On the Complementarity of Equilibrium Exchange-Rate Approaches

On the Complementarity of EquilibriumExchange-Rate Approachesroie_900 618..632

Agnès Bénassy-Quéré, Sophie Béreau, and Valérie Mignon*

AbstractBased on a simple, stock–flow adjustment framework, we show that existing concepts of equilibriumexchange rates can be viewed as realizations of the same model at different time horizons. We then comparefundamental and behavioral estimations of equilibrium exchange rates based on the same, econometricmodeling of the net foreign asset position in the long run, for a panel of 15 countries over the 1980–2005period.These estimations suggest that, although more robust to alternative assumptions, the BEER approachmay rely on excessive confidence on past behaviors in terms of portfolio choices. Symmetrically, FEERs mayunderestimate the plasticity of international capital markets because they focus on the adjustment of thetrade balance.

1. Introduction

Assessing the level of exchange rates encounters a number of difficulties. The mostimmediate one is to define what is meant by “equilibrium” exchange rates. There aretwo polar views on this issue. The first one considers that, to the extent that they aredetermined by market forces, observed exchange rates are always at a market equili-brium. Although it relies on fundamentals and on expectations about fundamentals,this market-equilibrium exchange rate is highly volatile due to noise and possiblyspeculative bubbles; hence it can largely differ from its “fundamental” value. At theother extreme, the purchasing power parity theory (PPP, hereafter) considers priceequalization as the appropriate long-run benchmark, at least for advanced economies.Thanks to the availability of very long time series and of panel cointegration tech-niques, there is now a consensus in the literature that PPP holds in the very long runamongst advanced economies. However, deviations from PPP are quite long to bereversed.1 More importantly, PPP is silent on the way global imbalances can beunwound. For instance, it does not address the issue of the United States temporarilyhaving to experience a weak dollar in order to raise its net foreign asset positiontowards some sustainable path.

From a practical perspective, thus, these two views—market equilibrium and PPP—are of limited usefulness, since (i) they basically say that real exchange rates are eitherunpredictable (in the short run) or constant (in the long run), and (ii) they do notaddress medium-term concerns about global imbalances. Therefore, a large researchavenue has been developed to provide medium- to long-run norms for the realexchange rate.The bottom line of these approaches is that, despite full capital mobility,

* Bénassy-Quéré: CEPII, 9 rue Georges Pitard, 75015 Paris, France. Tel: 33-1-53-68-55-41; Fax: 33-1-53-68-55-03; E-mail: [email protected]. Béreau: University of Paris Ouest, EconomiX-CNRS, 200 avenue de laRépublique, 92001 Nanterre, France. Tel: 33-1-40-97-59-63; Fax: 33-1-40-97-77-84; E-mail: [email protected]. Mignon: CEPII and University of Paris Ouest, EconomiX-CNRS, 200 avenue de la République,92001 Nanterre, France. Tel: 33-1-40-97-58-60; Fax: 33-1-40-97-77-84; E-mail: [email protected] are grateful to Philip Lane for helpful suggestions.

Review of International Economics, 18(4), 618–632, 2010DOI:10.1111/j.1467-9396.2010.00900.x

© 2010 Blackwell Publishing Ltd

current-account imbalances cannot grow forever, so some kind of exchange-rateadjustment will be needed at some point, although it is difficult to provide a precisetimetable. The Fundamental Equilibrium Exchange Rate (FEER) pioneered byWilliamson (1985), the Behavioral Equilibrium Exchange Rate (BEER) proposed byMacDonald (1997) and Clark and MacDonald (1998), and the Natural EquilibriumExchange Rate (NATREX) introduced by Stein (1994) are probably the most popularapproaches in this vein, and they have been routinely used by the InternationalMonetary Fund for exchange-rate assessment (see IMF, 2006).

In this paper, we argue that the various concepts of equilibrium exchange ratesproposed in the literature should be viewed as complements rather than substitutes.Our contribution to this literature is three-fold. First, we propose a simple, stock–flowadjustment model that embraces the various concepts of equilibrium exchange rates asequilibria corresponding to different horizons. Second, we calculate consistent setsof FEERs and BEERs for a panel of 15 countries over the 1980–2005 period. Theconsistency is obtained through relying on (i) a single concept of the equilibrium netforeign asset position that determines both the FEER and the BEER anchor values,and (ii) panel estimations rather than a country-by-country approach. Finally, weillustrate how those different concepts of equilibrium exchange rates can be combinedto assess the misalignments of a much-scrutinized bilateral exchange rate: the euroagainst the US dollar (USD).

We believe our approach contributes to filling the gap between the literature onequilibrium exchange rates and that on global imbalances. Indeed, it is worth notingthat the literature on global imbalances (e.g. Obstfeld and Rogoff, 2004; Blanchardet al., 2005; Lane and Milesi-Ferretti, 2007; Arghyrou and Chortareas, 2008) hasdeveloped largely aside from that on equilibrium exchange rates, whereas one ofits outcomes is to provide estimations of exchange-rate adjustments that are neededto unwind global imbalances.

The paper is organized as follows. Section 2 discusses the various concepts of equi-librium within a single, stock–flow model. Section 3 derives PPP exchange rates for theeuro against the USD. Section 4 then presents a unified methodology for calculatingFEERs and BEERs. Section 5 discusses the results. Section 6 concludes.

2. Theoretical Overview

One very general way of classifying equilibrium exchange-rate models is to considerthe real exchange rate qt at time t as a function of (i) a vector of economic “fundamen-tals” Zt, (ii) a vector of transitory factors Tt, and (iii) a random disturbance et (seeMacDonald, 2000; Driver and Westaway, 2004):

q Z Tt t t t= ′ + ′ +β θ ε , (1)

where b, q are vectors of coefficients. Three equilibrium concepts can then be derived:

• short-run equilibrium: q Z TtSR

t t= ′ + ′β θ ;• medium-run equilibrium: q Zt

MRt= ′β ;

• long-run equilibrium: q ZtLR

t= ′β , where Zt is the long-run equilibrium value of Zt.

