Homepage   International Economics

International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 152-176.

The Monetary Dynamics of International Adjustment under Fixed and Flexible Exchange Rates1

Robert A. Mundell

The basic criticism hitherto advanced against a system of fixed exchange rates -- that the powerful instruments of monetary policy are tied to the goal of external balance thereby ruling out a domestic rate of interest compatible with full employment -- has been the subject of continued debate over past decades. First advanced over a century ago during the bullionist controversy, and revived in this century by Fisher and Keynes, the argument poses the conflict between internal stability (stable employment and price levels) and external stability (balance-of-payments equilibrium at a fixed exchange parity). In the absence of trade restrictions, which cause inefficiency and invite retaliation, one of the targets implicit in the concepts of internal and external stability must be abandoned. But, so the argument runs, full employment is a prime goal of public policy, balance-of-payments equilibrium is a long-run necessity, and sufficient price flexibility does not exist in the modern world: The rate of exchange must therefore be freed.

The argument is based on money illusion: The community is unwilling to accept variations in real income through changes in money prices, but it will accept the same changes in real income through adjustments in the rate of exchange. A flexible exchange system may then be interpreted as a device for providing a more acceptable means (than employment changes) of altering the real income of the community. But what if money illusion is absent? Then, it is argued, there is no reason for changing to a system of flexible exchange rates: " If internal prices were as flexible as exchange rates, it would make little economic difference whether adjustments were brought about by changes in exchange rates or by equivalent changes in internal prices."2

In this chapter it will be demonstrated that although this view, under certain circumstances, may be valid in statics, it is entirely erroneous in dynamics. The dynamical differences between the two systems are based on an inversion of the roles, in the dynamic adjustment process, of the terms of trade and the rate of interest. In the fixed exchange system money income (the price level) moves to equilibrate the market for domestic goods and services, and monetary policy is directed at the requirements of the foreign balance; but in the flexible exchange system the rate of exchange moves to correct external disequilibrium, and monetary policy aims at the goal of internal stabilization. These dynamical dissimilarities have important implications for economic policy.

A dynamic analysis of the two systems is necessary to provide a description of the relative merits of fixed and flexible exchange rates-one system may work well (dynamically) under one set of static parameters and speeds of adjustment but badly under another. Moreover, the type of model that such an analysis requires reveals a conspicuous gap in the international trade literature. Since the days of Hume's classic analysis of the price-specie-flow mechanism, the adjustment process has been rightly recognized as dynamic. Yet it is seldom stated, or even hinted, in expositions of the gold-standard mechanism that an explicit dynamic model is necessary for examining processes that occur simultaneously but at different speeds. The conclusions that follow from this rich field of analysis are essential to even a minimal understanding of the meaning of the adjustment mechanism.

This chapter offers a simplified exposition of the dynamics of the international adjustment process and provides preliminary answers to the following questions: l. Under what conditions will one system be stable while the other system is unstable? 2. How is the cyclicity or directness of the paths to equilibrium, in each system, affected by the extent to which capital is internationally mobile? 3. To what extent should the central bank be concerned, in the fixed exchange system, about the absolute level of its reserves, as opposed to the situation in the current balance of payments? 4. To what extent can offsetting central bank action stabilize a system that is inherently unstable because of speculative capital movements?

I assume throughout that money prices are flexible unless stabilized by the monetary authorities. The purpose of this assumption is to maintain the static and real equivalence of the two systems and thereby isolate most clearly the dynamical dissimilarities. It will nevertheless become clear that the main conclusions would hold in an underemployed economy in which prices were rigid downward and flexible upward.

The Static System

The economic system to be investigated below is dominated by the conditions of equilibrium in two markets: the market for domestic goods and services, and the market for foreign exchange. Equilibrium in the goods-and-services market is assumed to prevail when the current world demand for domestic goods and services is equal to the current supply of domestic goods and services, a condition which is equivalent to the equality of the excess of domestic saving over domestic investment and the trade balance surplus. When the excess of domestic saving over domestic investment is greater than the trade balance surplus there is deflationary potential, and when it falls short of the trade balance surplus there is inflationary potential.

Equilibrium in the foreign exchange market requires equality of foreign exchange payments and receipts (excluding central bank transactions) or, equivalently, equality of the rate of lending (net capital exports) and the trade balance surplus. When this equality does not hold, there is a balance-of-payments surplus or deficit, depending on whether lending is greater or less than the trade balance surplus.

I assume that the goods-and-services market and the foreign exchange market are subject to two main influences: the domestic rate of interest, and the ratio of home and foreign prices (the terms of trade). The rate of interest is assumed to be determined by the monetary policy of the central bank -- which means that the latter must always supply funds to the public (through, say, open market operations) to make any given interest rate compatible with equilibrium in the capital market.3 I also assume that all foreign prices, incomes, and interest rates are constant during the period under consideration; this means that changes in the terms of trade can result only from changes in the exchange rate or variations in the domestic price level.

