Exchange Rate Policy for a Small Developing Country, and the Selection of an Appropriate Standard

Policymakers in a small developing country that seeks to fix its exchange rate in a world of generalized floating are faced with two principal questions: (a) Against what standard should the country fix the value of its currency, keeping in mind that to fix to any other single currency is to float jointly with that currency against the rest of the world? and (b) under what conditions should there be discretionary changes of the value of the currency vis-à-vis the chosen standard? This paper provides a framework for the discussion of these two questions.

Abstract

Policymakers in a small developing country that seeks to fix its exchange rate in a world of generalized floating are faced with two principal questions: (a) Against what standard should the country fix the value of its currency, keeping in mind that to fix to any other single currency is to float jointly with that currency against the rest of the world? and (b) under what conditions should there be discretionary changes of the value of the currency vis-à-vis the chosen standard? This paper provides a framework for the discussion of these two questions.

Policymakers in a small developing country that seeks to fix its exchange rate in a world of generalized floating are faced with two principal questions: (a) Against what standard should the country fix the value of its currency, keeping in mind that to fix to any other single currency is to float jointly with that currency against the rest of the world? and (b) under what conditions should there be discretionary changes of the value of the currency vis-à-vis the chosen standard? This paper provides a framework for the discussion of these two questions.

The hypothetical country under consideration is “small” insofar as it exerts neither monopoly power over its exports nor monopsony power over its imports; it is a “developing” country insofar as it lacks a well-developed financial system. The question of the optimal exchange rate system for such a country—that is, whether it should adopt a fixed, managed floating, or free floating exchange rate system—is not addressed in this paper.1 In general, the literature on this question tends to favor the adoption of a fixed exchange rate regime for a developing country: first, because exchange fluctuations will probably be exacerbated if the market for the currency in question is thin and, second, because the effects of transitory supply shocks—crop failures, for example—are cushioned by the use of reserves under a fixed exchange rate system.2 The framework in this paper is relevant, therefore, only after the authorities have decided to peg the exchange rate.

A discussion of exchange rate policy and, in particular, of the appropriateness of changes in the exchange rate must define some long-run equilibrium exchange rate against which to assess the actual exchange rate. This paper makes use of the purchasing-power-parity condition (PPP) to determine a long-run equilibrium toward which prices tend.3 PPP is based on two fundamental assumptions: (a) the law of one price, and (b) the long-run neutrality of money.4 If identical goods originating in two countries are priced identically by the market, and all relative prices are fixed (by the neutral money assumption) in the long run, then overall price indices must obey the PPP condition. However, money is not neutral in the short run, and there is some recent evidence5 that the law of one price does not hold, even over a number of years. Moreover, there is great difficulty in establishing the appropriate base period for a PPP calculation and even greater difficulty in allowing for real (for example, relative productivity) effects on relative prices over time. Various alternative methods of assessing the long-run equilibrium exchange rate have been suggested, all of which provide rather rough-and-ready rules of thumb; those more sophisticated than PPP require either a substantial investment in econometric modeling or a clear idea about how exchange rate expectations are formed.6 For these reasons, and because it is simple and widely understood, we have relied on the use of PPP in this paper.

The sections that follow introduce, in turn, questions that are important to the selection of an exchange rate standard and to the determination of appropriate adjustments against that standard. Where it is considered helpful, the discussion is illustrated by a case study of India. Although India is not a small country by most conventional measures, it is undoubtedly “small” in terms of the operational definition given above. The final section provides a summary of the material covered.

I. Costs of Fluctuating Exchange Rates, Terms of Trade, and Period Over Which Exchange Rate Changes Matter7

A gratuitous exchange rate change—that is, a change from a situation that appears to be in equilibrium—exerts a real effect on an economy when some other price in the economy is fixed so that the economy cannot return to the pre-change equilibrium set of relative prices. In disequilibrium, there will be real effects if changes in the exchange rate are faster or slower than relative price changes between the home country and the rest of the world or if exchange rates “overshoot”—that is, if they change by more than is warranted by relative price movements and then reverse to restore relative price equilibrium. A useful generalization that has emerged from the current experience with floating exchange rates is that among the major industrial countries, the amplitude of exchange rate fluctuations has been considerably larger than that of corresponding relative price changes between countries. This has led to frequent and sometimes prolonged deviations from purchasing power parity and has produced changes in the terms of trade among these countries.8

Such exchange rate fluctuations have led also to changes in the terms of trade faced by small countries. An example may serve to clarify this. Consider a small developing country that exports only to the United States and imports only from Japan, with prices set in the larger trading partner countries.9 An appreciation of the Japanese yen vis-à-vis the U.S. dollar that is not offset by price changes means an improvement in the Japanese terms of trade and a concurrent worsening of the terms of trade in our stylized developing country. The developing country in our example will suffer a rise in import prices relative to export prices independently of whether its currency is pegged to the U.S. dollar, the yen, or some combination of the two. If the country is on a U.S. dollar standard, import prices will rise in domestic currency, worsening its terms of trade; if it is on a yen standard, export prices will fall with the same effect. If its currency is pegged to a basket consisting of the yen and the U.S. dollar, domestic currency prices of imports will rise, though less than in the case of a U.S. dollar peg, and domestic currency prices of exports will fall, though less than in the case of a yen standard; the final result will be a change in the terms of trade that is identical to that which occurs with either of the other two standards.