The crucial point then is to disentangle fundamentals, transitory factors, and randomdisturbances.To do so, it is useful to start, as in MacDonald (2000), from the equilibriumof the balance of payments. Using the same notations as in Lane and Milesi-Ferretti(2002):

tb ki tr kot t t t+ + = , (2)

EQUILIBRIUM EXCHANGE RATES 619


where tbt denotes the trade balance, kit net capital income, trt current transfers,2 and kot

the amount of net capital outflows, all expressed in percentage of GDP (i.e. dollarvalues divided by nominal dollar GDP). The trade balance can be expressed as afunction of both domestic and foreign output gaps (yt and yt*), the logarithm of therelative price of foreign tradables,3 et, and the logarithm of terms of trade, tott, definedas the ratio of the unit value of exports to the unit value of imports:

tb e y y tott t t t t= − + +α α α α1 2 3 4* , (3)

where a1, a2, a3, a4 > 0. In turn, net interest receipts can be expressed as the product ofthe world nominal interest rate it* and the net foreign asset position (NFA) at the endof the last period, nfat-1 (in percentage of GDP), corrected for the growth rate ofnominal GDP, g t:4

ki infa

t tt

t

=+

−* .1

1 γ(4)

Finally, net capital outflows depend on the difference between the value, in t, of theNFA position inherited from the previous period, nfat-1| t, and the desired level of netholdings in t. Again, we follow Lane and Milesi-Ferretti (2002) and denote kgt* the rateof capital gains or losses on the NFA position, assuming the rate of capital gains is thesame on gross assets and liabilities and is expressed here in US dollars. The value ofthe NFA position (in percentage of GDP) inherited from the previous period is:

nfa kgnfa

t t tt

t−

−= ++1

111

( *) ,γ

(5)

where nfat-1| t must be compared with desired net holdings that depend on the expectedinterest-rate differential. This yields:

ko k nfa rkg

nfat te t

tt= + − +

+⎛

⎝⎜⎞

⎠⎟−μ

γΔ 1

11

*, (6)

where nfa represents the desired NFA position in the absence of expected returndifferential, m > 0 is the sensitivity of desired net foreign assets to the expected returndifferential, k > 0 represents the adjustment speed of asset holdings, and Δrt

e is theexpected return differential: Δ Δr r q rt

et t

et= + −* , where rt, rt* represent the real return

rates at home and abroad, respectively, and Δq q qte

te

t= − denotes the expected realexchange-rate variation.5 The relative price of foreign tradables in terms of domesticones derives from these three equations as follows:

e k r nfa nfai

nfa tr y yt te

t tt

tt t t t= + −( ) −

+− + − −− −

111

1 1 2 3 4αμ

γα α αΔ

** ttott

⎛

⎝⎜⎞

⎠⎟. (7)

The NFA position at the end of period t, nfat, is a predetermined variable that evolvesover time based on the following stock–flow relationship (see Lane and Milesi-Ferretti,2002):

nfa i kgnfa

tb trt t tt

tt t= + +

++ +−( * *) .1

11

γ(8)

Rearranging equation (8), we get:

620 Agnès Bénassy-Quéré, Sophie Béreau, and Valérie Mignon


Δnfai kg

nfa tb trtt t t

tt t t= + −

++ +−

* *,

γγ1

1 (9)

where Dnfat = nfat - nfat-1.Then, it is necessary to account for nontradables. Denoting by et

NT the (log of the)ratio of relative price of nontradables in terms of tradables abroad and at home,6 itcan be shown that, conditional on inter-industry labor mobility within each country(see MacDonald, 2000):

e ztNT

t= − , (10)

where zt represents the (log of the) relative productivity of the tradable goods and thenontradable goods sectors, relative to the rest of the world:

ztT NT T NT= −( ) − −( )π π π π* * , (11)

where p T, p NT denote the (log of) productivity in the tradable and nontradable sectors,respectively. Equations (10) and (11) together state that productivity catchup in tradedgoods should be accompanied by a rise in the relative price of nontradables because thelatter sector suffers from an increase in domestic wages without a rise in productivitysimilar to that in the traded goods sector (the Balassa–Samuelson effect).7 If h denotesthe share of tradables in the economy, the logarithm of the real exchange rate can bewritten as:

q e et t tNT= + −( )1 η . (12)

Plugging (7) and (10) into (12), we get:

q f r tot nfa nfa nfa tr y y zt te

t t t t t t t t= −( )⎛

⎝

+ − + − − + − −− −Δ , , , , , , *,1 1⎜⎜

⎜

⎞

⎠⎟⎟

, (13)

where the signs of the partial derivatives are indicated on the top of eachexplanatory variable.8 This general formulation states that the domestic currencyshould depreciate in real terms (qt should rise) following a rise in the expectedreturn differential on assets denominated in foreign currencies, a fall in terms oftrade, a decline in the net foreign asset position compared to the desired one,a rise in the domestic output gap, a fall in the foreign output gap, or a fall inrelative productivity in tradables compared to the rest of the world. We now need todistribute the explanatory variables detailed in equation (13) into the Tt, Zt, and Zt

vectors.In the very long run, prices and stocks have adjusted to equilibrium and productivity

levels are equalized. In equation (13), this translates into y yt t= =* 0, zt = 0, Δrte = 0,

and nfa nfa nfat t= =−1 . Note that the latter condition does not rule out net capitaloutflows: with Δrt

e = 0 and nfa nfat− =1 , equation (6) yields:

ko kkg

nfatt

t

= − ++

⎛

⎝⎜⎞

⎠⎟1

11

*.

