## 1. Introduction

Recently there's been a revival appealing in modelling the long-run behaviour of nominal bilateral exchange rates using 'fundamentals' such as relative prices. In general, this type of research has generated that for the recent floating period weak-form purchasing vitality parity (PPP) would seem to be to hold on a single money basis, but strong-form PPP does not. Additionally, the adjustment to equilibrium in PPP-based equations is painfully slow. In order to obtain strong-form PPP results, and relatively immediate adjustment, analysts have used long runs of historical time series data or -panel data sets described for the recent float.

However, it is still appealing, from both an academics and a policy perspective, to explain sensible long-run romantic relationships for an individual currency only using recent floating data. The main element to resolving the failing of strong-form PPP is based on understanding the causes that keep a nominal exchange rate from a PPP equilibrium. Absolutely, an element on this is related to the rigidity of prices when confronted with nominal shocks, while the remainder reflects the impact of real disturbances. MacDonald and Marsh (1997) have exhibited that proxying such real and nominal disturbances using rates of interest produces sensible PPP-based equilibrium exchange rates and also impressive out-of-sample forecasts. The target in today's paper may be seen as an attempt to specify the real factors proxied in the MacDonald and Marsh paper and to empirically model their impact on the equilibrium effect exchange rates of the united states dollar, German euro and Japanese yen over the period 1975, quarter 1 to 1993, one fourth 2.

There have been lots of previous attempts at modelling equilibrium real exchange rates for the recent floating period and such work has not proved particularly successful. For example, modelling exercises designed to use single currency data fail to establish a significant long-run hyperlink between real exchange rates and fundamentals, such as real interest differentials. Given the rather negative conclusions to stem out of this 'behavioural' books, can another study of this kind of modelling be justified? We imagine it can. One key concept to result from the literature on modelling nominal exchange rates would be that the econometric methods used, and also the model specs, can have an essential bearing on the conclusions of significant and sensible long-run connections for one currencies. In this particular newspaper we use the technique of Johansen (1988) and Johansen (1991) and article evidence of sensible and significant long-run connections. A nice-looking feature of this econometric method is so it also facilitates computing the short-run strong behaviour in our chosen exchange rates. Although this is a second objective of the work it is, nevertheless, appealing to look at how an exchange rate comes back to its equilibrium value after having a disturbance and also to pitch our active models against the random walk paradigm.

In conditions of the insurance plan question regarding equilibrium real exchange rates, much talk has centered on the idea of a simple equilibrium exchange rate (FEER), an explicitly normative strategy which offers an attractive thought process about the advancement of genuine and equilibrium real exchange rates. However, even though FEER theory has lots of attractive features, the primary difficulty associated with it is one of tractability in conditions of the need to have a completely given multilateral structural model and, further, it generally does not offer an empirical hyperlink between a real exchange rate and its determinants. An integral appeal of behavioural time series options for analysing single money real exchange rates is the relative ease with which they may be computed and the actual fact that they actually explain the links with the underlying fundamental determinants.

The outline of the rest of this paper is as follows. In the next section we use a decomposition of the real exchange rate which helps a conversation of the factors adding systematic trends in to the behavior of the equilibrium real exchange rate. These factors are identified in Section 3, and are labelled the fundamentals exclusive of real rates of interest (FERID); they include parameters such as online foreign asset deposition, output bias and fiscal balances. Using the true uncovered interest parity condition we continue, in Section 4, to define a static marriage for the existing equilibrium exchange rate in terms of the FERID parameters and the true interest differential (RID). We propose operationalising this model by using a vector error correction platform. In Section 5 our data resources receive and the building of the proxies for our parameters, introduced in Section 4, described. Our quotes of the long-run exchange rate associations and short-run active results are shown as well. The newspaper closes with a concluding section.