The terms of trade (t) in domestic currency terms may be written as

t=PxuseusPmjeus/e*=Pxuse*Pmj(1)

where Pusx ≡ price of exports in U.S. dollars

pjm ≡ price of imports in Japanese yen

eus ≡ domestic currency price of U.S. dollars

e* ≡ Japanese yen price of U.S. dollars

Clearly t in equation (1) is entirely independent of the domestic currency exchange rate arrangements. Furthermore, real income (Y) is dependent on the terms of trade. In the simplest case of a country that consumes only imports and produces only exports, with output (Q) exogenous in the short run,

Y=Qt(2)

In a world of floating exchange rates, fluctuating terms of trade represent a real economic cost that cannot be avoided. For a small developing country, the choice of an exchange rate standard or, indeed, of an exchange rate cannot influence either changes in the country’s external terms of trade or the attendant real income shocks.

If we assume that relative prices within the United States and within Japan are fixed and that purchasing power parity is maintained, changes in the nominal exchange rate exert no real influence. Using a dot (・) over a symbol to denote a proportionate change, and dropping our ξ and m subscripts, which are made redundant by the assumption of fixed internal relative prices, the terms-of-trade equation and the PPP condition may be written, respectively, as follows:

t˙=P˙usP˙j+e˙*(3)
e˙*=P˙jP˙us(4)

Clearly, if equation (4) holds, the proportionate change in the terms of trade is zero. It is, therefore, only sensible to discuss the effects of exchange rate changes over the disequilibrium period during which PPP does not hold.

II. Distribution and Allocation

Although the standard to which the domestic currency is pegged cannot influence the external terms of trade, it can influence income distribution in the country, the internal terms of trade, and the allocation of resources.

DISTRIBUTION

In the example given previously, it is clear that if the country fixes to the U.S. dollar (or, more generally, to an export-weighted basket), export prices in domestic currency are unaffected by the terms-of-trade shock while import prices rise. If the country fixes to the yen (or to an import-weighted basket), import prices are unaffected by the terms-of-trade deterioration while export prices fall. These two polar extremes and the continuum of possible exchange rate standards between them all have different distributional implications. To generalize this algebraically for the two extremes, we introduce three sectors: the exporting (x), import-competing (mc), and nontraded goods producing (nt) sectors. The output of each is denoted by Q, the price of this output per unit, in domestic currency, by P. In addition, two distributional groups are introduced: capitalists, whose real income (RR) is determined by the value of output less the wage bill deflated by the consumer price index (Pc) and workers, whose real income (WR) is the exogenously fixed wage rate (w) times employment (L) deflated by the consumer price index. The following equations describe the system.

Pc=aPm+bPx+zPnt(5)

There is some domestic consumption of exportables. Nontraded goods prices are assumed fixed over the period of the exchange rate fluctuation.

RP=PxQx+PmQmc+PntQntwLPc(6)
WR=wLPc(7)

Consider first the case where the country pegs to an export-weighted basket. Prices of exports and nontraded goods are fixed, while import prices rise in the face of an exchange rate induced deterioration in the terms of trade.

RP˙|P¯x=[(QmcRR.Pc)aPc]ΔPm(8)
W˙R|Px¯=(aPc)ΔPm(9)

Clearly, more of the burden here falls on labor than on capital. If, however, the import-competing sector (Qmc) is so small as to be insignificant, the proportionate decline in real income in the two sectors is identical, and an export-weighted basket serves best to maintain the distributional status quo.

Next consider the case in which the domestic currency is pegged to an import-weighted basket, so that import prices are fixed but export prices fall.

R˙R|Pm¯=[(QxPcRR)bPc]ΔPx(10)
WR|P¯m˙=(bPc)ΔPx˙(11)

In this case, the real income of labor actually rises with a deterioration in the terms of trade. The proportionate fall in the real income of capital is actually larger than that of overall real income. All of the burden and more falls on capitalists.

Finally, consider the case where the home currency is pegged to an average of export- and import-weighted baskets, so that

ΔPx=ΔPm(12)
RR˙=[QxΔPx+QmcΔPmPcRR][aΔPm+bΔPxPc](13)
WR˙=[aΔPm+bΔPxPc](14)

If the output of the export sector is identical to that of the import-competing sector, the distributional status quo is maintained. In the more usual case, however, where the exporting sector is far larger than the import-competing sector, most of the shock will be absorbed by capitalists.

While, in general, this section has described the terms-of-trade shock as a deterioration and has argued about the distribution of the burden, the same formalization holds for a gratuitous improvement of the terms of trade and the distribution of the windfall gain. The conclusion of the argument is that while the relation between an exchange rate induced terms-of-trade shock and the distribution of income depends upon the structure of the economy, a policy of pegging to an import-weighted basket will serve to alter the distribution of income under any structural circumstances.