γ(14)

For example, a country with a positive equilibrium NFA position will experiencepermanent capital outflows if GDP growth exceeds capital gains. In the very long run,



however, due to perfect arbitrage across markets, a1 can be thought as infinite inequation (3). Hence, net capital outflows and the NFA position have no impact on thereal exchange rate in the very long run (see equation (7)): qt is a constant value, whichamounts to purchasing power parity.

In the long run, only prices and stocks have adjusted. Output gaps have been closed( y yt t= =* 0) and the expected return differential is zero (or equal to a constant riskpremium), but productivity catchup is still under way (zt � 0), whereas the NFAposition is at its equilibrium level: nfa nfa nfat t= =−1 .9 Plugging equation (3) into(9) with y yt t= =* 0 and Dnfat = 0, we get:

ei kg

nfa tr tottt t t

tt t= − + −

++ +

⎛

⎝⎜⎞

⎠⎟1

114α

γγ

α* *

. (15)

Equation (15), which is embodied in (13), points to a depreciation of the realexchange rate when the NFA position falls, because the trade balance must behigher to compensate for lower interest receipts. Accounting for nontradables, thereal exchange rate also depends on the relative level of productivity in both sectors,with productivity catchup implying real exchange-rate appreciation (see equation(12)).

In the medium run, neither stocks nor productivities are at their equilibrium level.Only domestic prices have adjusted, which means that output gaps have been closed.Net capital outflows can be either positive or negative (see equation (6)). Consistently,the current account must be positive in the former case, negative in the latter one, whichhas implications for the relative price of tradables. Indeed, plugging (6), (4), and (3) into(2), and holding y yt t= =* 0, we get:

e k nfa rkg

nfai

nfa trt te t

tt

t

tt t= + − +

+⎛

⎝⎜⎞

⎠⎟−

+− −− −

1 11 11

1 1αμ

γ γΔ

* *αα4tott

⎡

⎣⎢⎢

⎤

⎦⎥⎥, (16)

which, again, can be combined with the Balassa–Samuelson effect. For instance,large net capital inflows can justify an appreciated exchange rate in themedium run, even if the NFA position is already negative. This is not the casein the long run, where a negative NFA position normally leads to a depreciatedcurrency.

In the short run, finally, prices have not adjusted, which means that output gaps havenot been closed. Hence, the equilibrium exchange rate is the solution of equation (13)with all variables at their observed, short-run values. This rate can be viewed as theshort-run fundamental market rate.

Turning to econometric estimations, one usual question is that of the endogeneity ofsome potential fundamentals. Regarding the output gap, this endogeneity is accountedfor since the FEER calculation will be based on an “underlying,” medium-run currentaccount where output gaps have been closed. Turning now to the real interest-ratedifferential, we do not include it in the estimations because this would be inconsistentwith the search for a (relatively) stable equilibrium exchange rate. Finally, although theexogeneity of terms of trade could be questioned on a bilateral basis among industrialcountries, this is less the case on a multilateral basis, especially for emerging countries,which are the majority of our sample. In any case, the use of a dynamic OLS (DOLS)procedure in the empirical part allows us to control for possible endogenous feedbackeffect.



3. The Very Long Run: PPP

Table 1 reports the PPP value of the euro–dollar, i.e. the nominal euro–dollar exchangerate that would have equalized prices across the Atlantic in 2007. The first two columnsdisplay traditional measures of PPP exchange rates that are calculated relying onconsumer prices (hence, measuring relative purchasing powers). Column (3) adds the“Big Mac” PPP measure, i.e. the exchange rate that would have equalized the price ofa “Big Mac” in February 2007 in the Euro area and in the United States. Finally,columns (4)–(6) present cost measures of PPP exchange rates, namely the bilateralexchange rate that would have equalized the hourly cost of labor in the manufacturingsector (or in the entire economy) to its level in the United States, at end 2007.

Three conclusions emerge from Table 1. First, consumption-based measures of thebilateral, PPP exchange rate are relatively close for Germany and France—between1.12 and 1.16 USD for one euro—but the measure based on labor costs leads to asomewhat lower PPP value for the euro in France and Germany (lower than unity).With an average nominal exchange rate of 1.35 in 2007, this means that the euro wasovervalued by 16%–20% against the USD in terms of consumer prices but more interms of labor costs. Second, the PPP value of the euro is higher and more homo-geneous across the different measures for Italy, and especially Spain, with an overvalu-ation in 2007 limited to 10%–17% in Italy and 0%–5% in Spain. Finally, the “Big Mac”index delivers a somewhat lower equilibrium value of the euro (1.10 USD) thanaggregate consumer prices.

4. The Medium to Long Run: FEERs and BEERs

FEERs versus BEERs

As highlighted in section 2, medium- and long-run concepts of equilibrium exchangerates all rely on the equilibrium of the balance of payments, albeit with differentassumptions on whether explanatory variables are at their equilibrium levels or not.Consistently, the literature has followed two different avenues to calculate equilibriumexchange rates.

The first approach is the FEER, a medium-run concept of equilibrium launched byWilliamson (1985). It is derived from equation (2) with net capital outflows kot exo-genously set at a “target” level that corresponds to “sustainable” net capital outflows

Table 1. PPP Exchange Rate: USD per Euro in 2007

Country

WDIconsumer

(1)

OECDconsumer

(2)

BigMac(3)

BLSmanuf.

(4)

Eurostatmanuf.

