Misalignment, debt accumulation and fundamental equilibrium exchange rates.

Artis, Michael J. ; Taylor, Mark P.

Introduction

Our objective in this article is to investigate the effects of hysteresis - operating through shifting international net asset stocks during periods of misalignment - on the fundamental equilibrium exchange rate. Although our discussion relies in large part on analytical arguments, our aim is to provide practical guidelines which are of use in assessing situations of exchange-rate misalignment.

The concept of the equilibrium exchange rate is not unique. As noted by Frenkel and Goldstein (1986), there are at least three approaches to determining the equilibrium exchange rate - corresponding to structural exchange rate models such as the monetary model or the portfolio balance model of exchange rate determination, the purchasing power parity approach, and the 'underlying balance' approach.(1)

In this article, we are concerned with the underlying balance approach. According to this approach, the equilibrium exchange rate is defined as the real effective exchange rate that is consistent with medium-term internal and external macroeconomic balance.

The condition of internal macroeconomic balance can be identified with equilibrium employment and output, which would be typically taken to be the non-accelerating inflation rate unemployment level or NAIRU. External balance can be identified with current account balance or, in the presence of sustainable medium-term capital inflow or outflow, a corresponding deficit or surplus. In any case, the current account should incorporate the flow of debt service payments or receipts (and other investment income) corresponding to the underlying net foreign asset position of the economy. These definitions are explored further below.

The underlying balance approach to the equilibrium exchange rate was largely developed by staff at the International Monetary Fund during the early-1970s (see International Monetary Fund (1984)).(2) More recently, the equilibrium rate associated with underlying balance has been labeled the 'fundamental equilibrium exchange rate' (FEER) (Williamson (1985)). The FEER has been used as an analytical device by a number of authors to assess exchange rate misalignment (Williamson (1985, 1990), Barrell and Wren-Lewis (1989)), as well as in the context of discussions of 'blueprints' for international policy coordination (Williamson and Miller (1987)), Frenkel and Goldstein (1986), Currie and Wren-Lewis (1989), and in discussions of the 'appropriate level' at which to join a pegged exchange-rate system such as the European Monetary System (EMS) (Wren-Lewis, et al. (1991)).

This article addresses an issue concerning FEER computations which, although it has not been entirely overlooked in the literature, has been given relatively little attention, namely: how sensitive is the FEER to the path chosen for convergence towards it? A given FEER trajectory has associated with it a particular path for the current account and debt service flows; a deviation of the actual rate from the FEER immediately implies a different current account and correspondingly a change in debt service flows compared to the original. The level of the real exchange rate consistent with medium-term external balance must therefore change. Thus, the final FEER arrived at will not be independent of the path chosen towards it.

Where equilibrium values turn out to be dependent on the dynamic path of adjustment, the situation is generally termed one of 'hysteresis' (Cross (1992)). Contemporary economic analysis is turning up a number of instances in which it appears that hysteresis effects may be important; for example, in the determination of the NAIRU (Lindbeck and Snower (1986)), and in the analysis of trade responses to exchange-rate variation, taking account of the sunk costs of setting up in overseas markets (Baldwin and Krugman (1986)). For economists trained in the neoclassical tradition, hysteresis is a troublesome feature since its presence renders inapplicable the method of comparative statics upon which much of modern economic analysis is founded.(3) The implicit use of something at least approximating the comparative static method is common in analyses involving the FEER.

In the remainder of this article we evaluate the importance of hysteresis effects on the FEER as they arise through the debt service consequences of misalignment.(4) That there are hysteresis effects of this kind is not in dispute; our aim is to provide a sense of their empirical significance. In particular, we provide broad rules of thumb by which to judge the importance of such effects for any given degree of perceived exchange-rate misalignment and desired period of monotonic adjustment towards the FEER.

We begin by discussing the issue of hysteresis in the FEER in more detail and by showing analytically that the FEER is not independent of the path chosen to achieve it. Then we derive our rules of thumb for assessing the importance of hysteresis effects for a given path of adjustment and set of initial conditions. In the following section we take - for purely illustrative purposes - estimates of the FEER for each of the G5 countries in 1990 provided by Williamson (1990), and analyse the importance of hysteresis effects assuming that the implied degree of misalignment is reduced to zero over either a five- or a ten-year period. A final section concludes.