ALLOCATION AND INTERNAL TERMS OF TRADE10

The question of allocation is closely related to the question of the relative rate of inflation between the home country and the aggregate of its trading partners. For analytical simplicity, however, the inflation question will initially be excluded from the discussion of allocation and will be introduced in a later section. We will continue to work, within the framework of our simple example, with three prices—Px, Pm and Pnt—and to assume that they change only because of exchange rate changes, so that

Px=eusPxusPm=ejPmj(15)Pnt=P¯nt

where ej ≡ domestic currency units per yen,

we define a price index for traded goods Pt such that

Pt=(Px)12(Pm)12(16)

As noted in Section I, the relative price of exportables and importables (PxPm) is quite independent of the domestic exchange rate arrangements. In the example given of a depreciation of the U.S. dollar vis-à-vis the yen, there will undoubtedly be an impetus to reallocate resources from the export sector to the import-competing sector. When the nontraded goods sector is brought into consideration, however, the domestic exchange rate arrangements become important.

Consider first the case of the country pegging its exchange rate to an export-weighted basket, in our example to the U.S. dollar, so that Px is fixed. The import and the overall traded goods price indices rise.

P˙m=e˙j=e˙*(17)
P˙t/P¯x=12e˙*>0(18)

This should induce a reallocation from the nontraded goods sector toward the import-competing sector, as well as the unavoidable shift from the export sector to the import-competing sector. In general, it should serve to reallocate resources away from nontraded toward traded goods.

Next consider the option of pegging to the yen—or, more generally, to an import-weighted basket—such that ėj = m = 0. Here the export price falls, as does the traded goods price index,

P˙x=e˙us=e˙*(19)
P˙t|P¯m=12e˙*<0(20)

This should induce a shift from the export sector toward both import-competing and nontraded goods, and an overall shift in production from traded to nontraded goods.

Finally, the authorities have the option of pegging their currency to an average of the export- and import-weighted baskets—in our example, to the U.S. dollar and the yen. Assume for simplicity that each currency makes up one half of the basket.11 Under this arrangement, the export price declines, but by less than under a yen peg;

P˙x=e˙us=12e˙*(21)

the import price rises, but by less than under a U.S. dollar peg;

P˙m=e˙j=12e˙*(22)

and the traded goods price index remains unchanged.

P˙t=0(23)

Clearly, the same incentive exists for a shift from the export sector to the import-competing sector. The price incentive for a shift from nontradables into importables is less than under the export-weighted basket arrangement; the incentive to shift production from exportables into nontradables is less than under the import-weighted basket arrangement. There is no net change in the relative price of tradables and nontradables. While this last arrangement serves to reduce the size of relative price changes between traded goods as a whole and nontraded goods, it does involve both independent relative prices changing, compared with only one change under either of the other schemes. Our analysis illustrates the fact that a basket can be chosen to offset exchange rate induced changes in any index of traded goods prices.12 The preference frequently expressed for the last basket arrangement is based presumably on the assumption that the transitory effects of a number of small relative price changes are less damaging, in terms of misallocation of resources, than the effects of fewer, larger changes in relative prices. In practice, of course, the extent of any shift in allocation, owing to a transitory change in relative prices, will depend upon the sensitivity of factors of production to price incentives—or the price elasticity of allocative mobility—and, more importantly, the length of time for which the new relative prices are expected to prevail. If changes in internal relative prices are truly transitory, and are generally regarded as such, there will be no incentive to shift allocation.

III. Choosing Basket Weights and Evaluating Alternative Baskets

The choice of weights to assign to currencies included in the currency basket must be made mostly on an a priori basis, because there are no clear-cut empirical criteria for preferring one basket to another. Suppose it is decided to choose a basket related to total trade, with the objective of minimizing the exchange rate induced fluctuations in the domestic currency price of traded goods. Three alternative weighting schemes immediately suggest themselves: (a) a trade-weighting scheme—that is, weighting each currency by its country’s share in trade; (b) a denomination currency scheme—that is, weighting each currency according to the proportion of trade denominated in that currency; and (c) a price-currency scheme—that is, weighting each currency according to the proportion of trade for which prices are fixed in that currency.

The first scheme, though frequently employed, has obvious problems. If, for example, gold is imported from South Africa at U.S. dollar prices ruling on the London gold market, an exchange rate change vis-à-vis the dollar will alter the domestic currency price, while an exchange rate change vis-à-vis the South African rand will have no impact effect. Clearly, the rand has no claim to inclusion in the basket. The difference between (b) and (c) is more subtle. The currency in terms of which the price of a traded good is fixed will not necessarily be the same as that in which trade is denominated unless prices are fixed by long-term trade contracts. In Western Samoa, for example, it has been suggested that although certain imports from Australia are denominated in U.S. dollars, their prices are fixed in terms of Australian dollars; and the U.S. dollar price is determined simply by the Australian dollar-U.S. dollar exchange rate on the transaction day. Clearly, this trade calls for the inclusion of the Australian dollar, rather than the U.S. dollar, in the currency basket. Thus, the basket most appropriate to the specified objective would be weighted according to the currencies in which traded goods prices are fixed. This too, unfortunately, is not an unambiguous concept. Prices in the world market for some homogeneous commodity may be fixed daily in terms of U.S. dollars, but if the United Kingdom consumes a large share of the particular commodity, a change in the dollar-sterling rate will undoubtedly affect the dollar price. Theoretically, therefore, the price is determined in a composite currency with the weights in the composite set to take into account price elasticities of demand and supply. The multilateral exchange rate model (MERM) provides sophisticated proxies for such a set of weights for developed countries; for developing countries, however, less sophisticated proxies must be sought.13