Given these assumptions it is possible to construct a simple geometric interpretation of the forces governing the rate of interest and the terms of trade. Consider first the foreign exchange market. This market can be divided into two components: the balance of trade governed primarily by the terms of trade, and the net flow of capital, influenced chiefly by the rate of interest. To every level of the terms of trade there will correspond a given balance of trade, and for every rate of interest there will be a specific rate of lending. At high levels of the terms of trade, other things equal, the balance of trade will be smaller than at low levels of the terms of trade.4 Similarly, at high rates of interest the net inflow of capital will be larger, or the net outflow will be smaller than at low rates of interest. For any given rate of interest, therefore, an increase in the price level or an appreciation of the rate of exchange worsens the balance of payments; and for any given level of the ratio of export to import prices, an increase in the rate of interest improves the balance of payments.5

One can now conceive of a schedule indicating what the terms of trade would have to be, for different rates of interest, to make the country's foreign exchange payments equal to its foreign exchange receipts (or its net capital exports equal to the balance-of-trade surplus). This curve, which we shall refer to as the "foreign-balance schedule," is plotted as the FF line in Figure 11-1. At any point on this line the balance of payments is in equilibrium, although its composition changes in favor of higher rates of borrowing and higher balance-of-trade deficits as we move upward and to the right along it. Any point below or to the right of FF represents a point of balance-of-payments deficit: The rate of interest is too low, or the price level or exchange rate is too high, for equilibrium. Similarly, any point above or to the left of FF indicates a point of surplus in the balance of payments: The rate of interest is too high, or the relative price of domestic goods is too low, for equilibrium. The economic system can be in equilibrium only on this line.

Figure 11-1. The Determination of Equilibrium.

It may be seen that there is a whole series of combinations of rates of interest and terms of trade at which the balance of payments is in equilibrium. But the entire economic system cannot be in equilibrium unless there is also balance in the market for goods and services. For this market to be in equilibrium, the balance of trade must equal the excess of saving over investment. Now the balance of trade, as we have seen, is affected primarily by relative prices: A rise in the price level or exchange rate worsens the balance of trade so higher levels of the terms of trade tend to cause an excess supply of goods and services. We must add to this, however, the deflationary effect of an increase in the price level or the exchange rate on the rate of saving. Because at high levels of the terms of trade real income is higher than at low levels of the terms of trade, the level of saving also tends to be higher.6 An increase in the price level for the exchange rates, therefore, is deflationary for two reasons: It lowers the balance of trade and it increases saving. On the other hand, changes in the rate of interest influence primarily the rate of investment spending. At high rates of interest the rate of investment is lower than at low rates of interest, so an increase in the interest rate is deflationary. Both increases in the price level or the exchange rate, and increases in the rate of interest, are deflationary.

One can now construct an "internal balance schedule" for the goods-and-services market analogous to the foreign balance schedule developed for the foreign exchange market. From any point on this schedule an increase in the rate of interest causes deflationary pressure and a fall in the price level or the exchange rate causes inflationary pressure. A hypothetical rise in the rate of interest, starting from a position of balance, must therefore be compensated by a fall in the price level or the exchange rate in order to retain balance. This means that the internal balance schedule, plotted as the XX line in Figure 11-1, must have a negative slope. At any point above and to the right of this line there is deflationary potential, and at any point below and to the left of this line there is inflationary potential. Only along XX is the goods-and-services market in equilibrium.

We have now described the conditions necessary for equilibrium in each of two markets. At any point on FF the balance of payments is in equilibrium, and at any point on XX the goods-and-services market is in equilibrium. The entire economic system can be in equilibrium only at the point common to both schedules, Q. The equilibrium interest rate is therefore r0, and the equilibrium terms of trade is p0.

It is necessary to point out, however, that equal percentage changes in the price level and exchange rate have different monetary effects inasmuch as a price-level increase reduces, while an exchange-rate appreciation increases, the real value of cash balances. An exact identification between the two is possible, however, if an exchange-rate appreciation is accompanied by an equal percentage reduction in nominal cash balances, or, alternatively, if an increase in the price level is accompanied by an equal percentage increase in nominal cash balances. Under these monetary assumptions there is no reason to expect a change in the terms of trade achieved through price-level adjustments or exchange-rate variations to have differential effects on the level of saving or the division of expenditure between home and foreign goods, except insofar as other contractual obligations fixed in terms of domestic or foreign currency have to be taken into account.

The Dynamic Systems

The static system described by the foreign balance schedule and the internal balance schedule provides a convenient framework for analyzing the dynamic responses appropriate to systems of fixed and flexible exchange rates. These responses are determined in part by free market reactions and in part by the stabilization policy of the central bank. In the absence of stabilization there is a tendency for the price level to rise or fall, depending on whether there is excess demand (inflationary potential) or excess supply (deflationary potential) in the goods-and-services market, and a tendency for the exchange rate to rise or fall depending on whether there is a surplus or deficit in the balance of payments. But, if the monetary authorities stabilize the exchange rate they must be prepared to buy and sell foreign exchange reserves at a fixed price and if they stabilize the price level they must buy and sell goods and services at a fixed price. To protect their reserve position (of foreign exchange in the one system, or of goods in the other system) they will pursue a monetary policy that tends to relieve the disequilibrium.

Consider first the case where the central bank pegs the exchange rate. It will raise the interest rate when there is a balance-of-payments deficit, and lower the interest rate when there is a balance-of-payments surplus.7 In this case the price level is free to respond to disequilibrium in the market for goods and services. Thus the interest rate will be rising at any point below and to the right of the foreign balance schedule and falling at any point above and to the left of the foreign balance schedule. Similarly, the price level will be rising at any point below and to the left of the internal balance schedule and falling at any point above and to the right of this schedule. These dynamic responses are described by the arrows in Figure 11-2.

Figure 11-2. Adjustment under Fixed Exchange Rates.

The points A, B, C, and D represent four points not on either of the two schedules. From the point A, the interest rate is rising because of the balance-of-payments deficit, and the price level is falling because of the deflationary gap. Similarly, at the point B both the interest rate and the price level fall; at the point C the price level rises and the rate of interest falls; and at the point D both the price level and the interest rate rise.

