Abstract
Since the development of the simple IS-LM framework, short-run macroeconomic policy questions have usually been analyzed—implicitly or explicitly—in terms of demand-determined models. 1 Analysis of stabilization policy has generally been in the context of developed economies, and the elegance and appropriateness of more or less sophisticated versions of the IS-LM framework (frequently extended to incorporate openness of the economy) have led, over time, to its becoming the accepted and familiar model. The need for policy formulation in less developed primary producing countries, subject to fluctuating output, calls, however, for an emphasis on the distinction between supply-constrained and demand-constrained situations.
Since the development of the simple IS-LM framework, short-run macroeconomic policy questions have usually been analyzed—implicitly or explicitly—in terms of demand-determined models. 1 Analysis of stabilization policy has generally been in the context of developed economies, and the elegance and appropriateness of more or less sophisticated versions of the IS-LM framework (frequently extended to incorporate openness of the economy) have led, over time, to its becoming the accepted and familiar model. The need for policy formulation in less developed primary producing countries, subject to fluctuating output, calls, however, for an emphasis on the distinction between supply-constrained and demand-constrained situations.
This paper develops some simple propositions about managing an economy under conditions of fluctuations in output, and contrasts them with the more usual case of fluctuations in demand. The focus is on short-run stabilization policy in a developing economy. Since output is exogenous, stabilization policy is defined to mean that policymakers aim to minimize fluctuations in domestic absorption. The economic authority does not ascribe any importance to the exchange rate, the price level, or the stock of foreign exchange in themselves—their only importance is in their effect on absorption. While the framework chosen is simple, it serves to bring together a number of points made in different contexts in a model sufficiently stark to reiterate them forcefully. The model is based on the absorption approach to the balance of payments. 2 There is no domestic bond market and no internationally traded financial asset. Stock disequilibria in the domestic money market are cleared over time and, in the interregnum, affect absorption. As may be expected, in a model where money is the only asset, although the balance of payments is explicitly characterized by an absorption equation, the results of the analysis are identical to those that would emerge from the monetary approach.
Recent agreement on the need for international surveillance over exchange rates has led to a discussion of the principles that should govern surveillance and the criteria by which the appropriateness of exchange rate policies should be judged. 3 A number of economists have argued that official intervention in foreign exchange markets is desirable where market forces lead, in the short run, to exchange rates substantially different from long-term equilibrium rates. The present analysis is aimed explicitly at the use of exchange rate policy, as one instrument of stabilization policy, for a developing country. This stylized developing economy is characterized principally by a lack of diversification and a consequent vulnerability to large and erratic fluctuations in its primary product sectors. The main argument in this paper is that the extent of official intervention in the foreign exchange market should depend upon the origin of short-term shocks to the economy, and that the confusion of various types of shock can lead to erroneous prescriptions that may be particularly serious for a developing country. This paper therefore makes a simple case for intervention in the exchange market under certain well-specified conditions.
It is frequently argued that insofar as flexible exchange rates insulate 4 an economy against shocks of foreign origin, an economy more volatile than the rest of the world should fix its exchange rate; one less volatile should allow its exchange rate to float freely. Such a prescription is, of course, globally inconsistent. In contrast, this analysis suggests that the origin of domestic shocks to the economy is of critical importance: shocks owing to fluctuations in output that are independent of demand are best contained by a more fixed exchange rate regime; shocks to demand that are independent of real output are best dealt with by a more flexible exchange rate regime. 5 Policy analysis is complicated by the difficulty of distinguishing demand shocks from supply shocks or indeed distinguishing “shocks”—which are defined here as transitory changes expected to be reversed in the near future—from more permanent changes in the economic environment.
The paper is set out as follows. Section I specifies a simple model of an open economy and examines the impact effects of two types of domestic shock to the system under different exchange rate regimes. Section II traces the time paths of the endogenous variables of the model after a shock and finds that even this very simple model leads to some interesting patterns of absorption and exchange rate overshooting. In general, however, the simple prescriptions that emerge from an examination of impact effects remain valid when the full disequilibrium dynamics are taken into consideration. Given the domestic component of base money, it is found that intervention in the exchange market can alter the time path of adjustment of absorption to a shock, but not the total amount of adjustment required. Section III introduces active monetary policy and finds that under any but a pure flexible exchange rate regime monetary policy can stabilize absorption. Successful monetary policy of this sort, however, requires that the authorities have perfect information about the time pattern of shocks and, where shocks originate in output, leads to greatly accentuated fluctuations in external reserves. Section IV presents an analysis, under extreme, simplifying assumptions, of exchange rate policy under external shocks—specifically, changes in import prices. Finally, Section V summarizes the conclusions of the analysis. The Appendix sets out some of the algebra of the exchange rate dynamics.