It is extremely difficult to compare alternative baskets. By construction, fixing to any basket will eliminate fluctuations in an effective exchange rate for which the identical weights are used. While no clear empirical choice criteria are available, one useful way of presenting the information on various baskets is to define hypothetical domestic currency units, each fixed to one of the proposed baskets over a recent historical period. It is then possible to compare the variance of each of these hypothetical currency units and of the actual currency vis-à-vis each of the currencies of the major trading partners. While this provides no clear answers, it is a method of presenting the data that provides an interesting historical perspective on the choice of weights.

An analysis of the exchange rate of the Indian rupee since the advent of generalized floating (in the second quarter of 1973) serves as a useful illustration. The rupee was pegged to sterling until September 1975. At that time, its link with sterling was broken, and it was linked instead to a basket of trading partners’ currencies. Our analysis defines an exchange rate index based on a unit value in some “normal” time period, and then considers variations in this index. For India, a logical “normal” period is the last quarter of 1975, on the assumption that the change in the exchange arrangements of September 1975 served to move the exchange rate to some “normal” or desirable level. Table 1 presents the trade shares of India’s major trading partners. Six major trading partners—of which two are oil producing countries that denominate most trade in foreign currencies—make up 75 per cent of the subtotal in Table 1. In defining proxies for the ideal set of basket weights, therefore, it is simpler, and not too unreasonable, to use a smaller set of countries than that listed in Table 1. Four such proxy baskets are defined: one based on export weights, one on import weights, one on trade weights, and one on vehicle-currency weights. The last of these is constructed based on the following assumptions: (a) that half of the trade not accounted for in the subtotal in Table 1 is denominated in U. S. dollars, the other half in pounds sterling, (b) that trade with oil producing countries is denominated in U. S. dollars, and (c) that all other trade is denominated in the currency of the trading partner concerned. The weights in each basket are normalized to sum to unity.

Table 1

India: Average Exports and Imports and Various Trade Weights, 1974–76

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Weights derived as proportions of the subtotal. The weight of the subtotal is a proportion of the world total.

In order to evaluate the different exchange rate strategies open to the authorities, four hypothetical “rupees”—fixed, respectively, to the export-weighted, import-weighted, trade-weighted, and vehicle-currency-weighted baskets described previously—have been defined. The variance of the rupee in terms of each of the four major currencies and the special drawing right (SDR) has been computed under the actual and the various hypothetical exchange rate schemes. The results are presented in Table 2 and Chart 1.

Table 2

India: Variances of Foreign Currency Values Per Unit of Domestic Currency

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Variances calculated from quarterly data over the entire period of generalized floating—that is, from the second quarter of 1973 through the second quarter of 1978.

Variances calculated from quarterly data over the period during which India has fixed the value of the rupee to a basket—that is, from the fourth quarter of 1975 through the second quarter of 1978.

Chart 1.
Chart 1.

India: Four Exchange Rate Indices Under Three Different Standards, Second Quarter 1973–Second Quarter 1978. 1

Citation: IMF Staff Papers 1979, 003; 10.5089/9781451972597.024.A001

1 An upward movement indicates a depreciation of the rupee.For convenience, and because they show a similar pattern to the trade-weighted standard, the export-weighted and import-weighted hypothetical standards are omitted.All indices are based on unit value in the fourth quarter of 1975.

Over the full period of generalized floating for which data are available—the second quarter of 1973 through the second quarter of 1978—any one of the hypothetical basket arrangements could have reduced the variance of the rupee with respect to the U. S. dollar, the Japanese yen, the deutsche mark, and the SDR, but the actual currency produced the lowest variance with respect to the pound sterling. This result is not unexpected as the rupee was fixed to sterling for the early part of this period. Notably, the import-weighted basket, which exhibited the lowest variance against all three other currencies and the SDR, exhibited the highest variance against sterling. This is interesting because, although this basket had the lowest weight for the pound sterling, other baskets had larger weights for both the dollar and the yen.

No valid conclusions can be drawn from the data over the full period of generalized floating because of the shift in exchange rate policy in 1975. The variances have consequently been recomputed for the period during which the rupee was fixed to a basket—that is, the period after September 1975—and the results are given in the lower half of Table 2. The vehicle-currency basket, as may be expected, displays the most stability with the principal vehicle currencies, the U. S. dollar and the pound sterling. It is also the most stable relative to the SDR. The actual rupee is relatively stable against both the dollar and the SDR—though less so than the vehicle-currency basket—and more stable than the vehicle-currency basket against the yen and the deutsche mark. It is clear from the calculations that the actual change in exchange rate arrangements in September 1975 increased considerably the stability of the rupee. It is not clear whether any of the hypothetical “rupees” could have done any better or, indeed, which of these would have done best. The choice among the various standards against which to peg the rupee depends upon the relative importance of stability with respect to each of the other currencies. It is important to realize, however, that the analysis thus far has focused solely on nominal exchange rates, and that, insofar as inflation rates differ among the trading partners, real exchange rates are more important.