## 2. A real exchange rate decomposition

(1)Image

(2)Image

where superscript T indicates that the variable is defined for bought and sold goods. If the prices in Eq. 2 are composite conditions then, as we will emphasise below, for Imageto be regular we must assume that all of the products prices which gets into Imagehas an comparable counterpart in Image, and the weights used to create each one of these composite prices will be the same. 7

(3)Image (3†)Image

(4) Image

Eq. 4 is illuminating since it shows three possibly important sources of long-run real exchange rate variability: non-constancy of the true exchange rate for traded goods, that will occur if the kinds of goods stepping into international trade are imperfect substitutes and there are factors (discussed below) which expose systematic variability into Image; actions in the relative prices of exchanged to non-traded goods between the home and foreign country, due to say productivity differentials in the traded goods sectors; differing time-variability of the weights used to construct the overall prices in the home and foreign country. We do not consider the second option opportunity in this paper. Let us consider the other resources of variability in a little more detail.

## 3 Resources of trends in the long-run real exchange rate

## 3. 1. The traded non-traded price 'ratio'

The first group of factors we consider relate with the relative price of traded to non-traded goods across countries, captured in Eq. 4 by the word Image. One way of interpreting this term is to think of it as capturing factors which impinge on the relative price of non-traded goods, without necessarily affecting the comparative price of traded goods.

## 3. 1. 1. Balassa-Samuelson

Perhaps the best known source of organized changes in the relative price of exchanged to non-traded goods is the Balassa-Samuelson effect. This presupposes that the nominal exchange rate steps to ensure the comparative price of traded goods is constant over time; that is, Image. Productivity dissimilarities in the development of exchanged goods across countries can add a bias in to the overall real exchange rate because production advances have a tendency to be focused in the bought and sold goods sector; the likelihood of such advances in the non-traded sector is bound. If the costs of bought and sold and non-traded products are associated with wages, wages linked to output and wages associated across non-traded and traded sectors, then the relative price of exchanged goods will surge less rapidly over time for a country with relatively high output in the tradeable sector: the true exchange rate, identified using overall price indices, appreciates for fast growing countries, even though the law of 1 price supports for traded goods; in conditions of Eq. 4, if the home country is a comparatively fast growing country it has a good Imageterm, thereby pushing Image, above Image (keep in mind the currency is defined here as the forex price of a device of home money).

## 3. 1. 2. The demand part and non-traded goods

The lifestyle of non-traded goods may allow a demand part bias which pushes an exchange rate from its PPP level identified using traded goods prices. Assuming unbiased productivity growth, Genberg (1978) has demonstrated that if the income elasticity of demand for non-traded goods is greater than unity, the comparative price of non-traded goods will go up as income goes up (that is, as income goes up homeowners will spend a disproportionate amount of the income on services). This comparative price change will be strengthened if, as seems likely, the share of government expenses devoted to non-traded goods is greater than the share of private expenses, in case income is redistributed to the federal government over time.

(5)Image

where PROD is a measure of production bias and DEM represents demand side bias. For the reason why noted above, a growth in the home value of either of these parameters will, cetirus paribus, make an understanding of the entire real exchange rate.

## 3. 2. Imperfect substitutability of traded goods prices

The factors within the last section make a difference the real exchange rate even if exchanged goods are perfect substitutes across countries and Imageis constant. The constancy of the real exchange rate defined regarding traded prices is not, however, uncontroversial. For instance, there is currently considerable information to suggest that the varieties of goods produced by industrial countries aren't perfect substitutes, and then the idea that price differences are quickly arbitraged away is totally unrealistic. We have now turn for some of the factors which might introduce organized variability into Image.

## 3. 2. 1. National personal savings and investment and the real exchange rate

The comparative price of bought and sold goods, Image, is a major determinant of the products and non-factor services element of the current bill. The current bill, subsequently, is influenced by the determinants of national savings and investment, and since one key element of national cost savings is the fiscal balance, it practices that the fiscal balance is a determinant of the Imagecomponent of the REER. Original interest in the partnership between the federal fiscal deficit and the true exchange rate was activated by the Reagen test in the 1980s and, recently, by the desire on the part of the Clinton supervision for fiscal consolidation. The result of fiscal coverage on the true exchange rate may be talked about by requesting the question: will fiscal consolidation strengthen or weaken the exterior value of any currency?

Both outcomes are in fact potentially appropriate - it just depends on which particular view of the world is used. In the traditional Mundell-Fleming two countries model, a tightening of fiscal policy, which heightens a country's nationwide savings, would lower the local real interest rate and generate a (everlasting) real money depreciation which, in turn, would create a permanent current accounts surplus. The true money depreciation would also arise in flexible price models. Whatever we are picking up in all these models is the 'crowding in' effect of the exchange rate depreciation; the necessity for aggregate demand to similar aggregate supply makes this result irrespective of the school of model.

