VoxEU Column Exchange Rates

New estimates of fundamental equilibrium exchange rates

Has the dollar fallen far enough? How large are unsustainable international imbalances? This column presents new estimates of fundamental equilibrium exchange rates, concluding that the US dollar has fallen enough with respect to the euro and pound but is overvalued against Asian currencies.

The dollar has fallen a great deal since autumn 2007 and the necessary adjustment to the US trade deficit has started. The depreciation was widely anticipated – by, for example, Paul Krugman and Marty Feldstein – but has the depreciation been large enough? Are remaining international imbalances sustainable as Giancarlo Corsetti argued?

The Peterson Institute for International Economics has always regarded it as meaningful to seek to identify equilibrium exchange rates. Naturally we have recognised that there is more than one concept of equilibrium, and we have therefore been specific in spelling out the concept and the contexts that we believe to be of policy relevance. Specifically, we are interested in identifying what we have described as “fundamental equilibrium exchange rates”, meaning the real effective rate that in the medium term can be expected to be consistent with an economy’s achievement of the optimal sustainable outcome. In practice this requires the analyst to lay out what s/he regards as desirable macroeconomic outcomes and then to seek the exchange rates consistent with those.

This is an undertaking that we believe will now be feasible for a large number of currencies on a regular basis, given the technology developed recently by one of the authors (Cline). It involves a four-stage process. First, it is necessary to specify what one expects to happen without any policy changes. For this purpose we take the forecasts published in the IMF’s World Economic Outlook. Second, one has to lay out a vision of what would be desirable. To this end we develop a series of current account balance targets for the areas served by the principal currencies whose fundamental equilibrium exchange rates (FEERs) we are seeking to establish. Third, we calculate how much change in each economy’s real effective exchange rate would be needed to achieve this target current account balance, on the assumption that any and every change in external demand is neutralised by an equal but opposite change in domestic demand. This is done by the application of an impact parameter that emerges from Cline’s work to the change in current balance that is needed to be induced according to the objectives and the IMF’s forecasts. Fourth, we apply Cline’s Symmetric Matrix Inversion Method to find the changes in nominal bilateral exchange rates that would simultaneously achieve (well, approximately achieve) all the desired changes in effective exchange rates.

The method of calculation

For the present exercise, we have taken the forecasts in the April 2008 issue of World Economic Outlook, and assumed that these embody lagged effects of exchange-rate changes that are already in the pipeline and any cyclical desynchronisation that is due to be corrected in the forecast period. To give adequate time for such effects to work themselves out, our first impulse was to work with the IMF’s forecasts for 2013, but in practice these do not differ greatly from those for 2009 so we have stuck with the latter. There has of course been one great change between the base period of Feb 2008 used by the IMF in constructing its April forecasts and July when our estimates were published in a Peterson Institute Policy Brief (08-7): the oil price has risen from $95 per barrel in February to a sum that has fluctuated greatly but has been over $140. This is one reason – though not the only, or most important, one – why in our central simulation we did not aim to estimate fundamental equilibrium exchange rates for oil-exporting nations. The fundamental equilibrium exchange rates of the remaining countries are probably not particularly sensitive to the price of oil.

The second part of the analysis involves specifying what we regard as normatively desirable. Since trade policy is fortunately no longer varied in the search for payments balance, and “internal balance” is essentially dictated by the condition that inflation not be allowed to accelerate, this amounts to setting out a set of current account balances that we would expect to maximise utility subject to the constraint of sustainability. These targets were based on the presumption that imbalances should not in general exceed 3% of GDP in the intermediate run. The 3% figure that we use is now conventional, so our results cannot be dismissed as resulting from quixotic assumptions. More importantly, as a maximum sustainable deficit it has at least a modicum of statistical support. We impose a similar figure as a maximum normal surplus in the interest of achieving a measure of balance in the obligation to adjust.