IV. Determining the Equilibrium Exchange Rate

It has been variously suggested that the exchange rate should be set to balance the “underlying,” “medium-term,” or “normal” trade balance, or the current account balance, or the overall balance. Before addressing this question directly, it is important to clarify two points. First, a fixed exchange rate system naturally provides financing of transitory deviations from balance. If the exchange rate is to be set to balance some account, it should be set to balance it under normal circumstances, rather than over any particular year. Second, domestic and foreign prices are inextricably bound up with the appropriate exchange rate. It is sensible to discuss the effect of the nominal exchange rate on trade or payments only if we assume a given set of prices.

The question of which balance to choose as the target for exchange rate policy is best addressed by initially considering the example of a stylized economy with trade but no capital account transactions. In this case, obviously, the exchange rate should be set to balance trade. Suppose foreign aid is introduced, and the transfer is fully effected in that the aid inflow is matched precisely by an increase in imports and a consequent trade deficit. Clearly, this does not call for any change in the exchange rate. In general, long-term capital flows should be viewed the same way. 14 For small developing countries, therefore, the overall balance—which consists of trade, services, aid, and long-term capital—is the relevant target for the exchange rate. It must be stressed again that the overall balance of consequence here is some normal overall balance, so that aid grants that are considered unsustainable over the time horizon of the decision makers would not be included.

For some countries, in particular for developed countries, substantial short-term capital flows, which may be either positive or negative in a particular year, differentiate the basic balance from the overall balance. If these short-term capital flows are simply stochastic errors that average out to zero over the long run, it is the basic balance, rather than the overall balance, that is relevant for evaluating the appropriateness of the exchange rate.

An alternative way of formulating this question is to say that the exchange rate should be set to produce an actual accumulation of reserves equal to the desired accumulation. This formulation, however, allows a country to set its exchange rate at a level that leads to an accumulation of reserves and thereby focuses attention on the question of global consistency. If the aggregate of countries desires more reserves, either the stock of international reserves has to increase or some countries’ desires will have to be frustrated. 15

V. The Exchange Rate and Relative Inflation Rates

In Section I, we argued that if relative prices move perfectly to offset exchange rate movements, these movements have no real effect. The illustrative model (equations (3) and (4)) included only traded goods, and it may be instructive first to re-examine that argument from the perspective of the resultant domestic rate of inflation and, second, to introduce nontraded goods.

In our simple model of a small country that exports to the United States and imports from Japan, with prices set respectively in those two countries’ currencies, there are no nontraded goods. The domestic price index can be written simply as

P=(ejPmj)α(eusPxus)βwhereα+β=1(24)

If relative prices within both Japan and the United States are fixed, we can drop the x and m subscripts. If our small country pegs to the U. S. dollar, we can rewrite equation (24) as

P=(1e*Pj)α(Pus)β(25)

or, in terms of proportionate changes, as

P˙=αPj+βPusαe*(25)

If purchasing power parity holds, that is,

e*=PjP˙us

the inflation rate reduces to

P=Pus(26)

Similarly, if the domestic currency is pegged to the yen, the domestic inflation rate will be the same as that of Japan.

If the domestic currency is pegged to a yen-dollar basket—for simplicity, a geometrically weighted basket with the yen having a weight of α and the dollar one of β—we can write

eus=αe*ej=βe*(27)

The domestic inflation rate may then be written as

P=αPj+βPus(28)

—that is, as a weighted sum of the U. S. and the Japanese inflation rates, with weights equivalent to those of the currency basket and the price index. 16

Before nontraded goods are introduced, these results are assured simply by the law of one price. With the introduction of nontraded goods, however, the small country is afforded a measure of independence in choosing its rate of inflation. If the small country with which we are concerned chooses to have an inflation rate different from that of its trading partners—perhaps because of budgetary considerations—purchasing power parity among its trading partners will not suffice to eliminate the real distortions that occur. These distortions, unlike those discussed earlier, are not simply unavoidable costs of the floating exchange rate system but are related to the choice of a domestic inflation rate.

Suppose that the law of one price holds for traded goods and that the domestic currency is pegged to an ideal basket, thereby fixing the effective exchange rate (ef). The inflation of traded goods prices will be a weighted average of trading partners’ rates of inflation for these goods (using an asterisk to denote the foreign price, Pt = Pt*). We can, therefore, write the domestic inflation index as

P˙=γP˙t*+(1γ)P˙nt(29)

Assuming that relative prices within other countries are fixed, the rate of change of the internal terms of trade (IT = Pnt - P t) will be a function of the difference in the inflation rates.