One of the arrows in each quadrant points in the direction of equilibrium, whereas the other arrow points in a direction that suggests a cyclical motion around equilibrium. This means that the equilibrium Q is a stable equilibrium, and that it may be approached cyclically. Consider, for example, the point Z. This point is in the same quadrant as the point D, so, from Z, the price level rises because of inflationary pressure and the interest rate rises because of the deficit in the balance of payments. These changes work in opposite directions on the foreign balance-capital is attracted while the balance of trade is worsened-but in the same direction on the goods-and-services market -- both the interest-rate and price-level changes relieve excess demand. The goods-and-services market is therefore equilibrated before the foreign balance is brought into equilibrium. Now, at the point S on the XX line, the internal market is in equilibrium but there is a deficit in the balance of payments; the interest rate thus continues to rise and this works to produce deflationary pressure in the goods-and-services market. In quadrant A the interest rate rises and the price level falls. Both these forces now operate to relieve the external disequilibrium, but they operate in opposite directions on the internal market; this time the foreign exchange market is cleared before the goods-and-services market. Now the path of the interest rate and the price level moves into quadrant B, in which the interest rate is lowered and the price level falls; and so the cycle continues in a counterclockwise direction.8

Now consider the flexible exchange system in which the central bank stabilizes the domestic price level. When there is an inflationary gap in the market for goods and services the central bank will tighten credit, raising the interest rate; and when there is a deflationary gap it will ease credit conditions, lowering the interest rate.9 On the other hand, the rate of exchange is in this system, free to move to preserve external balance. Under these conditions the interest rate will be rising at any point below and to the left of the XX line in Figure 11-3 and falling at any point above and to the right of this schedule. Similarly, the rate of exchange will be falling at any point below and to the right of the FF line because of the payments deficit, and rising at any point above and to the left of this line. The points A, B, C, and D represent four typical points in the four quadrants, and the directions of the arrows describe the paths of the interest rate and the exchange rate.

Figure 11-3. Adjustment under Flexible Exchange Rates.

As in the fixed exchange case one of the arrows always points in the direction of equilibrium, while the other arrow tends to impart a cyclical motion to the system; the system is stable but equilibrium may be reached cyclically. (Consider the point Z, referring to the same point of real disequilibrium as that analyzed in the fixed exchange case. From the point Z the exchange rate falls because of the external deficit, and the interest rate rises because of the inflationary pressure. Both changes work to correct the foreign balance, but they work in opposite directions on the internal market; the foreign balance is therefore equilibrated before the inflationary gap is relieved. The cycle may continue, as in the fixed-exchange system, but it moves in an opposite direction. The path to equilibrium under flexible exchange rates is clockwise but under fixed exchange rates it is counterclockwise.

Although the cycles around the real equilibrium Q may occur, they are not inevitable. From any of the quadrants the approach to equilibrium may be direct, depending, in part, on the relative speeds with which the interest rate and relative prices move in response to disequilibrium. I have described the cycles that may occur only to emphasize the difference in the nature of the approach to equilibrium. This difference does not, in itself, demonstrate that one system is superior to the other. But the difference in the paths that the interest rate and the terms of trade follow assumes more importance as we consider different values of the static parameters and the importance to the central bank of a given level of foreign exchange reserves.

The Importance of Capital Mobility

To show how the nature of the path to equilibrium is affected by the static parameters and the speeds with which the authorities respond to disequilibrium in each system, we shall demonstrate that one system may work well (in some definable sense) if capital is internationally mobile but badly if capital is immobile. To set the stage for the analysis, suppose that a position of initial equilibrium is disturbed by a reduction in the rate of interest below its equilibrium level. This creates inflationary pressure and a very large balance of payments deficit in the case, with which we shall begin, where capital is highly mobile.

Under fixed exchange rates and virtually perfect capital mobility, the approach to equilibrium is direct rather than cyclical.10 This may be understood by noting that the disturbance immediately creates a rapid rise in the rate of interest (because of the large balance-of-payments deficit) relative to the change in the domestic price level (due to the inflationary pressure). In the extreme case of perfect mobility the interest rate would bounce back to equilibrium without any increase in the domestic price level. In the less extreme case, on the other hand, the price level rises somewhat above its equilibrium value, and this, in conjunction with rapidly rising interest rates, results in deflationary pressure; the system moves into a quadrant in which there is deflationary pressure and balance-of-payments deficit. From this quadrant the interest rate will rise and the price level will fall until equilibrium is reached directly, there being no possibility of the rate of interest rising above the level required for the final equilibrium in the balance of payments. The process of adjustment will therefore be noncyclical under fixed exchange rates and perfect capital mobility.

This result contrasts with that obtaining under flexible exchange rates and high capital mobility, for in that case the deficit in the balance of payments and inflationary pressure results in a fall in the exchange rate and a rise in the rate of interest. But the exchange-rate movement swamps the interest-rate adjustment because of the high capital mobility. The exchange rate moves below its equilibrium level until external balance is again reached at a higher interest rate. Yet this position cannot be an equilibrium one, for there remains inflationary pressure in the commodity market, prompting further increases in interest rates and generating a balance-of-payments surplus, which in turn initiates a rapid appreciation of the exchange rate. The path of the interest rate and the exchange rate then moves past the point where internal balance is achieved, and a downward movement of the interest rate commences. The system does eventually get to equilibrium, but it can only approach it after oscillating around it.

The opposite conclusions tend to hold in the case where capital is immobile. In the fixed-exchange-rate case an interest rate below its equilibrium level creates inflationary pressure and a rise in the price level, which in turn generates a balance of trade and payments deficit, prompting a rise in the interest rate. The goods-and-service markets become cleared at a higher interest rate and increased price level, but there remains a balance-of-payments deficit. The interest rate continues to increase and the price level begins to fall until equilibrium is reached after a series of cycles, or at once, depending partially on whether interest rate policy adapts rapidly or slowly, respectively, to disequilibrium in the balance of payments. An oscillatory approach to equilibrium is possible, but it is not certain.