(5)

Eurostatall(6)

France 1.16 1.12 — 0.99 0.94 0.81Germany 1.13 1.14 — 0.78 0.92 0.89Italy 1.23 1.17 — 1.15 1.24 1.01Spain 1.28 1.30 — 1.35 1.54 1.40Euro area — — 1.10 — 1.09 1.04

Sources: World Development Indicators (WDI) 2007; OECD Economic Outlook 81, 2007; The Economist,February 2007; US Bureau of Labor Statistics (BLS), April 2007.



(“external balance”) and output gaps set at zero (“internal balance”). The current-account target can rely on structural factors (a structural model of saving–investmentimbalance, see e.g. Williamson and Mahar, 1998) on real return differentials, or onspecific information on the countries. The stock–flow adjustment (equation (9)) is notexplicitly accounted for in the basic version of the FEER, although current-accounttargets can be set so that the NFA position comes back to a “sustainable,” or “desired”level.10 As a matter of fact, except if the current account target is designed to ensureNFA stability, the FEER does not rely on a constant NFA position. As such, it is amedium-run rather than long-run concept.

The second research avenue—pioneered by Faruqee (1995), MacDonald (1997), andClark and MacDonald (1998, 2000)—relies on the direct estimation of equation (13).Because it is considered as a long-run relationship, this equation is estimated withcointegration techniques. Then, the BEER is derived as the prediction of the estimatedequation, and exchange-rate misalignments are calculated by comparing the BEERwith the observed exchange rate. One can either derive a long-run or medium-runBEER by setting explanatory variables at their equilibrium or observed values (equa-tions (7) and (15), respectively). The strength of the BEER approach is that, byconstruction, a deviation from the cointegration relationship will tend to be progres-sively reversed, albeit at a speed that can be relatively slow. Hence, there is a force inthe market that will push the exchange rate back to its BEER level, which can then beconsidered as a target level. This strength comes along with a weakness, since a rela-tionship estimated on the past may no longer be valid over the future, due for instanceto structural breaks in institutions (e.g. foreign exchange structural changes) or port-folio choices (e.g. diversification of official reserves, change in fly-to-quality standards,etc.).

Because it relies on a cointegration relationship, the BEER approach generallyprovides equilibrium exchange rates that are closer to observed rates than in the FEERapproach. However, the differences between the two views should not be overstated.First, Barisone et al. (2006) show that, in fact, like the BEER, the FEER is cointegratedwith the observed real exchange rate. Second, a consistent estimation of BEERsrequires that the same equation is used for all countries (since the exchange rate ofcurrency x against currency y is the inverse of that of y against x). By construction, thisyields larger misalignments than a country-by-country approach. Finally, the FEER canbe viewed as the medium-run exchange rate that would bring the NFA position back toits equilibrium level or path. In this sense, the FEER and the BEER are complementsrather than substitutes. Indeed, a “medium-run BEER” can be defined as the equilib-rium rate conditional on the markets perceiving observed NFAs as sustainable; theFEER then depicts exchange-rate adjustment that would be necessary to move NFAsto a sustainable path. Finally, the “long-run BEER” reflects a long-run equilibriumwhere no further adjustment of NFAs is needed. In the following, we try to articulateFEERs and BEERs over different horizons based on the same concept of equilibriumNFA.

The Sample

Contrasting with PPP, FEERs, and BEERs are multilateral concepts. Indeed, theexchange rate that is consistent with both internal and external equilibria is a real,effective exchange rate, not a bilateral one.Therefore, it is necessary to calculate a largeset of FEERs or BEERs before being able to derive bilateral equilibrium exchangerates. Here, we work on a sample of 15 countries accounting for 83.3% of world GDP.



The selected countries are all members of the G-20, a group of advanced and emergingcountries created in 1999 to deal with international financial stability issues, and thatsubstituted to the G-7 as the main international coordination forum in the wake of the2008–09 global crisis.11

Net Foreign Assets and Current Account Targets

We calculate several sets of FEERs and BEERs which we try to make consistent byrelating them to a single model of equilibrium NFA position. The equilibrium NFAmodel relies on Lane and Milesi-Ferretti (2001) and, from its estimation,12 an equilib-rium (or “target”) NFA position (nfa) can be derived that corresponds to the NFAposition that would fit the demographic structure, the public debt ratio and the GDPper capita for each country at each point of time, accounting for country-specific factorsthrough fixed effects.

Based on this NFA target model, we derive two sets of current-account targets: (i)medium-run current-account targets designed to progressively close the gap betweenthe NFA position of each country and its equilibrium level over five to 10 years; and (ii)long-run current-account targets based on a stock–flow equilibrium where the NFA-to-GDP ratio stays constant at its equilibrium level. For the sake of comparability, wealso use the current-account targets proposed by IMF (2006) and Williamson (2006).13

5. FEERs and BEERs: Estimated Misalignments

FEERs

Real effective misalignments14 obtained with the FEER approach for 2005 (which isour last point in the sample) are reported in Table 2 for our different sets of current-account targets. In all cases, a positive sign denotes undervaluation, whereas a negativeone denotes overvaluation of the observed exchange rate, compared to its FEER value.As expected, the US dollar and, to a lesser extent, the euro, appear overvalued in realeffective terms in 2005, but less so in the long run (where the NFA position is assumedto have reached its equilibrium value) than in the medium run (where a depreciationis needed to raise the NFA position). The US dollar and the euro are also undervaluedrelative to Williamson’s current-account targets, but to a lesser extent.