Debt accumulation and misalignment

The FEER is defined as that value of the real exchange rate which will reconcile internal and external equilibrium 'in the medium term'. As already explained, external equilibrium is defined in terms of a desired value of the current account balance; this value may be non-zero if there is a presumption about a 'normal' rate of capital inflow or outflow. Otherwise a zero value seems a plausible objective, corresponding as it does to a constant level of net foreign assets.(5) Internal balance is usually defined as potential full employment output; in most computations (e.g., those of Williamson (1985, 1990)) this appears to be assumed to be independently computed and to be independent of the real exchange rate itself and we shall follow that tradition here. This is illustrated in Figure 1, the NAIRU schedule is drawn as a vertical line in real exchange rate (S) and capacity utilisation (u) space. In a very open economy, the NAIRU may be modelled as a function of the real exchange rate. An appreciation of the real exchange rate allows a higher real wage (markup of wages over prices) for a given rate of utilisation, since holding the current account constant in volume terms, the improvement in the terms of trade implies an increase in real revenues which may be passed on to workers. This view, which is represented analytically in the Layard-Nickell (1985) 'Battle of the Markups' view of inflation is reflected in the econometric modelling work of Wren-Lewis et al. (1991). In terms of the diagram, the NAIRU schedule would be positively sloped from left to right. The current account (CA) schedule is drawn for a given level of the current account balance and slopes down from left to right for well-known (net import propensity) reasons: as utilisation increases, (net) imports tend to rise, requiring a devaluation of the real exchange rate as an offset. The solution for [S.sup.*], [u.sup.*] gives the FEER and the internal balance or utilisation rate.(6)

For given assumed values of the target current account and internal balance, then, the corresponding 'fundamental equilibrium exchange rate' (FEER) can be computed. It should be clear that the FEER needs to be computed as a trajectory if there is evolution in the values of the current account and internal balance targets, (or predictable change in the structure of the economy for given values of those targets), even if we set on one side all issues of hysteresis. (An example of a step change in an otherwise flat FEER trajectory is introduced below.)

It is easy to see from considering Figure 1 how hysteresis in the FEER can arise. Suppose that the actual exchange rate happens to correspond initially to its FEER value and that internal balance is at the optimal level - in other words, that there is no problem of the starting point or transition period. In terms of the figure, we are at ([u.sup.*],[S.sup.*]). Now suppose that in the next period the actual real exchange rate departs from its FEER value - specifically that it appreciates - whilst utilisation remains at [u.sup.*]. The appreciation causes the current account to deteriorate relative to the initial equilibrium target positions, which is assumed to be zero.(7) Then the FEER calculation must be performed afresh. The deficit increases net foreign indebtedness and creates an obligation to service debt interest. Even disregarding any desire to rectify the increase in indebtedness, the obligation to service more debt must cause the CA schedule to move in to the left: the real exchange rate which would have been consistent with the current account target in the absence of the increased debt-service will now produce a deficit due to the increased debt-service obligation. More precisely, the trade account target has changed to provide a surplus sufficient to cover the increased debt service obligation. The current account target remains the same since debt service is incorporated in it, but the 'structure' of the economy has changed, forcing CA to shift inward.

The departure of the actual exchange rate from its FEER value (trajectory) thus forces a revision of the FEER. A 'hysteresis loop' (Cross (1992)) would ensue if the previous FEER were to be re-established. The exchange rate would need to 'overdepreciate' in order to reinstate the previous schedule [ILLUSTRATION FOR FIGURE 2 OMITTED]. A displacement of the actual real rate of exchange from its FEER value - say, to point A - involves a real appreciation and a current account deficit (relative to the current account balance underlying CA). This requires a re-evaluation of the CA schedule, to CA', and a devaluation of the FEER from [S.sup.*] to [S.sup.*]'. For the FEER to be re-established at [S.sup.*], an overdepreciation would be needed to reduce the stock of debt to the original level, resulting in the 'hysteresis loop' shown.(8)