The basic Mundell-Fleming model, however, ignores the consequences of the stock-flow implications of the original current bill imbalance. Models which account for the stock implications of the original fiscal tightening are portfolio balance models and the asset market/balance of obligations synthesis model. Within the context of this category of model, the long-run is defined as a point at which the current consideration is well balanced or, to put it marginally differently, any interest revenue on net foreign belongings are offset by way of a equivalent trade imbalance. Hence, if the fiscal consolidation is long term, it'll imply a long term increase in online foreign investments and an understanding of the long-run real exchange rate. Other costs effects can be analysed in a similar fashion.

In conditions of national cost savings and investment, the other key determinant of the Imagecomponent of the REER is private sector net savings. It is assumed that such personal savings are relatively regular over time. This seems a sensibly practical working assumption for the US, but is most likely less so for a country like Japan. Given that there were secular moves in the Japanese personal savings rate for the post-war period, the self-employed effect of this online foreign asset position shouldn't be discounted. More generally, Masson et al. (1993) note: "demographic parameters that reflect the age structure of the populace seem to make a difference determinants of the cross-country variations of conserving rates and therefore should affect world wide web foreign advantage positions".

## 3. 2. 2. The true price of oil

Changes in the real price of engine oil can likewise have an effect on the equilibrium real exchange rate, usually through their effect on the terms of trade. The importance of this variable was outlined by the dramatic increases in the true price of petrol in the 1970s (for example, in the early 1970s the true price of olive oil rose by roughly 65%) and the evenly dramatic fall season in the mid-1980s (by roughly 50%). In assessing a country that is self-sufficient in oil with one that requires to transfer oil, the past, ceteris paribus, would show an appreciation as the price tag on oil rose in terms of the other country. More generally, countries that have at least some oil resources could find their currencies appreciating in accordance with countries which don't have petrol resources.

(6)Image

where FISC catches the effect of relative fiscal amounts on the equilibrium real exchange rate, PS signifies private sector savings and ROIL is the real price of petrol. The indicators above the parameters summarise the long-run effects of these factors on the true exchange rate.

(7)Image

In the next section we detail how Eq. 7 may be operationalised.

## 4. The modification of the real exchange rate to static equilibrium and econometric methods

(8)Image

(9)Image

(9†)Image

In our model, therefore, the genuine equilibrium exchange rate given by Eq. 9† comprises two components: the first component, Image, powered by the fundamentals exclusive of the true interest differential (FERID) talked about in the last section, and the true interest differential (RID). The equilibrium condition represented by Eq. 9 is static and it is unlikely to hold continually. How then will the genuine rate adapt to the rate distributed by Eq. 9?

(10)Image

where ‹· can be an (n-1) vector of deterministic parameters, and var epsilonis an (n-1) vector of white sound disturbances, with mean zero and covariance matrix ‹. Appearance (10) may be reparameterised into the vector error correction device (VECM) as:

(11)Image

where ‹ denotes the first difference operator, ‹i is an (n-n) coefficient matrix (equal to Image) is an (n-n) matrix (equal to Image) whose ranking determines the amount of cointegrating vectors. If ‹ is of either full get ranking, n, or zero get ranking, ‹ =0, there will be no cointegration amidst the elements in the long-run relationship (in these cases it'll be appropriate to estimate the model in, respectively, levels or first distinctions). If, however, ‹ is of reduced rank, r (where r

(12)Image

(13)Image

(12†)Image(13†)Image

Although an study of long-run exchange connections is instructive, it can nevertheless be difficult since an interpretation of the coefficients in the long-run relationship as, say, elasticities is dependant on the (often implicit) ceteris paribus assumption a unit shock doesn't have an impact on the other variables as well. For example, a fiscal great shock will likely have an effect on the true interest differential as well as perhaps also NFA (if it alters private sector savings). Since such interrelationships are summarised in our VAR model, we might use this to get a feel for these romantic relationships. To get this done, we use an impulse response representation of the VAR. This approach gets the more general benefit of illustrating the short-run active responses of the group of three exchange rates with regards to the fundamentals.