IT˙=f(P˙P˙*)(30)

If the initial relative price PntPt was in equilibrium, and if there has been no structural change in the economy, a nonzero IT leads to a distortion of production patterns and to a misallocation of investible resources. It is possible, however, to change the effective exchange rate—defined as an appropriately weighted sum of domestic currency prices of foreign currencies—at a rate that maintains the equilibrium relative price. Setting

e˙f=P˙ntP˙t*(31)

we find that

P˙t=e˙f+P˙t*=P˙ntP˙t*+P˙t*=P˙nt(32)

This policy is called setting the real exchange rate.

In practice, in order to observe changes in the real exchange rate, we make use of equation (31) in level form to define a log-linear real exchange rate index. Denoting equilibrium values by the subscript o, weights by ωis and the domestic currency price of each of the η trading partners’ currencies by ei we may write 17

In(RER)=rer=Σi=1ηωiIn[(eiPi*P)(PoeioPio*)](33)

This log-linear formulation is useful because it allows us to separate the real exchange rate index into its two constituents—an effective exchange rate (EER) index and a relative price (RP) index. Moreover, defining the logarithm of the nominal effective exchange rate as

In(EER)=eer=Σi=1ηωiIn(eieio)

and the logarithm of the domestic price relative to foreign prices as

In(RP)=rp=Σi=1ηωiIn(Pj*PoPPio*)

the variance of rer around its equilibrium may be written as 18

Variance(rer)=Variance(eer)+Variance(rp)+2Covariance(eerrp)(34)

equation (34) is useful for analyzing alternative currency baskets and movements in the exchange rate. We can envisage three cases that will produce different types of results. In the first case, where the actual exchange rate has moved to offset relative price changes, the covariance term will be large and negative. In the limit, where exchange rate changes have perfectly offset relative price movements, the covariance term and the two variance terms will be identical in magnitude and, since the covariance will be negative, there will be zero variance in the real exchange rate. In the second case, where actual exchange rate movements have been perverse—that is, they have exacerbated the effects of relative price changes—a positive covariance term will not offset the two variances, and the variance in the real exchange rate will be large. Alternatively, the covariance term may be negative but insufficiently large to offset the variance in the nominal effective exchange rate. This is not as unlikely a case as it may appear. In many cases, for historical reasons, a small country will peg its currency to that of a major trading country like the United States or the United Kingdom, although it neither trades much with that country nor experiences a similar pattern of price inflation. The third case worth considering is that where the country pegs its currency to a basket with weights identical with those used in the effective exchange rate calculation. In this case, the variance of the nominal effective exchange rate will be zero, and the covariance term in equation (34) will also be zero. The variance of the real exchange rate will be simply that of relative prices.

If a country is in the situation of the second case described—the case where nominal exchange rate movements exacerbate, rather than offset, relative price movements—it is always possible to suggest that it shift to a basket peg with weights determined by some plausible effective exchange rate calculation. This, in itself, will reduce the variance of real exchange rates, but, having shifted to this basket peg, the country can, in addition, change the value of its currency vis-à-vis the basket to offset any sustained deviation in relative price movements.

The usefulness of the foregoing analysis is best illustrated by returning to our case study of India. Calculations for India of the terms in equation (34), both for the full period of generalized floating and for the basket-peg period, are presented in Table 3 and Chart 2. Four sets of plausible effective exchange rate weights are used; these are identical with the four sets of basket weights used to define the hypothetical “rupees” in Section III. The calculations for the full period show results that are unambiguously in the second of the three classifications discussed. All of the covariance terms are positive, indicating a perverse movement in the nominal exchange rate. When one compares the first and the third row of the table, it is immediately apparent that the variance of the real exchange rate could have been sharply reduced in all cases by simply pegging to any one of the hypothetical baskets.

Table 3

India: Fluctuations of Real Exchange Rate Indices During Two Recent Periods1

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Variances and covariances are measured as percentage deviations about the base date equilibrium. Calculations use wholesale price indices.

Chart 2.
Chart 2.

India: Real Exchange Rate Indices and Their Components, Second Quarter 1973–Second Quarter 1978 1

Citation: IMF Staff Papers 1979, 003; 10.5089/9781451972597.024.A001

1 An upward movement indicates a depreciation of the rupee.For convenience, and because they are graphically similar to the trade-weighted indices, charts for the export-weighted and import-weighted indices are omitted.All indices are based on unit value in the fourth quarter of 1975.

The data in the lower half of Table 3, covering the period during which the rupee has been fixed to a basket, are quite different. In the case of the vehicle-currency weights, the results fall clearly into the first classification discussed. The covariance is negative, and the variance of the real exchange rate index is less than that of the relative price index, suggesting that the exchange rate moved to offset relative price movements. If all the weighting systems showed the same result, and it was believed that the weights of the actual basket were similar to one of them, there would be prima facie evidence that the authorities had not followed a strict peg but had moved the rate—at least within the permissible margins—to offset relative price movements. However, the other three weighting schemes do not show the same result. They show very small, but positive, covariances and variances of the real exchange rate index that are only slightly larger than the variances of the relative price index. This result does not fit unambiguously into any of the three categories in the classification given but falls somewhere between the second and third cases. Both the variances of effective exchange rates and the covariances are close to zero in all three weighting schemes. It seems likely that they are insignificantly different from zero in the actual weighting scheme—which perhaps is broader than that employed here—used by the Indian authorities. In any event, it is clear that the change in exchange rate arrangements of 1975 sharply reduced the variance of the effective exchange rate, thereby effecting a dramatic improvement in the stability of the real exchange rate index. Thus, the Indian experiment with a basket peg must be regarded as a notable success in achieving exchange rate stability.