How large a revision of the FEER is required as a result of misalignment? To derive an answer to this question, imagine again that starting from a favourable position, (i.e., where the current real exchange rate is at its FEER value and internal balance is realised), the current exchange rate departs from its FEER value by, say, x per cent. For concreteness, suppose this is an appreciation. Then a deficit in the current account will appear of x([Mu] + [Tau])X where [Mu] and [Tau] are, respectively, the import and export elasticities and X is the volume of exports (or imports - we suppose the two to be approximately initially equal). If this is a one-off deviation of 'one-year' duration, then the FEER will have to be devalued to the extent necessary to service the additional debt incurred. It is convenient to assume that the FEER adjustment depends on the same elasticities,(9) but the adjustment need only be large enough to service the cost of the debt incurred; then it is easy to see that, if the interest rate is r, the adjustment required is [Delta] = rx. (The FEER devaluation, [Delta], must yield rx([Mu] + [Tau])X to cover the debt service, or [Delta]([Mu] + [Tau])X = rx([Mu] + [Tau])X.) If the deviation is sustained for two 'years', the total adjustment required will be twice as large. Thus, each initial x per cent deviation of the actual from the fundamental equilibrium exchange rate will require a FEER adjustment of rx per cent in the opposite direction if FEERs are adjusted annually.(10)

Notice that this makes no allowance for what might logically be seen as the need to reverse the increment in debt acquired in this example through the appreciation of the current exchange rate over its FEER value. The reason this might seem logical is that the FEER external balance criterion is typically for a zero net foreign asset accumulation (or for a particular baseline growth in net foreign assets). Thus, an event that causes a departure from this initial desired condition should lead to an action calculated to offset it. In this case every x per cent appreciation of the actual rate over its FEER value should lead to a reduction big enough to pay back the debt over a defined period of time. The size of hysteresis effects will clearly be potentially much larger if the FEER adjustment is required to be big enough to repay the debt incurred rather than simply to service the additional interest obligation. In what follows, however, we calculate FEER adjustments on the more modest of the two possible criteria, looking therefore for a FEER adjustment sufficient only to cover the cost of the additional interest burdens arising from misalignment. This case is clearly the most conservative one to take and sets a natural 'lower band' to the size of the hysteresis problem. Had we chosen to assume that debt repayment objectives were involved, we should also have been obliged to specify - quite arbitrarily - the speed with which debt repayments were to occur. We now proceed to derive a formula for the FEER adjustment process. The result expresses formally the hysteresis effect - the dependence of the FEER on the path of the actual exchange rate.

Suppose that initially, in year 0, the actual real exchange rate is at its FEER value, which has a flat (stationary) trajectory at that point in time. Internal balance is assumed to be maintained at its optimal level throughout. Then any deviation of the actual rate from the FEER value implies a deviation from current account balance and requires a recomputation of the FEER on the lines indicated above.

Approximately, then:

[F.sub.n] = [F.sub.n-1] - r([S.sub.n-1] - [F.sub.n-1]) (1)

or

[F.sub.n] = (1 + r) [F.sub.n-1] - r[S.sub.n-1] (2)

where [F.sub.n] is the logarithmic value of the FEER in year n, [S.sub.n] is the logarithm of the actual exchange rate in year n, and r is the rate of interest.

Equation (2) implies that

[F.sub.n-1] = (1 + r)[F.sub.n-2] - r[s.sub.n-2] (3)

[F.sub.n-2] = (1 + r)[F.sub.n-3] - r[s.sub.n-3] (4)

Recursive substitution (of (4) and (3) into (2) etc.,) yields

[F.sub.n] = [(1+r).sup.n][F.sub.0] - r [summation of] [(1+r).sup.i-1][S.sub.n-i] where i = 1 to n (5)

Equation (5) shows how the initial stationary trajectory for F, [F.sub.0], will require updating in the light of the evolution of the actual real exchange rate. Thus, the FEER is not independent of the history of exchange-rate movements. In particular, if the authorities wished to move the current exchange rate to the FEER, at the end of n periods, they would need to choose a path for the real exchange rate ([S.sub.1], [S.sub.2] ... [S.sub.n]) such that [S.sub.n] = [F.sub.n] with [F.sub.n] as defined in (5). Thus, given a deviation of the actual rate from the FEER and a desire ultimately to equate the two, the FEER arrived at when the actual rate again coincides with it will not be independent of the path taken by the exchange rate towards this goal. Indeed, as equation (1) makes clear, if S deviates from F, F will actually move away from S at speed r per period. Intuitively, therefore, we should expect eventual convergence of F and S to require a movement of S towards F at a speed greater than r in the following period. In Artis and Taylor (1995), we demonstrate that this intuition turns out to be correct when we analyse the dynamics of adjustment more formally.(11)

Assessing the importance of hysteresis effects: rules of thumb

In Artis and Taylor (1995), we examine how important hysteresis effects may have been in the past by performing some illustrative exercises with respect to actual exchange rates over the period 1979-90. Overall, the results of this exercise demonstrate that hysteresis effects on the FEER, operating through the effects of debt accumulation or decumulation, may have been significant historically, particularly for countries whose real exchange rate has moved predominantly in one direction over a sustained period of time. For the US dollar during the 1980s, for example, we estimate that hysteresis effects of the kind outlined above may have generated a deviation of the actual real effective exchange rate from the FEER of as much as 14 per cent.