Under flexible exchange rates, on the other hand, oscillations are not possible if capital is immobile. An interest rate below equilibrium implies inflationary pressure that is promptly corrected by a rise in the interest rate. No change in the exchange rate need ensue. Yet, even if the exchange were above equilibrium while the interest rate were below it, such that there existed inflationary pressure and a balance of payments deficit, the exchange rate would depreciate and the interest rate rise until equilibrium is reached directly. There is no possibility of an oscillatory approach to equilibrium.

These conclusions are important for their own sake because they imply that a flexible exchange system may not work smoothly for an economy in which capital flows are highly sensitive to interest rates but may work better than a system of fixed exchange rates if capital is immobile. There is a simple economic explanation of this fact. Under fixed exchange rates, the interest rate corrects the balance of payments, and it is exceedingly effective in doing so provided the balance of payments is directly influenced substantially by the interest rate, which is the case when capital is mobile; if capital is immobile, however, the interest rate affects the balance of payments only insofar as it first creates inflationary or deflationary pressure in the goods-and-services market. The fixed-exchange-rate system, in other words, tends to work well when the interest rate has a direct impact on the balance of payments because the interest rate is itself the variable that adapts to the balance of payments.

A corresponding generalization holds under flexible exchange rates. When capital is immobile, the interest rate, which adapts to the requirements of internal balance, has a direct effect upon the goods-and-services market, whereas the exchange rate has a direct effect upon the balance of payments. But when capital is highly mobile, the interest rate effect upon capital imports swamps the interest-rate effect upon the goods-and-services market, so that internal stability is achieved more by the indirect effect of altered interest rates in attracting or repelling capital from abroad, and thus appreciating or depreciating the exchange rate, than it is by the direct effect upon the goods-and-services market itself. This indirectness of the mechanism imparts a cyclical tendency to the adjustment process.

We have now demonstrated (mathematical proofs are supplied in the Mathematical Appendix) that the ease of correcting a disequilibrium under systems of fixed and flexible exchange rates depends partially on the extent to which capital is internationally mobile. If capital is highly mobile the fixed exchange dynamic system leads directly to equilibrium, while the flexible exchange mechanism generally leads to cycles around equilibrium. On the other hand, if capital flows are insensitive to changes in the rate of interest, the fixed exchange system leads to cycles if the central bank reacts too quickly to a foreign deficit, whereas the flexible exchange system leads directly to equilibrium regardless of the speeds of adjustment.11

These conclusions illustrate a more general proposition, which is referred to below as the principle of effective market classification. Dynamic systems tend to work better when variables adapt dynamically to those markets on which they have a (relatively) dominant influence. In devising policy schemes, therefore, it is important to allocate particular instruments to those targets on which they exert the most influence.

The Stock of Reserves

As a description of central bank policy in the modern world, the validity of the above analysis of the fixed exchange system is subject to one important qualification. I have assumed that the central bank eases or tightens credit conditions depending on whether current foreign exchange receipts exceed, or fall short of, current foreign exchange payments. This leaves out of account the lingering effects of past deficits and surpluses on central bank policy. But past deficits and surpluses affect the level of foreign exchange reserves, so this implicitly assumes that the central bank is concerned only with changes in the level of reserves, and not at all with the absolute level, at any point in time. It is unrealistic, however, to suppose that the central bank would react to disequilibrium in the balance of payments in the same way at substantially different levels of reserves. If reserves are excessively high, the authorities are more likely to allow a deficit in the current balance to continue before remedial action is taken; and if reserves are too low, imperiling confidence in convertibility, the central bank is likely to keep tighter monetary conditions until reserves are again built up.

In this section we shall consider the extreme case where the central bank is concerned only with the level of stocks, in order to isolate the effects of this response. We assume that there is a normal or "optimum" level of reserves and consider what happens if the central bank aims at maintaining this level by raising or lowering the interest rate in proportion to the discrepancy between the desired and actual level. As before, we assume that the price level responds to any disequilibrium in the goods-and-services market.

For purposes of exposition it will be convenient first to drop some of the assumptions and then gradually reintroduce them. Suppose first that the price level does not exert any influence on the balance of payments; this means that there can be only one rate of interest at which there is external balance. The system is represented in Figure 11-4.

Figure 11-4.

Let the interest rate be initially r0 and the price level p0, so that there is equilibrium in the balance of payments and the goods-and-services market. This does not now imply equilibrium in the entire system because the level of central bank reserves may not be at the desired level. Suppose that reserves are below the desired level.

Consider first the movement of the system if the price level is fixed. From Q the rate of interest rises (because reserves are below the desired level) and capital is attracted from abroad. As the foreign balance improves reserves accumulate, reducing the discrepancy between the desired and actual level and slowing down the change in the rate of interest. But the rate of interest nevertheless continues to rise until stocks reach the required level. At a point such as S, the rise in the rate of interest stops: Reserves are at the desired level . But the point S cannot be an equilibrium point, because there is a surplus in the foreign balance. Reserves begin to accumulate and the rate of interest is moved downward. Throughout the return path from S to Q the foreign balance is in surplus, so reserves increase until the point Q is reached. At Q the discrepancy between actual and desired reserves reaches a maximum, and so does the speed with which the rate of interest is changing. The rate of interest now falls below Q and the excess reserves are gradually depleted until another point T is reached at which reserves are in equilibrium. The point T is below Q by as much as the point S is above Q. The cycle therefore continues in pure undamped harmonic motion with an amplitude of the interest rate fluctuation equal to ST. The motion exactly resembles that of a frictionless pendulum pivoted above Q.