(14)Image

where, of the terms not previously identified, ‹0=In and the infinite sum is thought as the limit mean square. This relationship may then be utilized to examine the result of shocks, as represented by the white noise disturbances, var epsilont, on the elements of the xt vector. However, a common problem with this is that since the covariance matrix ‹var epsilon is improbable to be diagonal, it is difficult to interpret the effects of a particular great shock on, say, the exchange rate. This is because the great shock will in all probability have a contemporaneous influence on other shocks which, in turn, will have an impact on the exchange rate, making it impossible to unravel the only real influence of the initial shock. A typical way of working with this problem is to use the MA representation with orthogonalised innovations. That is:

(15)Image

where the the different parts of are uncorrelated and a matrix P is chosen so that ‹ has device variance [that is, Image]. The matrix P can be any solution of PP '1=‹var epsilon as well as perhaps typically the most popular assumption is the fact that P is chosen, by using a Choleski factorisation, as a lower triangular non-singular matrix with positive diagonal elements; other decompositions, such as the 'structural' decompositions of Bernanke (1986) and Blanchard and Quah (1989), also exist. Within the (firm) case the ‹i converge to zero as i ' and ‹x(h) converges to the covariance matrix of xt as h ' ; however, this will not necessarily occur regarding unstable, included or cointegrated VAR processes. Nevertheless, even for such procedures it continues to be possible, as shown by Lutkepohl (1993), to construct ‹i and ‹i. In this newspaper we follow the strategy of Hendry and Mizon (1993), that involves reparameterising the problem correction element of the VECM and then proceeding with the standard Choleski factorisation.

## 5. Data options and definitions

We attempted two procedures of the real effective exchange rate. The first, LREER, is the multilateral CPI-based real effective exchange rate for the domestic country in accordance with its G7 spouse countries, portrayed in logarithms. The second, LREER1, is the same ULC-based real effective exchange rate. We use a number of FERID variables to capture the influence of the fundamentals mentioned in Section 3. We experiment with two variables to proxy for PROD. The first, LTNT, is the ratio of the local consumer price index to the wholesale price index in accordance with the equivalent overseas (trade weighted) ratio, indicated in logarithms. The second is LPROD, made of rates of development in real output in processing at home relative to the trade weighted foreign equivalent. We take the result of fiscal deficits using the word FBAL, which is the home fiscal balance as a percentage of GDP relative to the weighted sum of the partner countries (where the weights are those used to construct the effective exchange rates). NFA is the ratio of the local country's net international asset position to GDP and will also capture the effect of fiscal insurance policy on the real exchange rate, but also other factors more directly associated with private sector cost savings, such as demographics.

Two variables are being used to capture the result of commodity shocks. The conditions of trade, LTOT, are built as the ratio of home export unit value to import product value as a percentage of the equivalent effective foreign percentage, portrayed in logarithms. ROIL is the real price of oil thought as the percentage of the nominal price of oil to the local country's inexpensive price index, again expressed in logarithms. Finally, we use two comparative real interest terms: RRL, which is the long-term real interest differential constructed using the local 10 year nominal relationship yield minus a focused 12 1 / 4 moving average of the inflation rate without the equivalent overseas effective; and RRS, which is the same short-term differential, where three month treasury bill rates and a centered four 1 / 4 moving average were used (we also experiment with unconstrained interest rates). The effect of all of these factors on the static equilibrium exchange rate [Eq. 9] is summarised in:

(16)Image

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## 5. 1. Long-run connections: the lock between real exchange rates and real interest rates

(17)Image

Eq. 17 may be derived from Eq. 9† by presuming Image, a continuing; we allow real rates of interest be unconstrained in our estimation and it is expected that ‹†1>0 and ‹†2<0; we test the symmetry limitation that estimated coefficients are of similar and opposite signals. Utilize the Engle-Granger two-step cointegration method to estimate Eq. 17, for a variety of currencies and time periods, and find no proof a long-run romance. One reason for this may simply lie in the econometric strategy used to estimate Eq. 17. Thus, Banerjee et al. (1986) have observed that the tiny sample properties of the Engle-Granger method are poor. On top of that, if the regressors in Eq. 17 are endogenous and (or) the mistakes exhibit serial correlation, then your asymptotic circulation of the coefficients will depend on nuisance parameters. Researchers have exhibited that, in screening equilibrium human relationships for the nominal exchange rate, econometric methods robust to simultaneity bias and potential endogeneity can make a big change to the results. Is the same true in today's application? We estimate Eq. 17 using the techniques mentioned in Section 4. These methods should produce asymptotically optimal quotes because they incorporate a parametric modification for serial correlation (which originates from the underlying VAR structure) and the systems characteristics of the estimator means the estimates should be solid to simultaneity bias.