In this section, we seek to answer the following question: given an initial misalignment of the exchange rate, and a desire to correct the misalignment over a certain finite period, by how much does the required movement in the exchange rate differ from the initial misalignment? For example, suppose that the exchange rate is undervalued according to its value relative to the FEER, and that it is desired to correct this over a period of, say, five years. Assuming that the desired adjustment is monotonic (e.g., a constant percentage annual appreciation), then, by our arguments, the FEER at the end of the fifth year, when the misalignment is zero, will be higher than the initial calculated FEER. Thus, the total required movement in the exchange rate will be greater than the initial difference between the exchange rate and the FEER. The additional movement in the exchange rate over the five-year period (over the initial misalignment measure) is thus, in some sense, a measure of the importance of hysteresis effects arising during misalignment.

If the rate of capacity utilisation is held constant at 100 per cent, then the overall movement in the FEER will be equal to the cumulative misalignment each period multiplied by the interest rate.

Tables 1 and 2 give some illustrative examples of movements in the FEER, assuming an interest rate of 5 per cent, initial undervaluation or overvaluation of 10 or 20 per cent, and a constant annual percentage change in the exchange rate. These trajectories are essentially found by fine-tuning the annual percentage change in the exchange rate to find [S.sub.n] = [F.sub.n] (n = 5, 10) with [F.sub.n] as given in (5), for given [F.sub.0] and [S.sub.0].(12)

Consider first the results assuming five-year convergence (Table 1). These show that the effect of a changing net asset stock (due to misalignment) is to increase the total amount of required exchange-rate adjustment by some 1.5 percentage points for an initial 10 per cent misalignment, and by about 3 percentage points for an [TABULAR DATA FOR TABLE 1 OMITTED] initial 20 per cent misalignment. Note that the revision due to debt accumulation or decumulation is greater in the case of undervaluation, since the initial exchange rate on which the percentage is calculated is at a depressed level.

If the desired period of convergence is increased to ten years (Table 2), then the revisions increase to approximately 3 percentage points for an initial 10 per cent misalignment, to some 5 percentage points for an initial 20 per cent overvaluation and to a sizeable 7 percentage points for an initial 20 per cent undervaluation.

As a very rough rule of thumb, therefore, for economies operating near full capacity utilisation, the results of this section suggest the following: The initial measure of misalignment should be increased by about 1.5 percentage points for each 10 per cent of misalignment if the desired period of convergence is five years, and by some 3 percentage points for each 10 per cent of misalignment if convergence over ten years is desired. Thus, an initial misalignment of 15 per cent would suggest a required [TABULAR DATA FOR TABLE 2 OMITTED] exchange rate movement of about 17 1/4 per cent over five years.

Adjusting FEER trajectories: how good are the rules of thumb?

Our final exercise involves investigating what adjustments should be made to some actual FEER estimates, due to Williamson (1990), when a certain convergence path is assumed and hysteresis effects are taken into account. This allows an assessment of the rules of thumb derived in the previous section.

Williamson (1990) presents a range of estimates of FEERs for the G7 countries in 1990.(13) To illustrate the effects of hysteresis, we consider his base-case estimates obtained using the Global Econometric Model (GEM) developed by the National Institute for Economic and Social Research, since GEM appears to be Williamson's preferred model in this context (1990, p. 70). These estimates (Williamson (1990, Tables 6-7)) suggest that, at the end of 1989, the US dollar was overvalued relative to the FEER by some 9 per cent, the yen was undervalued by 15 per cent, sterling was overvalued by 10 per cent, the franc was overvalued by 8 per cent, and the D-mark was undervalued by about 18 per cent.(14) These figures were applied to real exchange rates for the G5 in the fourth quarter of 1989 to obtain an estimate of the FEER in 1990 which could be compared with the average real exchange rate for that year to gauge the initial degree of misalignment.(15) Given an initial estimate of capacity utilisation in 1990, we then assume that, over a five- or ten-year period, utilisation adjusts linearly to full capacity and the exchange rate adjusts by a constant percentage annual change in order to achieve convergence on the FEER at the end of the period. Essentially, this involves setting the trajectory for capacity utilisation exogenously, and fine-tuning the annual percentage change in the real exchange rate so that [S.sub.n] = [F.sub.n] as defined in (5) but with the exchange rate purged of changes due to movements in capacity utilisation.(16)