This cycle applies only when the price level does not respond to disequilibrium in the market for goods and services. In other words. we have thus far assumed a speed of response in the goods-and-services market equal to zero. But consider now the opposite case, where the price level responds instantaneously (that is, an infinite speed of response). In this case the initial rise in the rate of interest from Q causes deflationary pressure which induces an immediate fall in the price level. But above we have tentatively assumed that the price level does not affect the balance of payments (FF is horizontal) so the cycle of the interest rate, central bank stocks, and the foreign balance goes on undisturbed. The only difference from the previous case studied is that a price cycle is added. The interest-rate cycle induces the price cycle, but the price cycle does not, in turn, affect the interest-rate cycle. The cycle is described in the graph by movements back and forth along the segment VW of the XX line. The amplitude of the interest-rate fluctuation is the same as before, and the amplitude of the price-level fluctuation is given by the horizontal distance between V and W.

We have now examined two extreme cases: one in which the price level is unresponsive to excess demand in the goods-and-services market, and one in which it is instantaneously responsive. In the normal intermediate case the path of the initial departure from Q will fall somewhere between QS and QV. Eventually a point such as L is reached at which reserves are equal to the desired level. The slope of the path at L must be horizontal, since the interest rate reaches a maximum at that point. From L the price level continues to fall (if L is to the right of XX); and, because of the balance-of-payments surplus and the gradual accumulation of excess reserves, the interest rate begins to fall. When point K is reached, the decline in the price level is reversed, but the interest rate continues to fall until the balance of payments has been in deficit long enough to bring reserves down to the desired level. At point J reserves are again in equilibrium, but, because the balance of payments is in deficit, the cycle continues. The path of the interest rate and the price level is indicated by the elliptic orbit; it is an undamped cycle with the same amplitude of the interest rate as before.

All the above systems have resulted in pure cycles of the interest rate, the level of foreign exchange reserves, the balance of payments, and, in the last two cases, the price level; these cycles were neither damped nor undamped. But once we relax the assumption that the price level has no effect on the foreign balance, the conservative motion of the system turns into unstable motion. When the foreign-balance schedule has a positive tilt, price changes react on the balance-of-payments schedule and subject the rate at which reserves are being accumulated or run down to sustained "shocks" that continually increase the amplitude of the fluctuations. The system therefore leads to ever-increasing cyclic movements of reserves and to the paradoxical conclusion that the central bank needs an infinite quantity of reserves to follow a policy designed to maintain any given level of reserves!

I have not presented this system as an actual description of the policy followed by any central bank, or to suggest that the central bank should never be concerned with the level of foreign exchange reserves. It is more reasonable to suppose that the central bank governs its action according to both the level of reserves and the condition of the current balance. If reserves are too low, an interest rate high enough to develop a surplus in the current balance can be maintained, allowing reserves to build up gradually. Such a system is not necessarily unstable, as is shown in the Mathematical Appendix. It is important to note, however, that too great a concern for foreign exchange stocks may lead to instability. And because central banks are prompted to act more vigorously when reserves are too low than when reserves are too high,12 an effective system of international payments based on fixed exchange rates must be one which provides a reasonably high degree of international liquidity. The social cost of these reserves -- which is necessarily positive only when commodity money is used as international currency -- must then be weighed in considering the relative merits of fixed- and flexible-rate systems.

Speculation and Stability

The preceding analysis provides a useful introduction to an important kind of speculation inherent in the fixed exchange systems of today. The confidence in the permanence of existing exchange parities that prevailed under the gold standard no longer exists today. The decline of confidence means that the safety of capital values becomes a prime factor determining the international location of short-term capital. Fear of inconvertibility or devaluation often swamps the effects of small differences in rates of interest between money markets and encourages capital outflows. But confidence is generally linked to the level of exchange reserves. Other things being the same, confidence is higher the larger are the central bank holdings of foreign exchange: An increase in reserves makes a speculator more bullish with regard to the exchange value (or degree of convertibility) of a currency. The balance of payments therefore becomes a function of the level of exchange reserves with an improvement in the latter stimulating a capital inflow or restraining a capital outflow.

But is a system based on this type of speculative response stable? Intuition leads one to suspect that it may be stable or unstable, depending on the strength of opposing forces. Speculators and the central bank engage in a fight for reserves. On the one hand, the central bank acts, through interest rate changes, to correct any foreign imbalance; on the other hand, speculators operate to exaggerate any imbalance because of the change in reserves and confidence.

Figure 11-5.

To show that this view is substantially correct consider Figure 11-5 and the initial disequilibrium W. The deficit in the balance of payments and the inflationary gap cause the interest rate and the price level to rise. But the deficit also lowers the level of exchange reserves and causes the foreign balance schedule itself to shift in a northwesterly direction. There exists a different position of this schedule for every level of foreign exchange reserves. Now it may easily be seen that the stability of the system depends partially on how quickly the central bank reacts to a foreign deficit compared with the extent to which the FF curve is shifted because of speculation. For a new equilibrium to be established, the interest rate must move sufficiently fast, and foreign capital must respond quickly to the movement in the interest rate, to arrest (or reverse) the shift in the foreign balance schedule. A new equilibrium may, for example, be established at point V.

On the other hand, the interest rate may move too fast, turn the deficit into a surplus, and begin a downward path "chasing" the foreign balance schedule in the other direction. But in any case the system may be stable or unstable, cyclical or asymptotic, depending on the particular static parameters and speeds of response. It should be clear that a low sensitivity of the foreign balance to changes in reserves, a high sensitivity to the rate of interest, and relatively rapid response of the central bank are stabilizing.13 It is no longer true that central bank adjustment to stocks of reserves is destabilizing.