Combined with our stock–flow adjustment model, the FEER approach yields verylarge misalignments for the United States, Japan, China, and India. These results illus-trate the need for balance-of-payment adjustments to rely on other variables than thecurrent accounts. This conclusion is consistent with the recent literature showing that(unexpected) exchange-rate or asset-price variations may account for a large share ofthe adjustment through valuation effects (Lane and Milesi-Ferretti, 2007), wealtheffects (Fratzscher et al., 2007), or else demand- and supply-side adjustment (Algieriand Bracke, 2007; Engler et al., 2009).

To illustrate this point, we calculate alternative sets of FEER estimates for 2005where the initial value of gross US liabilities is reduced by 20% due to an asset–pricecrash in the United States. The loss is distributed equally across all other countries,depending on their gross foreign assets. The results are reported in Table 3 for the casewhere T = 5 (meaning that the NFA reaches its equilibrium level in five years).Columns (1) and (2) compare the current-account targets deriving from our basic,stock–flow calculation, with or without accounting for the crash. The current-account



target for the United States is dramatically reduced when the crash is taken intoaccount, from +2.7% to -0.7% of GDP. In contrast, the current-account target of theEuro area rises from 1.4% to 4.5% of GDP, while that of the UK increases from 2.6%to as much as 8.1% of GDP. The latter result derives from the very large gross assetstock of the UK, which suffers from a large loss in the crash scenario. Columns (3) and(4) then compare real effective misalignments in 2005 under the baseline scenario andunder the crash scenario. Unsurprisingly, the amount of USD overvaluation is muchreduced in the crash scenario, whereas that of the Euro area and of the UK areincreased.

A second problem is that FEER estimates are very sensitive to price elasticities ofimports and exports used in the calculation of the equilibrium value of the exchangerate. In Table 2, FEER estimates are derived using elasticities taken from the Multimodmodel of the IMF (Laxton et al., 1998). Recent research based on detailed trade dataand firm-level data tends to revise these elasticities upwards (see e.g. IMF, 2007), andsome authors have deliberately chosen to use higher elasticities of substitution betweendomestic and foreign goods (see Lane and Milesi-Ferretti, 2007). Higher elasticitiesautomatically translate into lower misalignments. As an illustration, column (5) ofTable 3 reports FEER misalignments with no crash but doubled price elasticities. Allmisalignments are dramatically reduced, and the USD appears overvalued by “only”30% in 2005, compared to 143% in the base case.

Table 2. Real Effective Misalignments in 2005 with the FEER Approach (in %)

CountryBenchmark

targetsa

Medium-run targetsb

Long-runtargetscT = 5 T = 7 T = 10

Canada -4.1 9.1 7.1 5.5 7.5Euro area -9.3 -21.8 -18.7 -16.3 -10.9Japan 33.4 108.0 95.4 86.0 54.1United Kingdom 6.0 -25.2 -20.6 -17.2 -9.5United States -48.5 -142.9 -131.3 -122.5 -91.8

Argentina 89.7 38.5 38.0 37.6 138.8Australia -40.1 -76.9 -67.3 -60.1 -31.7Brazil 30.6 -18.5 -9.9 -3.5 128.1China 73.9 161.7 144.7 132.1 120.5India -36.2 152.4 115.4 87.7 280.0Indonesia 30.4 63.3 55.0 48.8 44.0Korea -5.4 16.7 9.8 4.6 5.7Mexico -43.9 -27.6 -22.3 -18.3 27.0South Africa -22.4 -19.9 -24.5 -27.8 -28.0Turkey -52.9 -70.5 -61.9 -55.5 18.7

Notes: This table reports the FEER misalignments obtained on the basis of the following current accounttargets:a Williamson (2006) for United States, Canada, Japan, Euro area, UK, Korea, and China. Otherwise, IMF(2006).b Current account that would bring the NFA position to equilibrium in 5, 7, and 10 years respectively.c Current account consistent with a stable NFA position at its equilibrium level.See Bénassy-Quéré et al. (2008) for the values of these various current-account targets and for the detailedpresentation of the equilibrium NFA model. A positive sign points to an undervalued currency.Source: Authors’ calculations.



On the whole, our results suggest that FEER calculations are very sensitive tounderlying assumptions concerning valuation effects and price elasticities. One impli-cation is that the level of the FEER itself depends on the profile of exchange-rateadjustment: a sudden, unexpected depreciation of the dollar would have an immediate,powerful rebalancing effect on the US NFA, reducing the needs for further deprecia-tion afterwards. In contrast, an expected, smooth depreciation of the dollar would befactored in by the markets that would ask for higher returns in the United States,compensating for the valuation effect.

BEERs

Turning to BEER estimations, a panel cointegration relationship based on equation(13) is estimated on annual data over the 1980–2005 period for the 15 countries of thesample. Since we are dealing with a long-run relationship, return differentials andoutput gaps are set to zero. Specifically, the following equation is estimated through thepanel DOLS procedure:15

ˆ . . . ,. . .

q nfa tot zt t t t= − − +−( ) −( ) ( )

0 283 0 419 0 8783 37 8 73 15 14

(17)

where tott is the log of the export-price to import-price ratio relative to the rest of theworld,16 and zt stands for the relative productivity ratio, the later being proxied by the

Table 3. Alternative Measures of Real Effective Misalignments in 2005 with the FEER Approachand T = 5 (in %)

Country

Current-account targetsa Exchange-rate misalignmentsb

Basecase(1)

Crashscenario

(2)

Base case(T = 5)

(3)

UScrash(4)

Price elasticitiesdoubled

(5)

Canada -2.1 -0.8 9.1 3.7 2.7Euro area 1.4 4.5 -21.8 -46.9 -6.3Japan -6.0 -4.3 108.1 89.8 31.7United Kingdom 2.6 8.1 -25.2 -58.3 -6.6United States 2.7 -0.7 -142.9 -86.2 -30.6