In the previous exercises, we implicitly assumed a constant (full) level of capacity utilisation. In turning to an analysis of actual real exchange rates, albeit in a counterfactual exercise, we are however obliged to take account of a feature of real world experience from which we abstracted in the earlier sections. A glance at Figure 1, however, serves as a reminder that deviations of actual exchange rates from FEER values need not necessarily imply movement off the CA schedule. An appreciation of the exchange rate and a simultaneous fall in utilisation, for example, could imply that the economy has moved left along the CA schedule, with no consequences for debt service or FEER revision. When using historical data therefore it is necessary to purge movements in actual real exchange rates of that part which can be held to reflect changes in utilisation. In essence, this involves estimating the slope of the CA schedule. Empirically, one can use medium-term elasticities derived from an econometric macro model to do this. In this article, we employ elasticities derived from the IMF's multi-country macroeconometric model, MULTIMOD (Masson, Symansky, and Meredith (1990)).

A simple way of calculating the real exchange-rate changes due to such movements is as follows. Given values for changes in the rate of capacity utilisation, output elasticities yield the implied change in the current account. The real exchange rate elasticities then yield the change in the real exchange rate that would eliminate this. That is, if [[Epsilon].sub.y] is the output elasticity of net imports and [Delta]u the percentage change in utilisation, the corresponding real exchange rate change, [Delta]S, can be found from

[[Epsilon].sub.y][Delta]u X = X([Mu] + [Tau]) [Delta]S (6)

[Delta]S = [[Epsilon].sub.y] [Delta]u/([Mu] + [Tau]) (7)

where [Mu] + [Tau] is the sum of import and export elasticities with respect to the real exchange rate and X is the level of exports (or imports).

The results are reported in Tables 3 and 4. They tend to confirm the usefulness of the rules of thumb derived in the previous section. For example, with an initial misalignment of 9.33 per cent, five-year convergence on the FEER for the US dollar entails an extra 1.34 percentage point movement in the real exchange rate (over the initial 9.33 per cent), which corresponds closely to the '1.5 percentage points per 10 per cent of misalignment corrected over five years' rule. For convergence over ten years, an extra 2.5 percentage points of adjustment in the dollar is required, compared to the '3 percentage points per 10 per cent of misalignment corrected over ten years' rule. Similar results are obtained for the remainder of the G5 countries.

Table 3. Hypothetical five-year FEER trajectories for the G5(a)

Year Exchange FEER Utilisation
 rate rate

(a) United States

1990 62.53 56.69 100.29
1991 61.13 56.43 100.24
1992 59.77 56.21 100.18
1993 58.43 56.04 100.12
1994 57.13 55.92 100.06
1995 55.85 55.85 100.00

Initial misalignment = +9.33 per cent

Annual exchange rate movement = 2.23 per cent

Overall movement in the FEER = -1.48 per cent

Overall movement in the exchange rate = -10.68 per cent

Difference between initial misalignment and overall exchange
movement = 1.34 percentage points

(b) Japan

1990 115.00 141.11 100.96
1991 120.61 142.71 100.77
1992 126.50 144.00 100.58
1993 132.67 144.98 100.38
1994 139.15 145.63 100.19
1995 145.94 145.94 100.00

Initial misalignment = -22.70 per cent

Annual exchange rate movement = +4.88 per cent

Overall movement in the FEER = +3.43 per cent

Overall movement in the exchange rate = +26.91 per cent

Difference between initial misalignment and overall exchange
movement = 4.21 percentage points

(c) United Kingdom

1990 103.07 84.87 101.09
1991 98.57 84.12 100.87
1992 94.26 83.50 100.65
1993 90.15 83.00 100.43
1994 86.12 82.65 100.22
1995 82.44 82.44 100.00

Initial misalignment = +17.66 per cent

Annual exchange-rate movement = -4.37 per cent

Overall movement in the FEER = -2.86 per cent

Overall movement in the exchange rate = -20.01 per cent

Difference between initial misalignment and overall exchange
movement = 2.35 percentage points