I. The Model
Consider the following simple model. Real domestic absorption (A)—that is, consumption plus investment expenditure—is a function of current real income (Y) but is adjusted in disequilibrium by some proportion (γ), in each period, of the discrepancy between the supply of and the demand for real money balances (Ms – Md). The nominal money supply is some multiple (z) of reserve money. The latter consists of a domestic component (D) and a net foreign asset component (F). The domestic economy is small, all goods are traded, purchasing power parity holds continuously, and foreign prices are assumed to be fixed, by our choice of units, at unity. This simplification, which means that the exchange rate is the only price in the model, helps to focus attention on the principal question at hand. Since no relative prices are admitted, however, the real costs of exchange rate fluctuations are omitted from consideration. There are no capital flows in the model, and changes in net foreign assets are determined by the excess of domestic output over domestic absorption. Real output is determined exogenously.
Stock data are measured at the end of the subscripted time period. A bar (—) over a variable means that it is exogenous. The model may be characterized by the following equations:
Substituting equations (2) and (3) into equation (1) yields 6
The stock of external reserves is determined by the intervention function
The authorities choose the rate at which they are willing to allow the stock of foreign reserves to change in the event of a balance of payments disequilibrium; to the extent that this differs from the flow excess supply or demand in the foreign exchange market, the exchange rate (e)— defined as the domestic currency price of foreign currency—changes to equilibrate the market. The authorities’ intervention policy may be characterized as follows:
The extent of intervention is some proportion (1 – θ) of the notional balance of payments deficit at the equilibrium exchange rate, and
Consider Figure 1. Absorption is a negative function of the exchange rate because of the real balance effect. A shift of the absorption function from A to Aʹ would, at the initial exchange rate, lead to a deficit of BD. By varying the choice parameter θ, the authorities may decide where along the line BD they choose to be. Suppose they choose to intervene to the extent of BC, that is, BC = (1 – θ)BD, the exchange rate would rise to e1, with the emerging deficit of FE = BC. If θ = 1, there exists a pure floating exchange rate regime, and in this illustration e goes to e2; if θ = 0, there is a rigidly fixed exchange rate regime. 7 Between these extremes, as in the case described, there is a managed float. 8
Full stock equilibrium requires that the stock money demand and money supply are equal; flow equilibrium, however, requires only that
or,
and the exchange rate adjusts continuously to maintain this condition. Thus, rearranging equation (6) yields
The basic difference equations of this system and the time paths of the endogenous variables are given in the Appendix.
The system of three equations—(4), (5), and (6ʹ)—in three endogenous variables (A, F, and e) is quite general: where θ = 1, it becomes a pure flexible exchange rate system, and equation (5) drops out; where θ = 0, it becomes a rigidly fixed exchange rate regime, and equation (6ʹ) drops out. For all other values of θ(0 < θ < 1), the exchange rate system falls somewhere on the continuum between these two polar extremes.
This paper is concerned with the effects of two types of shock to this system: (a) an exogenous supply shock, whereby Y changes because of some random event, such as a crop failure; and (b) an exogenous demand shock, introduced here as a change in the money demand coefficient (k). 9 By differentiating the system, first with respect to income and then with respect to the money demand coefficient, we derive the impacts of these two sorts of shock. Setting θ at zero and at unity gives the effects under the polar exchange regimes. To facilitate comparison, these various impact effects under different exchange rate regimes are set out in Table 1.