The precarious nature of the stability conditions of the above system-its sensitivity to speculative capital movements-is based on the reactions of speculators to changes in central bank stocks. It has no practical counterpart in a system of flexible exchange rates because central banks, in that system, do not need to hold foreign exchange reserves; and, if they do hold reserves, the central banks may use them merely to even out what they consider "sporadic" fluctuations in the exchange rate.14

There may, however, be a type of speculation which applies to flexible exchange, but not to fixed exchange, systems. The greater ease, and lower storage costs, of buying and holding units of currency in the flexible exchange system than of purchasing collections of goods in a fixed exchange system may induce more direct speculation in the former system. Speculators may interpret a current change in the exchange rate as a signal indicating further changes in the same direction, or as a signal indicating that the direction in which the rate is changing will be reversed. Proponents of flexible exchange rates have argued persuasively that, when the exchange rate appreciates or depreciates because of a change in import or export demand-and-supply schedules, speculators are likely to consider this a signal for an eventual movement of the exchange rate in the opposite direction, basing their expectations on the tendency for elasticities to be greater in the long run than in the short run. The more conventional view, however, which was widespread after World War II, urges that a change in the exchange rate is likely to be interpreted as a signal for further changes in the same direction because speculators may extrapolate past trends. This view is certainly confirmed during periods of monetary instability-during inflation the exchange rate would, in a free market, depreciate more or less at the same rate that other prices are rising-but it is also irrelevant in this case: The main advantage of a flexible exchange system is that it permits central bank authorities to control price-level fluctuations.15

Nevertheless, it is easily proved that a system of flexible exchange rates may be stable even if speculators interpret a given variation in the exchange rate as a signal of further changes in the same direction. This is demonstrated in the Mathematical Appendix. Furthermore, stability depends both on the behavior of speculators and the speed with which the exchange rate responds to external imbalance. If, therefore, the system is unstable because of speculative capital movements, central bank intervention in the foreign exchange market can slow down the speed of the fluctuations and make the system stable. But this use of exchange equalization funds would not be necessary if speculators expected exchange rate changes to be reversed in direction, or if the extent of "destabilizing" speculation is small.

The Principle of Effective Market Classification

Before concluding, it may be useful to express in more general terms the problem initially posed. Society has two goals: full employment and balance-of-payments equilibrium. To achieve these goals it has two free variables: the terms of trade (the price level or the exchange rate) and the rate of interest (financial policy). Monetary authorities may stabilize the exchange rate, using financial policy to maintain external equilibrium and allowing the price level to maintain internal equilibrium; or they may stabilize the price level, using financial policy to maintain internal balance and allowing the exchange rate to preserve external balance. Which of these policies should be followed?

The answer was seen to depend on the values of the parameters and the speeds of adjustment. In the simple systems first studied, for example, it was demonstrated that the fixed-exchange-rate system operates most effectively if capital is highly mobile, whereas the flexible-exchange-rate system works best if capital is immobile. (" Best " is judged in terms of the directness of the approach toward equilibrium.) These conclusions have a useful application to economic policy. Equally interesting, however, is the general principle they illustrate.

The reason a high mobility of capital improves the effectiveness of the fixed-exchange-rate system is that the adjusting variable (the rate of interest) has a direct effect on the market to which it responds (the balance of payments) and the reason a low mobility of capital may lead to cycles in this system is that the rate of interest can affect the balance of payments only through interaction with the goods-and-services market and the price level. On the other hand, the flexible exchange system works badly if capital is mobile because the rate of interest has a more direct effect on the balance of payments than on the market to which it responds (the goods-and-services market); and it works effectively if capital is immobile because this indirect repercussion is small or nil. In both these cases, it should be noted, a system works best if variables respond to the markets on which they exert the most direct influence. It may be seen that this principle has a wider application to general problems in the theory of economic policy.16

In extreme cases this principle provides an unambiguous guide to "effective market classification": In addition to the example already cited, one can consider varying responsivenesses of the goods-and-services market to changes in the rate of interest or the terms of trade and verify, for example, that a high responsiveness of this market to the rate of interest is conducive to the effective operation of the flexible-exchange-rate system, whereas a low responsiveness hinders its operation. In the less extreme cases a mixed system -- where equilibrium conditions in both markets are considered before allowing any variable to adjust -- may be theoretically preferable.17

APPENDIX

I.

Some of the propositions advanced in the text require more rigorous proof. The purpose of this appendix is to furnish these proofs.

II.

Let X represent the excess demand for goods and services, so that

X = investment - saving + trade balance,

and let F be the balance-of-payments surplus, so that

F = trade balance-capital exports.

Both X and F are assumed to depend on the domestic rate of interest, r, and the ratio of home and foreign price levels, p. The equilibrium conditions are, therefore,

By differentiation of (1) we can obtain

and by differentiation of (2) we have

The subscripts of X and F denote differentiation with respect to p and r.

It can normally be assumed that Xp < 0 (appreciation of the exchange rate or an increase in the price level are deflationary in the sense that they lower the excess demand for goods); Xr < 0 (an increase in the interest rate is deflationary); Fp < 0 (appreciation or an increase in the price level worsens the balance of payments); and Fr > 0 (an increase in the interest rate improves the balance of payments). In the chapter we made the simplifying assumption that the price level or the exchange rate affects only the balance of trade, and that the rate of interest affects only the rate of capital imports or exports.

III.

The dynamic postulates of the fixed-exchange system can be approximated by

which states that the price level rises in proportion to the excess demand for goods and services, and

which states that the rate of interest rises and falls in proportion to the discrepancy between foreign exchange payments and receipts. The k's indicate the speed of response in each market.

Expanding Equations (5) and (6) in a Taylor series, and retaining only linear terms we obtain

where p0 and r0 refer to the price level and the rate of interest at equilibrium. This system has the characteristic equation

with roots

that, under the assumed signs, are negative if real and have negative real parts if complex.