(d) France

1990 96.72 86.30 101.16
1991 94.20 85.83 100.93
1992 91.75 85.44 100.70
1993 89.37 85.13 100.46
1994 87.04 84.91 100.23
1995 84.78 84.78 100.00

Initial misalignment = +10.78 per cent

Annual exchange-rate movement = -2.60 per cent

Overall movement in the FEER = -1.76 per cent

Overall movement in the exchange rate = -12.35 per cent

Difference between initial misalignment and overall exchange
movement = 1.57 percentage points

(e) Germany

1990 122.96 145.49 101.24
1991 127.86 146.83 100.99
1992 132.96 147.91 100.74
1993 138.26 148.72 100.50
1994 143.77 149.25 100.25
1995 149.50 149.50 100.00

Initial misalignment = -18.33 per cent

Annual exchange-rate movement = +3.99 per cent

Overall movement in the FEER = +2.76 per cent

Overall movement in the exchange rate = +21.59 per cent

Difference between initial misalignment and overall exchange
movement = 3.26 percentage points.

Notes:

(a) We assume an interest rate of 5 per cent per annum.

Conclusion

The efficient conduct of policy on matters relating to the international monetary system requires some basis for the evaluation of market-determined exchange rates. One such basis can be found in the concept of the fundamental equilibrium exchange rate (FEER) to which Williamson has appealed in his advocacy of exchange-rate target zones. The fundamental rate appeals to the notion that in the medium term it is desirable to obtain both internal balance and external balance. The FEER is simply that rate of exchange which fulfills this condition. It is reasonably straightforward, given estimates of the relevant elasticities, to compute values for the fundamental rate on 'medium-term' assumptions, that is to say, ignoring the dynamics of adjustment.

However, it appears that the true value of the FEER must depend on the path taken towards it. The reason is that, while the actual exchange rate deviates from its FEER value, so in general will the current account realisations deviate from those implicit in the initial calculation of the FEER trajectory. For this reason debt service obligations will differ from those assumed in the initial computation of the trajectory. The FEER will change and a recomputation is called for. The FEER is thus not independent of the path taken towards it, and suffers from hysteresis.

In this article we were able to show that this problem could be formalised in a fairly straightforward manner, enabling us to obtain a formal representation of the hysteresis effect on the FEER. As an indication of the potential importance of such effects in actual practice, we also derived rules of thumb for the updating of the FEER for a given degree of initial misalignment and for particular horizons and monotonic adjustment of the actual real exchange rate towards the FEER. Finally, we calculated by how much FEERs would change if values calculated in 1990 by Williamson were achieved by 1995 or by the year 2000. The results, which took account of the need to adjust capacity utilisation levels at the same time, largely confirm the rules of thumb suggested in the earlier exercise; just as important, the revisions emerged as significant in size when compared with the initial degree of misalignment.

Table 4. Hypothetical ten-year FEER trajectories for the G5(a)

Year Exchange FEER Utilisation
 rate rate

(a) United States

1990 62.53 56.69 100.29
1991 61.74 56.43 100.26
1992 60.97 56.18 100.24
1993 60.20 55.96 100.21
1994 59.45 55.76 100.18
1995 58.70 55.59 100.15
1996 57.96 55.44 100.12
1997 57.23 55.31 100.09
1998 56.52 55.21 100.06
1999 55.81 55.14 100.03
2000 55.10 55.10 100.00

Initial misalignment = +9.33 per cent

Annual exchange rate movement = -1.26 per cent

Overall movement in FEER = -2.80 per cent

Overall movement in exchange rate = -11.88 per cent

Difference between initial misalignment and overall exchange rate
movement = 2.5 percentage points

(b) Japan

1990 115.00 141.11 100.96
1991 118.13 142.71 100.86
1992 121.35 144.19 100.77
1993 124.66 145.53 100.67
1994 128.06 146.74 100.58
1995 131.55 147.79 100.48
1996 135.13 148.68 100.38
1997 138.81 149.40 100.29
1998 142.60 149.95 100.19
1999 146.48 250.30 100.10
2000 150.47 150.47 100.00

Initial misalignment = -22.70 per cent

Annual exchange rate movement = +2.73 per cent

Overall movement in FEER = +6.64 per cent

Overall movement in exchange rate = +30.85 per cent

Difference between initial misalignment and overall exchange rate
movement = 8.15 percentage points