Argentina 2.4 3.8 38.5 19.4 8.5Australia 2.1 3.1 -76.9 -85.4 -20.5Brazil 1.0 1.4 -18.5 -25.0 -4.2China -6.2 -5.6 161.7 156.2 31.1India -3.7 -8.8 152.3 473.2 29.0Indonesia -3.6 1.7 63.3 3.5 11.6Korea -2.7 -2.1 16.7 10.1 2.8Mexico 0.5 0.8 -27.6 -32.1 -3.8South Africa -1.7 -0.9 -19.9 -31.9 -3.0Turkey -1.4 -1.1 -70.5 -77.2 -7.6

Notes:a In % of GDP.b A positive sign points to an undervalued currency.Source: Authors’ calculations.



ratio of the consumer price index to the producer price index in the rest of the world,relative to the same ratio in the home country.17 In both cases, the aggregate for the restof the world is calculated with the same weighting matrix as for real effective exchangerates.

Equation (17) shows that the signs of the coefficients are consistent with the theory:the real exchange rate appreciates (q falls) in the long run if the NFA position rises, ifterms of trade increase or if the tradable-to-nontradable productivity ratio of the restof the world falls compared to the home ratio.These estimations are then used to derivetwo sets of BEERs: (i) “medium-run BEERs” which are predictions of equation (17)with observed NFA ratios, i.e. real effective exchange rates that would be consistentwith observed NFAs; and (ii) “long-run BEERs” which correspond to predictions ofequation (17) with NFAs set at their target levels, i.e. real effective exchange rates thatwould be consistent with equilibrium NFAs.

Table 4 reports corresponding real effective misalignments in 2005. As expected,misalignments are more limited than in the FEER case. The medium-run BEER(observed NFA) involves a 6.7% overvaluation for the USD and for the euro (ineffective terms) in 2005. As expected, the misalignment is reduced in terms of thelong-run BEER (target NFA): the USD and the euro appear overvalued by only 2.2%and 4.7%, respectively. Symmetrically, the Chinese yuan is found undervalued by 31%compared to the medium-run BEER but “only” 22% compared to the long-run one.The same pattern applies to the Japanese yen, albeit to a much lesser extent (7.9% and2.1% undervaluation compared to the medium-run and long-run BEERs, respectively).

The BEER and the FEER are complements in the sense that the BEER is consistentwith market equilibrium in the medium run (where the NFA position is not assumed toadjust) and in the long run (where the NFA position has adjusted), but not necessarilywith the unwinding of world imbalances. In turn, the FEER concentrates on current-account adjustment but may underestimate the plasticity of capital markets.

Table 4. Real Effective Misalignments in 2005 with the BEERApproach (in %)

Country Medium run Long run

Canada 8.3 5.8Euro area -6.7 -4.7Japan 7.9 2.1United Kingdom -15.9 -12.1United States -6.7 -2.2

Argentina 63.5 63.3Australia -4.3 1.4Brazil -29.2 -27.1China 31.0 22.3India 9.7 5.9Indonesia 13.1 10.1Korea -12.4 -15.9Mexico -15.8 -14.2South Africa 3.6 2.0Turkey -1.6 0.5

Note: A positive value points to an undervalued currency.Source: Authors’ calculations.



One way of interpreting Tables 2 and 4 is to use them as successive views of equi-librium exchange rates by the markets. In the medium run, the “medium-run BEER” isto prevail until markets decide that observed NFAs are nonsustainable. Once NFAs areviewed unsustainable, exchange-rate expectations are revised, which triggers current-account adjustments together with large exchange-rate variations (in line with theFEER).When NFAs are back to a sustainable, long-run level, the equilibrium exchangerate is the “long-run BEER.”

Bilateral Misalignments

We now turn to the bilateral misalignments, taking the euro/dollar exchange rate as anillustration. The equilibrium bilateral rate is calculated based on the whole set ofequilibrium, effective rates, by inverting the weighting matrix of effective rates.18 Sincethere are only 14 independent bilateral rates between 15 currencies, one equilibriumeffective rate needs to be dropped. Here we drop that of the USD.19 The results aredisplayed in Table 5.The first column reports the misalignments obtained for year 2005(a positive sign points to the euro being undervalued against the USD). The othercolumns derive the implications of this misalignment for the end of 2007, accounting forthe appreciation of the euro against the USD between 2005 and 2007 in real terms andassuming a constant bilateral, equilibrium exchange rate from 2005 to 2007.

The equilibrium euro/dollar rate is found around 1.15 dollars per euro at end 2007,according to both the medium-run and long-run BEERs. However, FEER estimatespoint to a much stronger euro: 1.60 dollars per euro for our benchmark case (i.e. withcurrent account targets taken from Williamson, 2006), and even more than two dollarsper euro when our stock–flow adjustment targets are used.Again, the results are shownto be very sensitive to underlying assumptions: when price elasticities are doubled, orwhen US liabilities are assumed to fall by 20% initially due to an asset–price crash, the

Table 5. Euro–Dollar Equilibrium Rate, FEER and BEER Approaches

ModelMisal.