Impact Effects Under Different Exchange Rate Regimes
Impact Effects Under Different Exchange Rate Regimes
| Fixed Exchange Rates |
Managed Floating Exchange Rates |
Flexible Exchange Rates |
||
|---|---|---|---|---|
| (I) |
|
|
|
0 |
| (II) |
|
1 – γk |
|
1 |
| (III) |
|
|
|
0 |
| (IV) |
|
γk |
|
0 |
| (V) |
|
0 |
|
|
| (VI) |
|
0 |
|
|
Impact Effects Under Different Exchange Rate Regimes
| Fixed Exchange Rates |
Managed Floating Exchange Rates |
Flexible Exchange Rates |
||
|---|---|---|---|---|
| (I) |
|
|
|
0 |
| (II) |
|
1 – γk |
|
1 |
| (III) |
|
|
|
0 |
| (IV) |
|
γk |
|
0 |
| (V) |
|
0 |
|
|
| (VI) |
|
0 |
|
|
The comparison in Table 1 seems to accord with intuition; the managed floating case always falls between the two polar cases. The prima facie prescription that emerges is that countries subject principally to demand-type shocks should operate a pure flexible exchange rate; those subject most frequently to supply-type shocks should fix their exchange rate. For the broad group of countries somewhere in between—that is, subject to both types of shock—managed floating is the superior strategy. The logic of this view is simple. Insofar as the economic authority is concerned to stabilize domestic absorption, the policies work as follows. Under fixed exchange rates, reserves are used to cushion the impact of shocks; absorption can differ from output with reserve changes financing the difference. Clearly, if desired absorption remains on target while output behaves erratically, reserve movements can be used to stabilize absorption. In the opposite extreme, with output on target but demand behaving erratically (owing, in this particular example, to an unstable demand for money), the economic authority can best stabilize absorption by allowing exchange rate movements to constrain absorption to output, that is, by pure flexible exchange rates. In the normal case of a country subject to demand-type and supply-type shocks, the intervention policy—that is, the size of θ—should depend on which of the two dominates. The impact effect of demand shocks diminishes, and that of supply shocks increases, as θ moves from zero to unity.
The intuitive simplicity of these prescriptions is persuasive, but the full disequilibrium dynamics of the model under the different regimes must be considered in order to evaluate them properly.
II. Disequilibrium Dynamics
time paths of endogenous variables
The concern here is with stabilization policy where the disturbances to the system—“shocks”—are transitory aberrations rather than sustained shifts. For ease of exposition, it is assumed that each shock lasts only one (arbitrary) period before the variable in question returns to its equilibrium value. In this section, the time paths of the endogenous variables of the model in response to a shock are investigated. This is done in order to ascertain the validity of the simple prescriptions, based only on impact effects, outlined in Section I. 10
Consider initially the fixed exchange rate regime subjected to a one-period fall in income. Absorption falls on impact and may rise or fall further in the next period. In any event, the decline in absorption summed over these two periods will be less than the initial decline in income and, of course, less than the fall in absorption that would occur on impact under pure flexible exchange rates. In subsequent periods, absorption will increase at a decreasing rate until it once again achieves its initial level. The level of external reserves falls on impact then increases (at a declining rate) back toward the initial equilibrium. 11 The logic of these developments is intuitive. The reserve-cushioning effect of the fixed exchange rate regime allows the use of reserves to finance a level of absorption greater than that of income during the shortfall. Thereafter, however, absorption must necessarily be less than income to make up the loss in reserves.
A money demand shock under fixed exchange rates—that is, an increase in k in period t that is fully reversed in t + 1—leads to an overshooting pattern of absorption. Absorption falls on impact, as the country accumulates external reserves to satisfy its increased appetite for money. The following period, however, will see a rise in absorption greater than the initial fall, as the country sheds its now excessive money balances. Thereafter, absorption declines asymptotically back toward the initial equilibrium. Correspondingly, the stock of external reserves, which at first increased owing to the money demand shock, falls asymptotically to the equilibrium level. 12
The case of the pure flexible exchange rate regime is easier to describe. Since absorption is always equal to income, the full impact of an income shock is exhausted within the period of the deviation. A money demand shock has no effect on absorption. Exchange rates change to assure these results. Both a fall in income and a fall in money demand elicit an immediate increase in the exchange rate—that is, a depreciation of the domestic currency—to restore monetary equilibrium. This is reversed in the following period. 13
The time paths of absorption and of external reserves after an income shock under a managed float look similar to those described under the fixed exchange rate regime. The larger is θ, the larger is the initial change in absorption and the smaller the initial change in external reserves. A fall in output, fully reversed in the next period, leads, on impact, to a rise in the exchange rate, but in the next period to an even greater fall. Thereafter, the exchange rate rises at a decreasing rate back toward the initial equilibrium. The explanation for this overshooting is straightforward. In the period of the initial shock, there is a loss of reserves that leads in subsequent periods to an excess demand for money. The excess demand for money lowers the exchange rate, and income exceeds absorption until the reserves have been recovered. 14
An increase in the money demand coefficient (k) under managed floating elicits, on impact, a fall in absorption and the exchange rate, and a rise in reserves. From the next period onward, reserves decline, at a decreasing rate, back to their initial level. Absorption increases in the second period by more than it fell on impact, and then declines gradually back to its initial level. The exchange rate rises in the second period by more than it fell in the first, and declines thereafter gradually toward the initial equilibrium. 15 Once again, the logic is quite straightforward.