(c) United Kingdom

1990 103.07 84.87 101.09
1991 100.53 84.12 100.98
1992 98.05 83.43 100.87
1993 95.63 82.80 100.76
1994 93.27 82.24 100.65
1995 90.97 81.73 100.54
1996 88.73 81.30 100.43
1997 86.54 80.93 100.33
1998 84.40 80.64 100.22
1999 82.32 80.43 100.11
2000 80.29 80.29 100.00

Initial misalignment = +17.66 per cent

Annual exchange rate movement = -2.47 per cent

Overall movement in FEER = -5.39 per cent

Overall movement in exchange rate = -22.10 per cent

Difference between initial misalignment and overall exchange rate
movement = 4.44 percentage points

(d) France

1990 96.72 86.30 101.16
1991 95.30 85.83 101.04
1992 93.30 85.40 100.93
1993 92.52 85.01 100.81
1994 91.16 84.65 100.70
1995 89.82 84.34 100.58
1996 88.50 84.06 100.46
1997 87.20 83.83 100.35
1998 85.91 83.64 100.23
1999 84.65 83.50 100.12
2000 83.41 83.41 100.00

Initial misalignment = +10.78 per cent

Annual exchange rate movement = -1.47 per cent

Overall movement in FEER = -3.35 per cent

Overall movement in exchange rate = -13.76 per cent

Difference between initial misalignment and overall exchange rate
movement = 2.98 percentage points

(e) Germany

1990 122.96 145.49 101.24
1991 125.70 146.83 101.12
1992 128.49 148.06 100.99
1993 131.35 149.17 100.87
1994 134.27 150.17 100.74
1995 137.26 151.04 100.62
1996 140.31 151.77 100.50
1997 143.44 152.37 100.37
1998 146.63 152.81 100.25
1999 149.89 153.10 100.12
2000 153.22 153.22 100.00

Initial misalignment = -18.33 per cent

Annual exchange rate movement = +2.22 per cent

Overall movement in FEER = +5.31 per cent

Overall movement in exchange rate = +24.61 per cent

Difference between initial misalignment and overall exchange rate
movement = 6.29 percentage points

Notes:

(a) We assume an interest rate of 5 per cent per annum.

NOTES

(1) See Taylor (1995) for a recent survey relating, inter alia, to the first two of these approaches. Frenkel and Goldstein (1986) discuss the relative merits of the three approaches.

(2) See also Nurske (1945) and International Monetary Fund (1970) for precursors of this approach.

(3) The locus classicus on the method of comparative statics is Samuelson (1947). Cuthbertson and Taylor (1987, chapter 1) provide a textbook discussion.

(4) Note that we specifically do not address hysteresis effects that might arise in other ways, e.g., through shifts in the NAIRU or on account of the presence of set-up costs in international trade.

(5) Although we follow standard practice in predicating the FEER on an assumed desired current account flow, a referee has pointed out that a more appropriate underlying target may be total or net external wealth. On this view, what follows, in essence, assumes hysteresis in implied wealth targets in the face of shocks.

(6) In some computations, a desired value of the fiscal deficit is also involved, but the assumption here is that there is no additional effect of fiscal policy to be allowed for on top of its effect on u - i.e., that changes in fiscal policy will not shift the schedules. To a good first approximation, this seems a reasonable assumption.

(7) Throughout this article, for analytical simplicity, we ignore j-curve effects.

(8) To some extent, this problem may be mitigated by adjustment of the market adjustment rate towards the equilibrium level brought about by the effects on domestic absorption of changes in net foreign asset holdings - see Masson, Kremers and Horne (1994).

(9) It might be objected that the short-run elasticities differ from the medium-run elasticities used in constructing the FEER. A further adjustment could be made for any such differences.

(10) It may be worthwhile noting in this connection that market exchange rate instability may ensue when a country becomes a net foreign debtor - see Masson (1981) and Buiter (1984).

(11) In particular, we derive the full set of dynamic solutions to the problem when the real exchange rate adjusts by a proportion of its deviation from the FEER, and derive restrictions on the partial adjustment process which are necessary in order to ensure eventual conergence on the FEER.

(12) In fact, the precise calculations were slightly different because we used percentage differences rather than logarithmic differences, as in equation (1). A spread sheet program was used to perform the calculations.