The question of whether a country should fix its real exchange rate has often been raised. Many countries that run inflation rates significantly different from those of their trading partners do, in fact, have frequent and systematic changes in their exchange rates, thereby effectively fixing their real exchange rates. As has often been pointed out in the theoretical literature, however, the wisdom of any general rule that requires a country to fix the real rate is questionable. 19 Clearly, insofar as shocks to the economy are purely financial, the setting of the real exchange rate will serve to diminish resultant distortions. If, however, shocks to the economy, while transitory, are of a real nature (a crop failure, for example), fixing the real exchange rate could exacerbate the effect of the shock. With a fixed nominal rate, a supply shortfall at home, which tends to raise prices even infinitesimally, will elicit a compensating inflow of goods from abroad and a temporary trade deficit. With a fixed real rate, shortages at home that raised prices would immediately raise prices of imports as the domestic currency depreciated. 20

The most common prescription, then, is for a small country, and in particular for a developing country, to fix its nominal exchange rate in terms of a basket of major trading partners’ currencies. If, however, the real exchange rate index moves out of equilibrium and remains, for any sustained period, substantially above or below the initial equilibrium, there is prima facie evidence of the need for a change in the exchange rate vis-à-vis the basket. In general, such situations will be coupled with a continued accumulation or diminution of external reserves and often, too, with evidence of a misallocation of resources among sectors.

VI. Summary and Conclusions

The foregoing sections examined two questions: (a) What basket of currencies should a small developing country use as the exchange rate standard for its currency? and (b) when are discretionary changes of the value of its currency against this standard warranted?

Section I discusses the costs of exchange rate fluctuations among trading partner countries and shows that over the disequilibrium—that is, the period during which there are departures from PPP—real costs owing to terms-of-trade fluctuations are imposed on the small country under consideration. These external terms-of-trade shocks are completely independent of whatever exchange rate arrangement the country adopts. Section II goes on to show that while external terms-of-trade shocks cannot be influenced by exchange rate arrangements, the distribution of income, the allocation of resources, and the internal terms of trade are sensitive to exchange rate policy. In the final analysis, however, the effect of different types of baskets on income distribution depends upon the structure of the economy, and the effect on resource allocation depends crucially on the relative sensitivity of factors of production in different sectors to price incentives or, alternatively stated, on the price elasticity of allocative mobility. As a result, although a framework for analysis is set up in this section, empirical questions remain, and no final conclusions can be arrived at without reference to the particular economy being investigated.

Section III discusses the difficulty of finding an ideal basket and suggests some proxies for the ideal basket. It goes on to describe a useful way of considering alternative baskets. For each basket, a hypothetical currency is defined with its value fixed in terms of the associated basket. It is possible then to compare, over some chosen historical period, the variance of the actual currency and each of the hypothetical currencies against the currencies of each of the country’s major trading partners. This is a suggestive way of comparing the alternative baskets, but, although it provides a useful perspective on the exchange rate history, it does not provide any unambiguous criteria for determining the best basket. A case study of India is used to illustrate the methodology.

Which account of the balance of payments is the appropriate target of exchange rate policy? This question is addressed in Section IV, which concludes that if reserves are at an equilibrium level, the exchange rate should be set to balance the overall balance of payments, or, alternatively stated, the exchange rate should be set to match the actual and desired accumulation of reserves. It is stressed, however, that the relevant overall balance is some medium-term or normal overall balance rather than the balance over any particular period, which may be influenced by transitory factors.

Section V first, on the assumption that PPP holds, shows that the adoption of different standards for fixing the value of the domestic currency would result in different domestic inflation rates. Then, introducing nontraded goods and the possibility of divergent rates of inflation between the home country and its trading partners considered as a group, it shows how the real exchange rate, or the internal terms of trade, is really the important variable both for resource allocation and the balance of payments. A real exchange rate that is too low—or, alternatively stated, an overvalued domestic currency—will distort allocation toward an excessive production of nontraded goods and an insufficient production of traded goods. Consumption will be distorted in precisely the opposite direction, and these distortions will serve to increase the trade balance deficit or to reduce the surplus. Clearly, therefore, in order to judge the appropriateness of the exchange rate and the need for discretionary changes, it is important to monitor developments in the real exchange rate.

At this point, two caveats are introduced. First, changes in the real exchange rate should not be the only indicator used to judge the necessity for a change in the nominal exchange rate. Various other indicators, such as reserve developments and the transitory or permanent nature of the shocks buffeting the economy, are important. Second, no simple formula that fixes the real exchange rate should be followed. Such a formula could serve to exacerbate the impact of transitory real shocks by impeding the normal reserve cushioning function of a fixed exchange rate system.