Our results from Eq. 17 using, on the other hand, brief and long rates are reported in Table 1 and Table 2, respectively.

Table 1. Real exchange rates and real short-term interest rates

Image

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Table 2. Real exchange rates and real long term interest rates

Image

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In Desk 1, the LB, LM and NM statistics are multivariate residual diagnostic lab tests: LB is Hoskings multivariate Ljung-Box statistic, LM(1 and 4) are multivariate Godfrey (1988) LM-type reports for first and fourth order autocorrelation, and NM(6) is a Doornik and Hansen (1994) multivariate normality test. Reported quantities are p-values and point out, generally, an absence of serial relationship, although there is some evidence of non-normality in the Japanese yen and US dollars systems. In terms of the coefficients of perseverance, the explanatory electric power ranges from 0. 16 for the dollars to 0. 36 for the euro.

In Stand 2 an identical group of results as those portrayed in Table 1 is offered for real exchange rates and real long-term interest levels. The picture here's broadly similar to that reported in Table 1. There exists again proof significant long-run romantic relationships for everyone three currencies, interest coefficients are generally correctly authorized (in addition to the coefficient on the international rate in the Japenese equation).

In amount, then, what is perhaps the simplest real exchange rate model will not do too terribly in accordance with the metric set by other experts, and also in terms of producing statistically significant long-run interactions which, in turn, produce dynamic equations that make clear a reasonable percentage of the in-sample performance associated with an exchange rate change.

## 5. 2. Long-run romantic relationships: a non-constant real equilibrium exchange rate

For the overall exchange rate model where the equilibrium real exchange rate, Image, is time dependent and assumed to be always a function of the parameters within the vector FERID. As regarding the simplest model, we attempted both short and long interest levels. The ‹»Potential and Trace statistics for the systems comprising brief and long interest levels, respectively. On the basis of the standard set of significance worth (that is, the principles unadjusted for small sample bias), there is very strong evidence of cointegration for everyone three currencies, regardless of the interest rate solution. For both buck and yen systems we've let the interest rate conditions be unconstrained. This is founded partly on the pretesting noted in Table 1 and Desk 2 and also on the actual fact that the interactions with the unconstrained interest levels produced the more desirable cointegrating vectors. We've therefore fine-tuned the Trace and ‹»Maximum figures using the Reimers (1992) small sample correction, reported in the columns labeled T 'np. With these changed statistics the picture changes - there is now one statistically significant vector for every single money. We therefore proceed based on one significant cointegrating vector for every of the currencies.

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Estimates of the cointegrating vectors from the largest eigenvalues for every single system for both short and long rates. Each of the vectors has been normalised on the exchange rate (that is, the LREER has a coefficient of '1, therefore the coefficients are written in equation format). Across all of the exchange rate combinations there's a very good reach record in terms of correctly signed coefficients. Thus, basically six out of 46 are appropriately agreed upon and of plausible magnitude. The magnitude of coefficients is around comparable across the two sets of systems, although there are a few sign changes: real rates for the Japanese yen are effectively agreed upon in the short rate system but incorrectly agreed upon in the long rate system. Observe that the coefficient on FBAL has an indicator constant with a stock-flow model for Japan and the US but a 'traditional' Mundell-Fleming signal for the euro. In utter conditions the fiscal balance is also more very important to the euro. The Balassa-Samuelson impact, proxied here by the LTNT variables, enters all of the equations with relatively large coefficients, and signifies a more than proportional response of the true exchange rate in four from the six conditions.

Of course, this type of discourse begs the question of whether the actual data basics used here to establish the long-run equilibrium were calibrated at sustainable levels throughout the test. For example, it may be that the fiscal stance of the united states in the early 1980s was not the most likely and therefore you need to recalibrate the equilibrium exchange rate using prices of the comparative fiscal position which more directly mirror sustainable prices.