The system approaches equilibrium asymptotically or cyclically, depending on whether the discriminant D is positive or negative. But D > 0 if Fr is very large (capital mobility); and D >/< 0 depending on whether k2/k1 (relative speeds of adjustment) is small or large, if Fr = 0 (capital immobility).18

IV.

The assumed dynamic postulates of the flexible exchange system are as follows:

which states that the exchange rate rises and falls in proportion to the surplus or deficit in the balance of payments, and

which states that the central bank raises or lowers the interest rate in proportion to the inflationary or deflationary gap in the goods-and-services market.

After linearizing equations (11) and (12) we find that the roots of the characteristic equation are

These roots are negative if real, and have negative real parts if complex, so the system is stable.

If capital is immobile (Fr = 0) the discriminant is necessarily positive, so the roots are real; the system leads directly (asymptotically) to equilibrium. On the other hand, if capital is highly mobile the roots are complex and the approach to equilibrium is oscillatory.

V.

One can now consider a generalization of the above systems based on the following system of equations:

This is the fixed exchange rate system with h1 and h2 zero, and the flexible exchange rate case with k1 and k2 zero. For stability of the linear system

the "trace" (sum of the diagonal coefficients) must be negative and the basic determinant positive. Roughly, the larger the absolute values of the diagonal elements are, relative to the absolute values of the off-diagonal elements, the more direct will be the approach to equilibrium. This explains, in more general terms, the conclusion that a high degree of capital mobility causes cycles in the flexible exchange system but not in the fixed exchange system, and that a low degree of capital mobility interferes with a direct approach to equilibrium under fixed exchange rates and conduces to a direct approach under flexible exchange rates. The reader can easily demonstrate for himself other propositions relating to differences in the values of other parameters. It also helps to explain the "principle of effective market classification": instruments (that is, variables) should be directed at those targets (that is, markets) on which they have the most direct influence.

VI.

Consider now a system of fixed exchange rates in which the central bank bases its monetary policy on a discrepancy between the desired reserves of foreign exchange, Q0, and actual reserves, S0t F(p, r)dt (past accumulations), according to the new system

Equation (19) states that the interest rate moves in proportion to the difference between desired and actual reserves, the constant b indicating the speed of the reaction.

This system, linearized, has the following characteristic equation:

By Descartes rule, it has no positive real roots. It does, however, have complex roots with positive real parts, so the system is unstable; the system moves ever further from equilibrium in an expanding spiral.

Note that if the price level is fixed, the path of the interest rate is

an undamped harmonic. This also holds if Fp is zero. These results justify the validity of the step-by-step exposition in the text.

VII.

Suppose now that the central bank takes account of both the current balance and the level of stocks in the fixed exchange system. Then we have

which has the characteristic equation

with no positive real roots. But it will have complex roots with positive real parts unless

k1(FpXr - XpFr)[k2/b(k2Fr - k1Xp) - 1] + Fr(k2Fr - k1Xp) > 0.

The lower is the weight attached to stocks (b small) and the higher is the degree of capital mobility (Fr large), the more likely it is that the system is stable.

VIII.

Next, suppose that speculators react to a change in the level of central bank reserves (q), and that the central bank responds to the current balance. Then we have

which has a characteristic equation

where Fq is the change in the foreign balance which results from a change in the level of reserves, assumed to be positive. From (27) it is clear that the system has one zero root and that high values of Fq and low values of Fr and k2 are destabilizing.

IX.

Consider now speculation under flexible exchange rates. Suppose that speculative purchases of foreign exchange depend not only on the exchange rate but also on its rate of exchange. Then

(29) has the characteristic equation

in which a = h1/(1 - h1nu) and nu is the speculative outflow due to the changing exchange rate (it is a variant of the coefficient of expectations). A necessary and sufficient condition for stability, given the assumed signs, is that h1nu < 1. Note that nu < 0 is not a necessary condition of stability: Even if speculators believe the exchange rate will continue to move in the same direction that it is currently moving, the system may be stable.

______________________________________

Notes

1 Adapted from The Quart. Jour. Econ., 74, 227-257 (May 1960). Copyright (c) Harvard University Press.

2 Friedman [16], see also Meade ([56], p. 190) for a similar statement. It is, of course, recognized that monetary differences between the two systems exist based on consideration of fixed debts.

3 For the entire system to be in equilibrium stock and flow markets for domestic and foreign goods, securities, and money must be cleared. The present analysis constitutes an attempt to sidestep many of the complications and unresolved difficulties associated with general equilibrium of an open economy, problems which exist even in analysis of a closed economy. At the present stage of the development of the subject, this pragmatic theoretical approach seems amply justified, although final verification of the theoretical results must await the creation of a complete and exact model.

4 This is necessarily the case if domestically produced goods are not "Giffen goods" in world consumption, or if the sum of the elasticities of demand for imports is greater than unity.

5 I assume that expenditure on goods and services is affected by a capital inflow only insofar as the latter affects the domestic rate of interest. This assumption can be justified -- especially in a short-run analysis -- for some types of capital movements but not for others. The analysis traditionally associated with the transfer problem can easily be incorporated into the present analysis, but it would complicate the exposition without affecting the conclusions fundamentally. The assumption that the trade balance is not directly affected by the rate of interest is made for simplicity, and would have to be modified if durable goods bulked large in imports.

6 An excellent survey of the extensive literature on the effects of a change in the terms of trade on the rate of saving has been provided by Johnson [32].

7 The central bank adjusts interest rates to prevent changes in its reserve position. Later we shall consider the effect of a monetary policy which attempts to maintain a given level of reserves.

8 A formal proof of stability, based on a linear system, is given in the Mathematical Appendix. The assumption of linearity is an important one. It must be expected that central bankers-not governed by the restrictions of mathematical laws-would anticipate future positions and modify their reactions accordingly. But the linear system must be stable if the nonlinear system is to be stable.