Charts 1 and 2 illustrate a particular numerical example of the system under fixed, flexible, and managed floating exchange rates.
Effect of a One-Period Income Shock on Endogenous Variables1
Effect of a One-Period Money Demand Shock on Endogenous Variables1
the implications for stabilization policy
The total adjustment of absorption over time in response to either of the two shocks discussed is independent of the exchange regime. The model is set up to illustrate the principle that there is no such thing as a free lunch—that is, our policies can alter the time path of adjustment but not the total adjustment required.
Let us characterize Y0 as the initial equilibrium income level, and
and
where j = 1, … , ∞
Under pure flexible exchange rates, clearly all the adjustment occurs in the first period. That is, θ = 1 and
Under any system of exchange intervention, summing the deviations of absorption from equilibrium over the entire time path yields
The size of the intervention parameter θ affects only the time path of absorption. In any event, over time, absorption must be reduced to the full extent of the initial shock. Exchange rate policy can be used as an instrument of stabilization only in that the size of the initial shock is positively related to θ; that is, reserves may be used to buy time for adjustment.
The same principle may be demonstrated for the money demand shock. Defining
and
where j = 1, … ,∞
Here, once again the exchange regime cannot provide resources but can merely alter the time path of absorption. In the pure flexible exchange rate case, the monetary shock has no effect on absorption. Under the fixed or the managed floating regime, the monetary shock does affect absorption, although these effects sum to zero over time. There is an overshooting of absorption in these cases, that is, an increase in the demand for money (which lasts only one period) lowers absorption below equilibrium in the first period, then raises it above equilibrium in subsequent periods as the additional reserves are slowly dissipated. Under regimes other than the pure floating exchange rate, the sum of the absolute values of deviations from absorption equilibrium are increased, the smaller is θ. Thus, the variance of absorption is unambiguously decreased as θ approaches unity.
Insofar as we are concerned to diminish the amplitude of fluctuations in absorption, the findings of this section generally support the simple prescriptions of Section I. Fixed exchange rates are preferable where only output shocks occur, flexible exchange rates where only demand shocks occur. When both types of shock occur, a managed float is preferable, with θ set according to which type of shock predominates.
III. Active Monetary Policy
Domestic credit, or the domestic component of the monetary base (D), has, thus far, been held constant through time and generally not given any time subscript. Active monetary policy means, in the context of this model, the manipulation of this domestic base money by the stabilization authority to offset fluctuations in absorption that are due either to income or to money demand shocks.
In the model, monetary flows are motivated by the discrepancy between actual stocks at the beginning of the period (end of previous period) and desired stocks at the end of the period. Since stocks have been consistently defined as end-of-period stocks, the absorption function is defined to make absorption in period t depend on the money supply (and hence both the foreign (F) and domestic (D) components of the base) at the end of period t–1. 16 For consistency, therefore, the monetary authority will operate on Dt-1, to stabilize absorption during period t. Of course, one could redefine stocks as beginning-of-period stocks to eliminate this difference in time subscripts. In actuality, the authority would probably act on ΔDt, that is, the flow supply of domestic credit over the period. The time notation does, however, highlight the fact that for fine-tuning it is essential that monetary policy anticipate all shocks perfectly.
Under any exchange rate regime that permits some intervention, domestic credit policy can stabilize absorption in the face of income shocks. This stabilization requires the authorities to be able to perfectly anticipate, in their monetary policy, the time pattern of income shocks. The enhanced stability of such a perfectly executed policy does not come free of charge, but requires greatly accentuated fluctuations of external reserves. Consequently, the stabilization authorities will have to maintain a higher level of reserves, and to bear the attendant loss in seigniorage.
Under managed floating, to fix absorption in the face of an income shock in period t, which is fully reversed in period t + 1, the authorities are required to manipulate domestic credit such that
and
Summing these changes over the two periods yields the total (Sum D):
Sum D = –e Δ Yt
The effect of the shock to income and the monetary policy on the foreign component of the monetary base is as follows:
By the end of period t + 1, the system is back at its initial equilibrium, the change in the real value of domestic credit having been exactly offset by the change in external reserves.
Exchange rate changes over the period accommodate. That is, given the intervention by the authorities in the domestic credit and foreign exchange markets, the exchange rate changes to ensure financial flow equilibrium. Thus,
The changes, of course, sum to zero over the two-period disequilibrium.