(13) More exactly, end-1989.

(14) These estimates are used for purely illustrative purposes. They are not endorsed either by the present authors or by the International Monetary Fund.

(15) Real exchange rate data were taken from the IFS data tape.

(16) Again, the actual computations were slightly more complex since actual percentage changes, rather than log-linear approximations, were used.

REFERENCES

Artis, M.J., and M.P. Taylor, (1995), 'The effect of misalignment on desired equilibrium exchange rates: some analytical and applied results,' in C. Bordes, E. Girardin and J. Melitz (eds), European Currency Crisis and After, Manchester University Press.

Baldwin, R., and P. Krugman, (1986) 'Persistent trade effects of large exchange rate shocks', Working Paper no. 2167, National Bureau of Economic Research, Cambridge, Mass.

Barrell, R., and S. Wren-Lewis, (1989), 'Equilibrium exchange rates for the G7', Discussion Paper no. 323, Centre for Economic Policy Research, London.

Buiter, W.H., (1984), 'Exchange rate policy after a decade of 'floating': comment', in J.F.O. Bilson and R.C. Marston (eds) Exchange Rate Theory and Practice, pp. 108-12, University of Chicago Press.

Cross, R., (1992), 'On the foundations of hysteresis in economic systems', International Centre for Macroeconomic Modelling, University of Strathclyde, Discussion Paper no. 4.

Currie, D., and S. Wren-Lewis, (1989), 'Evaluating blueprints for the conduct of international macropolicy', American Economic Review, vol. 79, pp. 264-69.

Cuthbertson, K., and M.P. Taylor, (1987), Macroeconomic Systems, Blackwell, Oxford.

Frenkel, J.A., and M. Goldstein, (1986), 'A guide to target zones', International Monetary Fund, Staff Papers, vol. 33, pp. 633-73.

International Monetary Fund, (1970), The Role of Exchange Rates in the Adjustment of International Payments: A Report by the Executive Directors.

International Monetary Fund, (1984), 'Issues in the assessment of the exchange rates of industrial countries', Occasional Paper no. 29.

King, R., and S. Rebelo, (1989), 'Low-frequency filtering and real business cycles', Working Paper no. 205, Rochester Center for Economic Research.

Layard, R., and S. Nickell, (1985), 'The causes of British unemployment', National Institute Economic Review, no. 111, pp. 62-85.

Lindbeck, A., and D. Snower, (1986), 'Wage setting, unemployment and insider-outsider relations', American Economic Review, vol. 76 (1986), pp. 235-39.

Masson, P.R., (19??), 'Dynamic stability of portfolio balance models of the exchange rate', Journal of International Economics, vol. 11 pp. 467-77.

Masson, P.R., J. Kremers and J. Horne, (19??), 'Net foreign assets and international adjustment: The United States, Japan and Germany', Journal of International Money and Finance, vol. 13, pp. 27-40.

Masson, P.R., S. Symansky, and G. Meredith, (1990), 'MULTIMOD Mark II: A revised and extended model', International Monetary Fund, Occasional Paper no. 71.

Nurske, R., (1945), 'Conditions of international monetary equilibrium', Essays in International Finance, no. 4, Princeton University Press.

Prescott, E.C., (1986), 'Theory ahead of business cycle measurement', Federal Reserve Bank of Minneapolis Quarterly Review, Fall, pp. 9-22.

Samuelson, P.A., (1947), Foundations of Economic Analysis, Cambridge, Massachusetts: Harvard University Press.

Taylor, M.P. (1995), 'The economics of exchange rates', Journal of Economic Literature, vol. 33, pp. 13-47.

Taylor, M.P., and H.L. Allen, (1992), 'The use of technical analysis in the foreign exchange market', Journal of International Money and Finance, vol. 11, pp. 304-14.

Williamson, J., (1985), 'The exchange rate system', Institute for International Economics, Washington.

Williamson, J., (1990), 'Equilibrium exchange rates: an update', mimeo, Institute for International Economics, Washington.

Williamson, J., and M. Miller, (1987), 'Target zones and indicators: a blueprint for the international coordination of economic policy', Institute for International Economics, Washington.

Wren-Lewis, S., P. Westaway, S. Soteri, and R. Barrell, (1991), 'Evaluating the United Kingdom's choice of entry rate into the ERM', Manchester School, vol. 59, Supplement (1991), pp. 1-22.