2005 (%)RER variation2005–07 (%)a

Misal.2007 (%)

EUR/USDDec. 2007

Eq. EUR/USDDec. 2007

BEER MR -4.7 -14.8 -19.5 1.45 1.17

FEER bench. 25.0 -14.8 10.2 1.45 1.60FEER (T = 5) 67.9 -14.8 53.1 1.45 2.22FEER (T = 7) 60.6 -14.8 45.8 1.45 2.11FEER (T = 10) 55.3 -14.8 40.5 1.45 2.04

FEER (T = 5) elas2b 14.8 -14.8 -2.2 1.45 1.42FEER (T = 5) crashc 13.3 -14.8 -1.5 1.45 1.43

BEER LR -5.9 -14.8 -20.7 1.45 1.15

Notes:a Real exchange rate variation based on a 16.6% nominal appreciation of the euro and of a 4.3% and 6.1%cumulated inflation in the Euro area and in the United States, respectively.b Refers to FEER results when Multimod trade elasticities are doubled.c Refers to FEER results when assuming a US asset price crash that affects both the US and equally all itstrade partners.MR = medium run; LR = long run.Source: Authors’ calculations.



euro/dollar appears very close to its equilibrium value at end 2007—around 1.45.Thesevarious FEER estimates confirm that world imbalances cannot be solved only throughexchange-rate adjustment, so other variables such as savings or asset prices need toadjust simultaneously, reducing the needs for further dollar depreciation.

6. Conclusions

In this paper, we have tried to provide a unified view of equilibrium exchange rates byarguing that each concept corresponds to a specific time horizon. We illustrate theseviews on a panel of G-20 currencies and then focus on the euro/dollar case. Assumingthat observed net foreign asset positions are viewed as sustainable by the markets or,alternatively, that they have converged to their long-run target values, the equilibriumeuro/dollar rate is found to be around 1.20 at end-2007, which is not very far from thepurchasing power parity rate of Germany and France (around 1.15).These figures pointto a much lower euro than calculations based on target current-account ratios, i.e.exchange rates that would be consistent with the unwinding of global imbalances. UsingWilliamson’s (2006) current-account targets, the equilibrium value of the euro/dollarrises to 1.60 at end-2007. Furthermore, we show that current-account targets derivedfrom stock–flow adjustment towards equilibrium net foreign asset positions lead toeven higher values for the euro. Our analysis illustrates that valuation effects will bekey to solving global imbalances. Although more robust to alternative assumptions,the BEER approach may rely on excessive confidence on past behaviors in terms ofportfolio allocation. Symmetrically, FEERs may underestimate the plasticity of inter-national capital markets because they focus on the adjustment of the trade balance.

References

Akram, Qaisar F., “PPP in the Medium Run: The Case of Norway,” Journal of InternationalMoney and Finance 22 (2006):105–35.

Alberola, Enrique, Susana Cervero, Humberto Lopez, and Angel Ubide, “Global EquilibriumExchange Rates: Euro, Dollar, ‘Ins’, ‘Outs’ and other Major Currencies in a Panel Cointegra-tion Framework,” IMF working paper 99/175 (1999).

Algieri, Bernardina and Thierry Bracke, “Patterns of Current Account Adjustment,” ECBworking paper 762 (2007).

Arghyrou, Michael G. and Georgios Chortareas, “Current Account Imbalances and RealExchange Rates in the Euro Area,” Review of International Economics 9 (2008):747–64.

Barisone, Giacomo, Rebecca L. Driver, and Simon Wren-Lewis, “Are our FEERs Justified?”Journal of International Money and Finance 25 (2006):741–59.

Bénassy-Quéré, Agnès, Sophie Béreau, and Valérie Mignon, “Equilibrium Exchange Rates: AGuidebook for the Euro–Dollar Rate,” CEPII working paper 2008-02 (2008).

———, “Robust Estimations of Equilibrium Exchange Rates within the G20: A Panel BEERApproach,” Scottish Journal of Political Economy 56 (2009):608–33.

Bénassy-Quéré, Agnès, Pascale Duran-Vigneron, Amina Lahrèche-Révil, and Valérie Mignon,“Burden Sharing and Exchange-Rate Misalignments within the Group of Twenty,” in C. F.Bergsten and J. Williamson (eds), Dollar Adjustment: How Far? Against What?, Institute forInternational Economics Special Report 17 (2004).

Blanchard, Olivier, Francesco Giavazzi, and Filipa Sa, “The U.S. Current Account and theDollar,” NBER working paper 11137 (2005).

Clark, Peter and Ronald MacDonald, “Exchange Rates and Economic Fundamentals: AMethodological Comparison of BEERs and FEERs,” IMF working paper 98/00 (1998).

———, “Filtering the BEER—A Permanent and Transitory Decomposition,” IMF workingpaper 00/144 (2000).



Driver, Rebecca L. and Peter F. Westaway, “Concepts of Equilibrium Exchange Rates,” Bank ofEngland working paper 248 (2004).

Engler, Philipp, Michael Fidora, and Chistian Thimann, “External Imbalances and the USCurrent Account: How Supply-Side Changes Affect the Exchange Rate Adjustment,” Reviewof International Economics 17 (2009):927–41.

Faruqee, Hamid, “Long-Run Determinants of the Real Exchange Rate: A Stock–Flow Perspec-tive,” IMF Staff Papers 42 (1995):80–107.

Fratzscher, Marcel, Luciana Juvenal, and Lucio Sarno, “Asset Prices, Exchange Rates and theCurrent Account,” ECB working paper 790 (2007).

Imbs, Jean, Haroon Mumtaz, Morten Ravn, and Hélène Rey, “PPP Strikes Back: Aggregationand the Real Exchange Rate,” Quarterly Journal of Economics 120 (2005):1–43.

IMF, “Methodology for CGER Exchange Rate Assessment,” Research Department (2006).IMF, “Staff Report on the Multilateral Consultation on Global Imbalances with China, the Euro

Area, Japan, Saudi Arabia, and the United States,” 29 June (2007).Lane, Philip R. and Gian Maria Milesi-Ferretti, “Long Term Capital Movements,” NBER

working paper 8366 (2001).———,“External Wealth, the Trade Balance, and the Real Exchange Rate,” European Economic

Review 46 (2002):1049–71.———, “Europe and Global Imbalances,” Economic Policy 22 (2007):519–73.Laxton, Douglas, Peter Isard, Hamid Faruqee, Eswar Prasad, and Bart Turtelboom, “MULTI-

MOD Mark III the Core Dynamic and Steady-State Models,” IMF occasional paper 164(1998).