From the general managed floating case described, one can easily derive the polar cases of fixed exchange rates and freely floating exchange rates. Setting θ = 0 for the fixed exchange rate case, we note that
and that the changes in external reserves are unchanged at
Exchange rate changes turn out, of course, to be zero. The same principle emerges, namely, that a shortfall in income can be prevented from diminishing absorption only at the cost of the full foreign exchange value of the shortfall.
Setting θ = 1 for the pure flexible exchange rate case shows that under a freely floating system no amount of financial intervention can offset a real fall in income. This is most easily illustrated by differentiating the absorption function for period t
Clearly, dAt = dYt if θ = 1. This is independent of the extent of manipulation of domestic credit
The case of a money demand shock is more straightforward than that of an income shock. Under a pure floating exchange rate regime, of course, monetary shocks exert no influence over absorption. Using monetary policy to stabilize absorption makes sense therefore only insofar as the authorities want to offset exchange rate changes. Under these circumstances, the effect of a money demand shock, in period f, on absorption can be fully offset by setting
Over the two periods the changes in domestic credit sum to zero. In both periods, as may be expected, there is no change in either the exchange rate or the stock of foreign reserves. Once again our monetary fine-tuning requires perfect information on the part of the stabilization authority. 17
Before concluding this section, it should be noted that while the model has explicitly taken an absorption approach to the balance of payments, it differs in no way from the simple monetary approach. Any once-and-for-all increase in domestic credit in time t leads, over time, to an equal and opposite change in foreign reserves. Changes in the exchange rate and changes in absorption sum to zero over the disequilibrium, but the integral of actual-minus-equilibrium absorption is positive over the disequilibrium.
IV. External Shocks
One further consideration is important before turning to the implications of the argument for exchange rate surveillance. While the distinction between supply shocks and demand shocks has been made, both sorts of shock have been assumed to originate in the domestic economy. Consider, as an example of an external supply shock, a sudden decrease in supply (or increase in price) of an import. Clearly, the model is not set up to examine questions of this nature, since it makes no distinction between importables and exportables. By disaggregating the model slightly and making the simplifying assumption that there is no price-elastic substitution in expenditure or output, we may, however, make some tentative statements about this problem.
It is important first to note that there are two sorts of price index in the economy: one applicable to output, and the other applicable to expenditure. All goods are classed as either exportables (E) or importables (I). Both types of good are consumed domestically and are traded; domestic production of exportables is in excess of domestic consumption, while the opposite is true of importables. Let us define separately the price of exportables (Pe) and the price of importables (P1). Superscripts d, s, n, and * refer, respectively, to demand, supply, nominal, and foreign.
The price indices for absorption (P1) and output (P2) may be written as
or,
By explicitly considering the two separate price indices, it becomes clear that as long as there is trade the two indices will differ insofar as α1 ≠ β1 and α2 ≠ β2. It is thus clear that while an increase in
Consider the effects on absorption of a change in the world price of importables
Given that importables have a larger weight in absorption than in income, the effect on absorption of a rise in the price of importables is negative. Clearly, the larger is θ—that is, the closer to pure flexible exchange rates along the exchange policy continuum—the smaller is the fall in absorption on impact.
The lagged effect on absorption of a change in the price of importables is
Under pure flexible exchange rates, therefore, the entire adjustment occurs contemporaneously and is exhausted with the reversal of the initial shock in the period t + 1. Under any other regime (0 ≤ θ < 1), however, adjustment takes much longer. Summing deviations from the initial equilibrium level of absorption (A0) over time yields
The message is again quite intuitive. The total summed deviation is identical under fixed, managed, and pure flexible exchange rates. The time paths of absorption under fixed (---) and flexible (—) exchange rates may be illustrated graphically. 20 (See Figure 2.) The variance of absorption is unambiguously larger under fixed exchange rates and therefore, insofar as the task of the stabilization authorities is to minimize the variance of absorption, flexible exchange rates are preferable. 21
V. Conclusions and Some Implications for Exchange Rate Surveillance
results of the model
The paper has been addressed to the problems of stabilization policy in an open, less developed economy subject to various sorts of transitory 22 shocks, specifically demand and supply shocks of domestic origin, and terms of trade shocks. In the context of the extremely stylized model in the paper, if the authorities’ objective is to minimize fluctuations in absorption around some sustainable long-term level, shocks originating solely in demand should be dealt with directly through flexible exchange rates. Shocks originating in supply fluctuations are best dealt with by intervention in the exchange market to maintain a fixed exchange rate. Where both sorts of domestic shock occur, a managed floating system is the superior strategy, with the extent of intervention (1 – θ) positively related to the predominance of supply shocks. The particular terms of trade shock modeled in this paper under extremely restrictive assumptions—fixed proportions in production and consumption, and expenditure related to the current absorptive capacity of income rather than permanent income—argues for a flexible exchange rate regime.