Exceptions (a 6% of GDP imbalance) are allowed for certain countries that appear to desire and be capable of handling large debts (Australia and New Zealand) or save abnormally much abroad (Singapore and Switzerland). Together with a presumption that most developed countries (exceptions being the chronic-deficit United States and United Kingdom, which are nevertheless limited to 3% of GDP) should not normally be in deficit nor developing countries be in surplus, these rules suffice to give us targets for 24 of the 34 economies separately identified in our analysis. Another 4 of the 34 are classified by the IMF as oil exporters. That leaves 6 economies—China, Hong Kong, Japan, Malaysia, Taiwan, and Sweden – which have a major surplus exceeding 3% of GDP. If they all were required to cut their surpluses to the 3% mark, the result would be to impose a $79 billion increased surplus on the Rest of the World. To avoid imposing an obligation to adjust on small countries simply because they have not been separately identified, we limited the required adjustment of the large-surplus countries and allowed them to retain surpluses somewhat exceeding 3% of GDP.

Required adjustments were derived by comparing IMF forecasts with our normative targets. How large a change in the real effective exchange rate would be needed to accomplish the desired change in the current account balance was calculated by dividing the latter by an impact parameter equal to the product of the export price elasticity and the share of exports in GDP. In principle one would like to use individual export elasticities for each economy, but in practice we used a standard formula in which the elasticity declines from unity for a relatively closed economy to 0.5 for one with exports as large as GDP (to account for rising supply constraints).

This much could have been done at any time in the past 30 years. The last step embodied the technical advance, using Cline’s Symmetric Matrix Inversion Method. This solves for a set of bilateral exchange rate changes against the dollar that is consistent with a target set of changes in effective exchange rates. This is the solution to a matrix algebra problem:

Z = B-1R

where Z is a vector of bilateral exchange rate changes against the dollar (percentages), R is a vector of effective exchange rate changes (percentages), and B = I – A, where I is the identity matrix and A is the matrix of trade weights. However, with 35 economies (including the Rest of the World), there are 35 possible solutions, but only 34 unknown exchange rates against the dollar, because the dollar is the numeraire. We dealt with this problem of overdetermination by averaging 34 sets of exchange rate changes, excluding the equation in which the own-currency effective rate was omitted and the economy’s bilateral exchange rate was only estimated indirectly as needed to generate other economies’ effective exchange rates.


The results of the analysis are shown in Table 1 for the principal currencies. (These are the results of our central case: we also calculated the results of using higher elasticities (which give a smaller global discrepancy), of subjecting oil exporters to the same rules as other countries (which require very large revaluations by Saudi Arabia and Norway), and of requiring countries to stabilise their ratios of net foreign assets to GDP as in the “third approach” of the IMF.) The figures were originally worked out from the February 2008 base used in the IMF projections, so those results are shown in the first two columns. They implied a set of bilateral exchange rates against the dollar, which one assumes will not have altered much since February so these FEER-equivalent rates against the dollar are shown in the third column. The fourth column shows actual rates in the first half of July, while the final column then shows the required percentage change in each currency against the dollar in order to have reached all fundamental equilibrium exchange rates simultaneously.

Table 1 Currency realignments required to reach fundamental equilibrium exchange rates

 Precent change from basea Currency level against the dollar   

Trade-weighted average Bilateral vs the dollar FEER equivalent July 1-15,2008 % change needed
Industrial Countries          
Canada -4.1 -1.5
Euro Areab
United Kingdomb
United States
Developing Asia
Other Developing
South Africa
a. February 2008
b. Dollars per currency unit


The calculations suggest that the dollar is still overvalued, but solely with respect to a number of Asian currencies (plus the Swiss franc and Swedish krona), not with respect to the euro, pound sterling, Canadian dollar, etc. Indeed, the latter have overshot with respect to the dollar, but not greatly so. Most of their overvaluation would be corrected by an appreciation of the Asian currencies. The largest undervaluations are those of Singapore and Switzerland, even though they were assigned larger current balance targets than the norm. The largest overvaluations are those of South Africa and Turkey; the Polish zloty and (not shown) Hungarian forint were also found to be overvalued. The two US neighbours, Canada and Mexico, both appear roughly correct at present. Canada and Australia are both close to parity with the US dollar, reflecting the strength of energy and raw material prices. The effective changes of the Asian currencies would be far smaller than their bilateral changes vis-à-vis the dollar, reflecting the importance of Asian intra-trade.