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## 5. 3. Short-run dynamics and the random walk

Ever since the seminal newspaper by Meese and Rogoff (1983), the benchmark where a fundamentals-based exchange rate model is evaluated is in comparison to a simple random walk. Even as noted previous, such comparisons havent favoured real exchange rate models. Although we do not assume that beating a random walk should be the last phrase on the performance of your exchange rate model, in particular when the primary aim of that model is to find something about the longer-run trends in trade rates, we, nevertheless, thought it advantageous to subject matter our models to a random walk horse competition. This seems useful since there exists evidence that whenever the types of dynamic mistake modification models utilised in this newspaper are being used to calculate nominal exchange rate models these models have the ability to beat a random walk at 'short' horizons, which is taken to be a period of less that thirty six months.

## 5. 4. Short-run dynamics: impulse response functions

The impulse response of the logarithmic change of the real effective exchange rates in our three long interest rate systems (the qualitative picture from the brief rate systems is similar) are analysed with respect to orthogonalised shocks in each one of the underlying fundamental factors. In each one of the information the impulse reactions are bounded by two standard mistake bands, determined using bootstrap methods. Specifically, these bands were made using the test standard deviation of the empirical distribution from a bootstrap simulation on the reduced form problems with 2000 replications. The adjustable buying in these systems is: FBAL, ROIL, NFA, LTNT, LTOT, RRS/L, LREER. The ordering is intended to reflect the comparative exogeneity of the series (FBAL most exogenous, LREER least exogenous). The overall tenor of the results within these figures would be that the short-run exchange rate dynamics in response to a distress are abundant, and the impact of your impact is often relatively long-lived.

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For example, regarding the US, a 1% rise in the house real interest rate produces a 1% exchange rate understanding by 1 / 4 2, the exchange rate then depreciating. Both the productivity and terms of trade shocks produce (positive) exchange rate overshoots in the first quarter. The net overseas asset shock ends in a less than proportionate appreciation of the real rate and the understanding is long-lived. The fiscal balance distress in the beginning produces an understanding of the exchange rate, although this is rather quickly reversed and there are a preponderance of negative changes after 1 / 4 2.

For Germany, there is no evidence of overshooting with respect to any of the variables and, in addition to the real interest shock and online foreign asset great shock, the time profiles for the exchange rate act like their US counterparts. Possibly the major difference between your US and Germany's systems is that in the last mentioned all the exchange rate changes are insignificantly different from zero by about quarter 16. The response of japan yen rate to the set of shocks is broadly like the German circumstance.

## 6. Brief summary and conclusions

In this paper we have re-examined the determinants of real exchange rates in a 'long-run' environment. We provided a style of the equilibrium exchange rate which presented productivity and terms of trade results, in addition to fiscal balances, net foreign assets and real interest levels, as key fundamental determinants. Our model was shown to produce significant and practical long-run connections for the true effective exchange rates of the euro, money and yen, and it looked much better suitable for describe the long-run developments in effective exchange rates than comparative prices. We also reported proof significant long-run interactions for a simplified version of our own model and we observed that such significance contrasted with almost every one of the extant research on this relationship.

Although our main emphasis in this newspaper was the long-run determinants of real exchange rates, it has become the acid test of the fundamentals-based exchange rate model that it should outperform a random walk model in conditions of having less root mean rectangular error. We found that our general real exchange rate model passed this test for every of the currencies. Generally, systems including long maturity interest rates did much better than systems with brief rates. The base-line real exchange rate model (that is the model with a constant equilibrium real exchange rate) did not achieve this task well in conditions of the forecasting criterion. The short-run behavior in our model was further analyzed by calculating impulse response functions for real exchange rates regarding orthogonalised shocks inside our fundamental variables. The impulse response evaluation provided a set of results that have been intuitively plausible and statistically significant.

We believe our modelling exercises can be interpreted as indicating that basics do come with an important, and significant, bearing on the conviction of both long- and short-run exchange rates. One way in which our work could be extended would be to utilise the methods of this paper to decompose real exchange rate behaviour into both nominal and real components.

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