The model, before active monetary policy is introduced, is a simple expenditure specie flow mechanism. After any sort of shock, the restoration of equilibrium requires a return to the original fixed proportions between the foreign and domestic components of the monetary base. As a result, the summed deviations from equilibrium after any shock are independent of the exchange rate regime. Essentially, it is made clear that the use of reserves cannot indefinitely stave off adjustment, but can only alter the time path of adjustment. 23
When active monetary policy is introduced, it is shown that an omniscient monetary authority can permanently offset shocks to the economy. For demand shocks, however, given the omission of relative price effects on output, pure flexible exchange rates automatically achieve the same result as would an active monetary authority with perfect foresight. For an output shock—a supply shortfall, for example—absorption is reduced both directly, by the effect of a lower income on expenditure, and indirectly, by the loss of reserves and consequent diminution of the money supply. If absorption is to be stabilized, domestic credit policy cannot be used simply to maintain the money supply but must be made to counteract the negative impact of reduced income. Under these circumstances, appropriate policy may require domestic credit not only to offset the depletion of external reserves but also to increase the overall money supply. This policy response to a balance of payments deficit, which seems perverse if considered in the context of an orthodox demand-determined model, appears quite straightforward in the present context.
Where active monetary policy is used to offset the effects on absorption of real supply shocks, the enhanced stability comes only at the cost of greater fluctuations in external reserves. This, in turn, presumably requires the authorities to hold a larger stock of reserves, and the country to bear the attendant loss in seigniorage.
weak conclusions, strong conclusions, and implications for surveillance
Judicious use of the policy implications of the model requires that its limitations be understood. The objective function implicit in the model contains only one argument—aggregate absorption. Prices, that is, exchange rates, are left out of consideration, and there are no internal relative price effects to distort allocation or distribution. Clearly, in such a model, real costs associated with exchange rate fluctuations are omitted. Where the model prescribes a floating exchange rate, this limitation should be borne in mind. Most other arguments for flexible exchange rates contain either the same or a related weakness; implicitly, either it is assumed that, in a world of flexible exchange rates, rates will tend to be stable or it is assumed that exchange rate fluctuations are relatively costless. 24 The conclusions of the model that prescribe fixed exchange rates—that is, where shocks to the system originate in autonomous fluctuations in domestic output—are much stronger conclusions. They would be strengthened rather than weakened by taking account of the costs of exchange rate fluctuations.
Our argument has, if anything, complicated the question of exchange rate surveillance by making another case for intervention. The current literature on surveillance has recognized the effects of several factors, such as changes in the restrictiveness of the trade and payments regime and changes in international relative rates of inflation, on exchange rate policy. The phenomenon modeled in this paper—namely, that disturbances from different sources should elicit different exchange rate policy responses—has not been stressed in this literature, although, of course, it is the principal raison d’ être for the compensatory financing facility of the Fund. For less developed countries, with erratic primary product sectors, the origin of short-run disturbances is an important consideration in the choice of an exchange rate policy.
APPENDIX Dynamics of the Model
Suppose that the initial condition is one of full-stock equilibrium in period t-1, that is, Ft-1 = F0,
Consider the case of an income shock in period t,
The final equation for F is as follows:
Defining δ = [1 γz(1 -θ)], the solution of the difference equation in F is
for j = 0, … ,∞
As long as the stability condition (-1 < δ < 1) is met,
Similarly, the final equation for A may be written
so that
j = 1, … ∞,
For a money demand shock in period t,
The solution of the difference equation in F is
for j = 0, … , ∞
so that
Similarly, the final equation for A may be written
so that
j = 1, …,∞
Under both sorts of shock, the exchange rate changes to ensure financial flow equilibrium in each period.
