European Monetary System

1988

The Forward Exchange Rate Bias: Explanation

A New

Adequacy of International Transactions and Position Data for Policy Coordination

Nominal Interest Rate Pegging Under Alternative Expectations Hypotheses

The Dynamics of Uncertainty or The Uncertainty of Dynamics: Stochastic J-Curves

Devaluation, Exchange Controls, and Black Markets for Foreign Exchange in Developing Countries

aan International Banking Facilities Panic, Liquidity and the Lender of Last Resort: A Strategic Analysis Real Interest Rates During the Disinflation Process in Developing

Countries

International Comparisons of Labor Costs in Manufacturing

Interactions Between Domestic and Foreign Investment

The Timing of Consumer Arrivals in Edgeworth's Duopoly Model

Competition by Choice

AUTHOR(s)

Hali J. Edison Eric Fisher

Ross Levine Lois Stekler Joseph E. Gagnon

Dale W. Henderson

Jaime Marquez

Steven B. Kamin

Sydney J. Key Henry S. Terrell

R. Glen Donaldson

Steven B. Kamin David F. Spigelman

Peter Hooper Kathryn A. Larin

Guy V.G. Stevens Robert E. Lipsey

Mare Dudey

Mare Dudey

Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the

Federal Reserve System, Washington, D.C.

20551.