9 To stabilize the price level the authorities must be willing to buy and sell domestic goods at a fixed price in terms of local currency; the monetary policy may then be interpreted as an attempt to prevent further changes in the stocks of goods held by the government, theoretically, quite analogous to the role of monetary policy under fixed exchange rates in preventing changes in external reserves.

10 For rigorous proofs of the propositions established in this section see sections III and IV in the Appendix of this chapter.

11 My conclusions conflict with the analysis of Professor Meade ([56], pp. 255 258), who writes: "The reader is left to himself . . . to establish the fact that the mobility of labour and capital upon the ease of adjustment is similar for both the gold-standard and the variable-exchange-rate mechanisms of price adjustment." He then speaks of different spontaneous disturbances and how, for each case, the process of adjustment will be affected by the extent to which capital is mobile.

Meade defines the ease of the adjustment process in static terms: in the extent to which the terms of trade must adjust to correct a disequilibrium caused by a spontaneous disturbance. His method can be described in my model by shifting the two curves and comparing the terms of trade at the new equilibrium with the original level.

As suggested in the introduction, I believe that one should discuss the "process" or ease" of adjustment in dynamic terms. Meade's textual exposition (unlike his Mathematical Supplement [54]) hints at a dynamic process, but without the use of an explicit model all the implications cannot be derived.

12 Compare, for example, the British reaction to a deficit in the summer and fall of 1957 with the German reaction to a surplus in recent years.

13 The destabilizing nature of this type of speculation has been described by Friedman [16] and Meade [56].

Among the more important factors influencing speculation under the fixed-exchange-rate system that we have not considered, may be included: (1) the extent of short-term liabilities and the so-called "flight-capital ratio"; (2) international credit facilities such as IMF drawing rights; (3) the "lead-and-lag" effect on the trade balance; (4) the relation between spot and forward markets and the rate of interest; (5) international speculation in spot and forward commodity markets; and (6) the fact that much international speculation is of a once-and-for-all character.

14 There is, however, an analytical parallel. The central bank or the government (through fiscal policy) must buy and sell goods at a fixed price to be completely successful in stabilizing the price level. There would be a direct analogy if speculation in commodity markets were conditioned by the level of commodity reserves of the government.

15 The relation between speculation and the stability of the foreign exchange market has been discussed by Friedman [16], Meade [59], [56], Lutz [44], [47], Baumol [4], and Tsiang [101].

16 The mathematical counterpart of this principle, which has obvious applications to a planned economy in which the "Ministry of Production" sets prices, is that variables should respond to markets in such a way as to make the diagonal elements of the characteristic matrix dominate. This, of course, may not always be possible.

17 Nurkse has argued [80] that it is invalid to identify one instrument with a specific target (employing Tinbergen's terminology), since each instrument affects both markets: Devaluation stimulates employment and improves the balance of trade, and changes in the interest rate affect the balance of payments in addition to the level of employment. In the mathematical system discussed in section V of the Mathematical Appendix it is implicitly argued that both the k's and the h's should be positive. This is the mixed system referred to above.

With perfect information, and international collaboration to prevent beggar-thy-neighbor policies, this recommendation would be justified. In the absence of these conditions simpler rules are necessary.

18 Incidentally, this example illustrates a minor misconception which has developed in the theoretical literature on the stability of equilibrium. Metzler [62] proved that the Hicks conditions are necessary, but not sufficient, if a system is to be stable for all possible speeds of adjustment. This theorem has been interpreted by Samuelson ([88], p. 273) and by Arrow and Hurwicz [1] to apply for positive speeds of adjustments. But any matrix with a pattern of signs

[-   +]
[-   0]
(the fixed exchange system with capital immobile)

is stable yet the Hicks conditions are not satisfied. Metzler's theorem applies, as his proof indicates. to all possible nonnegative speeds of adjustment.

______________________________________

Literature Cited

[1] K. J. ARROW and L. HURWICZ, "On the Stability of the Competitive Equilibrium, I," Econometrica, 26, 522-552 (Oct. 1958).

[16] M. FRIEDMAN, "The Case for Flexible Exchange Rates," Essays in Positive Economics. Chicago: University of Chicago Press, 1953.

[4] W. J. BAUMOL, "Speculation, Profitability and Stability," Rev. Econ. Stat., 39 (Aug. 1957).

[32] H. G. JOHNSON, "The Transfer Problem and Exchange Stability," Jour. Pol. Econ., 64, 212-225 (June 1956).

[44] A. P. LERNER, "The Symmetry between Import and Export Taxes," Economica, 3, 308-313 (Aug. 1936).

[47] F. A. LUTZ, "The Case for Flexible Exchange Rates," Banca Nazl. Lavoro (Dec. 1954).

[54] J. E. MEADE, "A Geometrical Representation of Balance-of-Payments Policy," Economica, 16, 305-320 (Nov. 1949).

[56] J. E. MEADE, The Balance of Payments. London: Oxford University Press. 1951.

[62] L. A. METZLER, "Stability of Multiple Markets: The Hicks Conditions," Econometrica, 13, 277-292 (Oct. 1945).

[80] R. NURSKE, "The Relation between Home Investment and External Balance in the Light of British Experience,1945-1955," Rev. Econ. Stat., 38, 121-154 (May 1956).

[88] P. A. SAMUELSON, "The Stability of Equilibrium: Comparative Statics and Dynamics," Econometrica, 9, 97-120 (April 1941).

[101] S. C. TSIANG, "A Theory of Foreign Exchange Speculation Under a Floating Exchange System," Jour. Pol. Econ., 66, 399-418 (Oct. 1958).

© Copyright, Robert A. Mundell 1968