For notational simplicity, in what follows we write
1. The fixed exchange rate regime subjected to an output shock
If an output shock occurs in time t and is reversed in t+1, the pattern of changes in absorption is as follows:
and
where j = 2, … , ∞
The pattern of changes in external reserves is as follows:
where j = 1, …, ∞
2. The fixed exchange rate regime subjected to a money demand shock
Changes in absorption and in external reserves, after a money demand shock in period t, are, respectively, as follows:
where j = 2, … , ∞
where j = 1, … , ∞
3. The flexible exchange rate regime
Since absorption is always equal to income, the full impact of an income shock is exhausted within the period of the deviation. A money demand shock has no effect on absorption. Exchange rates change to assure these results; under an income shock
and under a money demand shock
4. The managed floating regime subjected to an output shock
An important clarification, with regard to the characterization of the fixed exchange rate absorption function A(e0), is necessary in analyzing the disequilibrium dynamics of the managed floating case. One of the arguments of A (e0) is the stock of foreign reserves at the end of the previous period. Setting e = 1, θ = 0, and substituting equation (5) lagged into (4) gives the following fixed exchange rate absorption function:
This function assumes that past disturbances have affected the stock of foreign reserves as they would under a fixed exchange rate regime; it is not the appropriate function for A(e0) within our managed floating system. This may be illustrated by considering the example of a fall in income in period t – 1 that is fully reversed in t. Under a fixed exchange rate regime, dFt-1 = γkdYt-1; under a managed float, dFt-1 = (1-θ)γkdYt-1 (a much smaller change). In the subsequent period, with the restoration of equilibrium income, A(e0)t will be less if one assumes (incorrectly) that the stock of reserves is lower by γkdYt-1 than if one assumes (correctly) that it is lower by only (1-θ)γkdYt-1. Consequently, the assumed discrepancy between income and absorption will be larger, and the amount of intervention greater—perhaps even greater than the actual discrepancy—under the former assumption than under the latter. Correctly then, we will evaluate A (e0)t within our managed floating system always using the actual stock of reserves at the end of the previous period.
The time paths of changes in absorption and in external reserves after an output shock under managed floating are analogous to the fixed exchange rate case. The difference is in the intrusion of θ. The larger is θ, the larger is the initial change in absorption and the smaller the initial change in external reserves.
ΔAt = [1 − (1 − θ)γk]ΔYt
ΔAt+1 = [γ2kz(1 − θ)2 − (1 − (1 − θ)γk)] Δ Yt
and
ΔAt+j=−[γ3z2k(1−θ)3−(1−(1−θ)γz)j−2]ΔYt
where j = 2,… ,∞
ΔFt = (1 − θ)γk Δ Yt
and
ΔFt+j = [γ2kz (1 − θ)2 (1 − (1 − θ)γz)j−1]ΔYt
where j = 1,… ,∞
The exchange rate overshooting in this case differs from most cases cited in the flexible exchange rate literature insofar as financial assets are not traded in this model. Changes in exchange rates are as follows:
and
where j = 2, … , ∞
5. The managed floating regime subjected to a money demand shock
The effects of a money demand shock on the endogenous variables over time may be summarized as follows:
and
where j = 2, … , ∞
and
where j = 1, … , ∞
and
where j = 2, … , ∞
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Mr. Lipschitz, economist in the Asian Department, is a graduate of the London School of Economics and Political Science.
The author is indebted to Carlos Rodriguez and to colleagues in the Fund for comments on earlier drafts of this paper. They are not, of course, responsible for remaining errors or for views expressed in this article.
Most of the debate on fixed versus flexible exchange rates was within this paradigm. Two interesting departures may be found in Laffer (1973) and Mundell (1973).
See Alexander (1952) and Johnson (1958). The link between the absorption approach and the monetary approach is illustrated in Dornbusch (1973) and Mussa (1974).
Some papers in the discussion are the following. Artus (1978) discusses methods of identifying the long-run equilibrium exchange rate. The literature on excessive exchange rate variability is reviewed in Schadler (1977). McKinnon (1976) and Day (1977) discuss risk in the foreign exchange market in a framework that readily leads to a case for intervention. That case is, however, quite different from the one made in this paper. Artus and Crockett (1978) discuss the need for surveillance, and various criteria that might be employed in its conduct.
See Laursen and Metzler (1950) for a dissenting view.
Black (1976) suggests a similar principle without formalizing or generalizing it. Fischer (1977) comes to conclusions similar to those in the present paper. Earlier drafts of the two papers were written independently at about the same time.
For simplicity of expression, it is assumed that capital gains and losses on reserve holdings are monetized. This assumption serves also to simplify the dynamics in the following section without detracting from the generality of the argument. It could be removed simply by substituting
See Shinkai (1975).