In order to illustrate the arguments in this section, data from India are again introduced. A real exchange rate index is defined, and its variance is decomposed into the variance of the nominal effective exchange rate, the variance of relative prices, and the covariance of the two. Two results are possible: (a) If the nominal exchange rate had moved to offset relative price movements, the real exchange rate index would have fluctuated less under the actual exchange rate policy pursued than under a policy that fixed the effective exchange rate; (b) if, alternatively, nominal exchange rate movements were perverse—that is, if they tended to exacerbate relative price fluctuations—a policy of fixing the effective exchange rate would have reduced the variance of the real exchange rate. The case study of India unambiguously supports the latter interpretation if the entire period of generalized floating is considered. During the more recent basket-peg period, the results are mixed and the conclusions not as clear cut. It is clear, however, that since September 1975 the basket peg has succeeded in stabilizing the real exchange rate.

An important qualification must be made with respect to the computations in the paper. The historical comparison of different exchange rate regimes holds all other variables at their historical levels and thereby abstracts from the simultaneous nature of exchange rate determination. Insofar as each different regime would elicit a different response from other variables in the economy, which would, in turn, feed back into the determination of real and nominal exchange rates, there is a simultaneity that is ignored. Ideally, one would characterize the different regimes as different reaction functions in a complete model of the economy that was capable of picking up the interaction among all the relevant variables. It is not clear, however, that the additional complexity and the investment in modeling is warranted by the extent of the bias. In any event, the computations used in this paper are best regarded as relatively cheap first approximations.

In general, the discussion and the evidence adduced suggest that there is a particularly cogent case to be made for adopting a basket peg when a country has a rate of inflation that is not persistently different from the weighted average inflation rate of its trading partners. There will be less likelihood of a need for frequent discretionary changes in the exchange rate if the country pegs to an appropriately weighted basket than if it pegs to a single currency. The choice of a properly weighted basket could serve, therefore, to minimize the need for discretionary changes.

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*

Mr. Lipschitz, economist in the Asian Department, is a graduate of the London School of Economics and Political Science.

In addition to colleagues in the Fund, the author is indebted to Carlos Rodriguez and John Williamson for comments on earlier drafts of this paper.

1

The weight of various factors in the actual, historical choice of an exchange rate regime by a number of countries is discussed in Heller (1978). There is a vast literature on factors that ought to be taken into account in such a choice. Recent articles are Black (1976), Fischer (1977), and Lipschitz (1978).

3

Officer (1976) provides a useful survey of the voluminous literature on PPP. Two interesting recent papers on the topic are Sundararajan (1976) and Brillembourg (1977).

4

This is neatly illustrated in Knight (1976).

5

See Isard (1977) and Kravis and Lipsey (1977).

6

See Artus (1977).

7

In this section and in Section II, the author is indebted to discussions with Arturo Brillembourg and to Brillembourg (1978).

9

This is simply the extreme case of a country for which an export-weighted basket and an import-weighted basket are quite different. The example can be easily generalized.

10

Bruno (1976) is an excellent discussion of the questions addressed in this section. Dornbusch (1973) reintroduced many of these considerations into the recent literature.

11

The basket used here is a geometrically weighted average of the yen and the U.S. dollar.

12

In countries with rapidly adjusting expectations in an inflationary environment, confusion between relative price changes and changes in the overall price index can generate expectations that undermine incomes policies and sustain inflationary pressures. Lucas (1973) provides an interesting discussion of this point.

13

The MERM is developed in Artus and Rhomberg (1973). Bélanger (1976) describes a similar analysis for primary producing countries; Feltenstein, Goldstein, and Schadler (1979) provide a more complete approach to this problem.

14

Long-term capital that is used to finance consumption, or investment in nontraded goods with prices that are above equilibrium, provides the exception to this generalization.

15

Unless the global supply of reserves is infinitely elastic, so that reserves are demand-determined. This, however, implies that only the aggregate of countries besides the reserve currency countries could run a surplus while the aggregate of reserve currency countries would have to run a deficit.

16

Where these two sets of weights differ, the weights of the Japanese and U.S. inflation rates in the domestic rate are more complicated combinations of the two sets of weights.

17

Ideally, this should be

In(RER)=Σi=1ηωiIn[(ejPit*Pnt)(PntoeioPito*)]

An index of nontraded goods prices is not usually available but, assuming relative prices within partner countries are fixed, so that P* is a good proxy for Pt*, the ratio of the overall price indices given in equation (33) is a good proxy.

18

Black (1976) discusses similar calculations.

19

See Fischer (1977), Lipschitz (1978), and Gray (1978). Gray develops an interesting parallel for the setting of real versus nominal wage rates.

20

John Williamson has pointed out that this mechanism assumes that price adjustments precede quantity adjustments. Of course, insofar as there are no price adjustments—owing, for example, to perfect commodity arbitrage—there is no distinction between fixing the real or the nominal exchange rate after a transitory real shock.

IMF Staff papers: Volume 26 No. 3
Author: International Monetary Fund. Research Dept.