MacDonald, Ronald, “What Determines the Real Exchange Rate? The Long and the Short ofIt,” IMF working paper 97/21 (1997).

———, “Concepts to Calculate Equilibrium Exchange Rates: An Overview,” EconomicResearch Group of the Deutsche Bundesbank discussion paper 3/00 (2000).

Obstfeld, Maurice and Kenneth Rogoff, “The Unsustainable U.S. Current Account PositionRevisited,” NBER working paper 10869 (2004).

Rogoff, Kenneth, “The Purchasing Power Parity Puzzle,” Journal of Economic Literature 34(1996):647–68.

Schnatz, Bernd, Focco Vijselaar, and Chiara Osbat, “Productivity and the (‘Synthetic’) Euro–Dollar Exchange Rate,” ECB working paper 225 (2003).

Stein, Jerome,“Estimating Equilibrium Exchange Rates:The Natural Real Exchange Rate of theUS Dollar and Determinants of Capital Flows,” in J. Williamson (ed.), Estimating EquilibriumExchange Rates, New York: Jerome Stein (1994).

———, “NATREX Model,” in Stochastic Optimal Control, International Finance and DebtCrises, Oxford: Oxford University Press (2006).

Williamson, John, The Exchange Rate System, Washington, DC: Institute for InternationalEconomics/Cambridge, MA: MIT Press (1985).

———, “The Target Current Account Outcomes,” manuscript, Peterson Institute for Inter-national Economics, prepared for the seminar on Global Imbalances: Time for Action,Washington, DC (2006).

Williamson, John and Molly Mahar, “Current-Account Targets,” in S. Wren-Lewis and R. Driver(eds), Real Exchange Rates for the Year 2000, Policy Analyses in International Economics, 54,Washington, DC: Institute for International Economics (1998).

Xu, Zhenhui, “Purchasing Power Parity, Price Indices, and Exchange Rate Forecasts,” Journal ofInternational Money and Finance 22 (2003):105–35.

Notes

1. According to the seminal survey by Rogoff (1996), the half-life of deviations from PPP istypically between three and five years. More recent studies tend, however, to find shorterhalf-lives; see, for example, Xu (2003), Imbs et al. (2005), and Akram (2006) among others.2. Here, net labor income is included in trt so as to restrict kit to net interest receipts.



3. In this paper, following the bulk of the literature, all the components of the real exchange rateare defined as the relative price of foreign goods in terms of domestic ones.4. g t and it* represent a growth rate in USD and a return rate. Here the interest rate on grossforeign assets is assumed to be equal to that on gross foreign liabilities.5. qt is the logarithm of the real exchange rate. For homogeneity purposes, it is expressed in thesame direction as the relative price of tradables, et, i.e. as the relative price of the foreignconsumption basket: an increase (resp. decrease) in qt denotes a domestic currency depreciation(resp. appreciation).6. That is, e p p p pt

NTt

NTt

TtNT

tT= − − −( )( * * ) , where p is the log of the price index and the NT, T

superscripts represent the nontradable and tradable sectors, respectively, the asterisk represent-ing foreign variables.7. An alternative interpretation of this effect is that a positive shock on productivity in thetradable sector leads to a rise in intertemporal income, hence on the demand side for bothtradables and nontradables. Because nontradables cannot be imported, their relative price rises,which amounts to an exchange-rate appreciation. See, for example, Schnatz et al. (2003).8. The impact of it*, which depends on the sign and magnitude of the NFA position, is omittedhere.9. As will be made clear in the empirical section, the equilibrium NFA position itself can moveslowly over time due to structural factors, including economic catchup.10. A variant of the FEER is the Natural Real Exchange Rate (NATREX) developed by Stein(1994, 2006), where the target current account is estimated based on structural determinants ofsaving and investment, notably the NFA position and the capital stock, which leads to accountingfor stock–flow adjustments. In the following, we propose to reconcile the FEER with the stock–flow adjustment by estimating a target level for the NFA position rather than for the currentaccount balance.11. Our sample covers all G-20 countries except Russia and Saudi Arabia. France, Germany, andItaly are grouped into the Euro area. Hence the country list is the following:Argentina,Australia,Brazil, Canada, China, the United Kingdom, Indonesia, India, Japan, Korea, Mexico, Turkey, theUnited States, South Africa, and the Euro area.12. The derivation and estimation of the equilibrium NFA model are detailed in Bénassy-Quéréet al. (2008).13. The reader can refer to Bénassy-Quéré et al. (2008) for all details concerning the numericalcurrent-account targets, as well as the “underlying” current accounts.14. Bilateral real exchange rates are taken from World Bank, World Development Indicators andDatastream for the EUR/USD exchange rate. The real effective exchange rates are calculatedwith 2005 trade weights based on IMF, Direction of Trade Statistics data.15. Panel unit-root tests show that all series included in the estimations are I(1). The results areavailable upon request. In equation (17), t-statistics are given in parentheses.16. Source: World Bank, World Development Indicators.17. Source: World Bank, World Development Indicators and IMF, International FinancialStatistics. Three additional proxies of productivity are used in Bénassy-Quéré et al. (2009), withsimilar results.18. See Alberola et al. (1999) and Bénassy-Quéré et al. (2004) for a detailed description of thismethodology.19. As robustness checks, we used the euro and the yen as alternative numéraires. The obtainedresults were very similar and are available upon request from the authors.



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On the Complementarity of Equilibrium Exchange-Rate Approaches