A fixed exchange rate regime, in a world of generalized floating, must necessarily define the standard to which it is fixed. To fix the exchange rate in terms of one other currency is to float against all the rest. In this note, a fixed exchange rate refers to a rate effectively fixed in terms of an appropriately weighted basket of trading partner currencies, such that the effects of bilateral changes with individual currencies in the basket sum to zero. See Thakur (1975); Rhomberg (1976).
This characterization of the intervention function is analogous to a rational expectations model insofar as the authorities are postulated to act as if they know the model.
Notably, this is only one sort of demand shock. The standard Hicks-Hansen model distinguishes between shocks that are due to changes in autonomous expenditure and those that are due to monetary instability. Our demand shock is a shock to money demand, but our analysis of demand shocks would not be altered qualitatively if we used a money supply shock or an autonomous expenditure shock.
If the model is to display plausible properties, the stability condition –1 < 1 –(1 – θ)γz < 1 must be met. Alternatively stated, stability requires that a change in base money alters absorption in the following period by a multiple of less than 2. The logic is easiest for the fixed exchange rate case. Suppose that the domestic component of the money base were to rise above equilibrium by 10 units. (i) If the multiplier with respect to absorption were less than 2—say, 1.5—absorption would rise by 15 and external reserves would fall by 15, leaving the money base below equilibrium by 5 but closer to equilibrium than the initial 10-unit discrepancy. Successive changes would oscillate back toward equilibrium. (ii) If the multiplier were greater than 2—say, 2.5—absorption would rise by 25 and external reserves would fall by 25, leaving the money base 15 units below equilibrium. Successive changes would increase the amplitude of oscillations, and the model would be explosive. (iii) If the multiplier were less than unity—say, 0.8—absorption would increase by 8 units and the money base would move to 2 units above equilibrium. The system would not oscillate but would move monotonically back toward equilibrium. In the discussion that follows, it is assumed in the text, for simplicity of exposition, that (1-θ)γz ≤ 1. If in fact (1 – θ)γz > 1, there would be some change in the description of the time paths to equilibrium, but, as long as the model was stable, no change in the basic conclusions.
See Foley (1975) for a discussion of stocks and flows as beginning-of-period and end-of-period models.
This states simply that any transitory changes in money demand are accommodated, and amounts to a repetition of the standard prescription that, insofar as disturbances arise from the monetary system, the money supply process should be accommodating. In the IS-LM framework, which includes a financial market, this argues that if the LM curve shifts about, the authorities should fix the interest rate. (See Poole (1970).) The “demand shock” in this model is a monetary shock, not an autonomous expenditure shock. While the accommodating-money-supply prescription would not hold for an autonomous expenditure shock, flexible exchange rates would stabilize absorption under any sort of demand shock.
See Miller (1976) and Rodriguez (1976).
In the absence of any monetary-stock disequilibrium, absorption equals the absorptive capacity of income. Changes in the terms of trade will therefore alter absorption both directly and via monetary effects. It is quite simple to construct instead a permanent income model, where absorption is not directly affected by short-term fluctuations in the terms of trade. This would lead to what has been termed a “vicious circle” situation, with domestic agents attempting to maintain real absorption in the face of a reduced real output in terms of their absorption commodity basket. In a richer model, with some goods produced only domestically and some produced only abroad, this system would precipitate an accelerating balance of payments (or exchange rate) crisis, or sharp substitutions out of foreign goods into domestic goods.
The changes in exchange rates are as follows:
Deviations from the initial equilibrium sum to zero. Changes in external reserves are as follows:
j = 1, …, ∞
Deviations from the initial equilibrium sum to
The most interesting problems in this example of an externally generated change in the terms of trade are unfortunately beyond the scope of this simple model. A model including nontraded goods and allowing for some substitution in expenditure could examine the effects of such a shock on the nontraded goods sector. While a substitution effect will reorient expenditure toward nontraded goods, an income effect will decrease demand over all. Here the effect in the nontraded goods sector—and hence employment, prices, and output—will depend on the price elasticity of demand for importables and the behavior of savings.
It has long been well understood that transitory, cyclical shocks require a different policy response than that required by more persistent exogenous changes. This formulation, of course, begs the question of how short must the cycle be for one to characterize a shock as cyclical. See Nurkse (1945).
Stein (1963) considers the optimum time path of absorption. Using his analysis in conjunction with that in the present paper, one should, in principle, be able to find the optimum extent of intervention.
The assumption that rates will be relatively stable seems to imply a harmonization of national economic policies, which, of course, dispenses with the need for flexibility. As noted in Schadler (1977), the evidence from the current period of floating refutes this assumption. There is no adequate measure of the costs of exchange rate fluctuations.
