The Consequences of Real Exchange Rate Rules for Inflation: Some Illustrative Examples

Charles Adams; Daniel Gros

doi:10.5089/9781451972887.024.A002

Author:

Mr. Charles Adams

Mr. Charles Adams https://isni.org/isni/0000000404811396 International Monetary Fund

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and

Mr. Daniel Gros

Mr. Daniel Gros https://isni.org/isni/0000000404811396 International Monetary Fund

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Publication Date:: 01 Jan 1986

eISBN:: 9781451972887

Language:: English

Keywords:: price level; money stock; rate of exchange; rate depreciation; economic system; Real exchange rates; Inflation; Exchange rates; Monetary base; Demand for money

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Recently, several countries have adopted exchange rate rules that consist in depreciating the nominal exchange rate in line with a measure of the difference between inflation at home and abroad. The aim of these policies is to keep the real exchange rate constant and to avoid any slippage in the adjustment effort that would arise from losses of competitiveness.1

Abstract

Adopting such rules has certain advantages over discretionary exchange rate changes—exchange rate adjustments are made more regularly, and their determination is removed from the area of political debate. In addition, these rules may give rise to improvements in the balance of payments in the short run. This paper argues, however, that the rules are likely to lead to a host of monetary problems. Specifically, it is argued that countries risk losing control over the inflationary process when following these rules and that rapidly increasing inflation may result under certain conditions.²

The reasons for the possible loss of control over inflation are straightforward: the adoption of real exchange rules may serve to index both the nominal exchange rate and, through the balance of payments, the money supply to the price level. Under these conditions, a real exchange rate rule may imply that there is no exogenous nominal anchor that can tie prices down; a target for domestic credit will not provide such an anchor because money can flow through the balance of payments.³ A real exchange rate rule can therefore represent a policy of complete monetary accommodation; that is, an increase in domestic inflation from any source can be automatically accommodated by a faster rate of exchange rate depreciation and by a faster rate of monetary growth.

The approach adopted in the paper is to consider five examples of economies with sticky prices or sticky expectations of inflation and to derive the behavior of inflation when real exchange rate rules are followed.⁴ By considering examples that differ in the number of commodities that are traded (or in the nominal variables that are sticky) and that differ in the way in which the real exchange rate rule is implemented, we are able to illustrate the general proposition that the authorities’ control over the inflationary process and the price level can be lost when real exchange rate rules are followed. Although the models constructed are kept deliberately simple, they are sufficient to illustrate our general point. Indeed, the kind of loss of control over the inflationary process that may be implied by following real exchange rate rules will hold in a wide class of models of the international adjustment process (see the papers collected in Frenkel and Johnson (1976)).

The paper begins with a nontechnical introduction (Section I) that discusses the concept of a nominal anchor to tie prices down and identifies the nature of the nominal indeterminacy implied by following real exchange rate rules.⁵ Section I also introduces the concepts of “indeterminacy,” “instability,” and “uncontrollability” as they relate to following real exchange rate rules and distinguishes between these concepts as they are applied in the remainder of the paper. It is argued that targets for domestic credit, in combination with real exchange rate rules, in general do not provide an exogenous nominal anchor that can tie prices down.

The remaining sections of the paper are intended as more technical illustrations of how inflation may behave in the absence of an exogenous nominal anchor for prices. What all the stochastic examples have in common is that, in the absence of an exogenous anchor, inflation tends to be whatever it was in the past, modified by the shocks to prices during the current period. We describe this characteristic of inflation as a “random-walk” property, which captures two aspects of the inflation process under real exchange rate rules: first, the inflationary process tends to be unstable and fails to converge to any long-run equilibrium level; second, shocks to inflation during any period have, on average, a tendency to change inflation in all future periods.⁶ In more detail, the examples in the paper cover the following issues.

The first example (Section II) examines the effects of uncertainty on the inflationary process when all goods are traded, nominal prices are sticky, and the nominal exchange rate is adjusted according to a measure of the difference between inflation at home and abroad in the previous period. Inflation is shown to have a random-walk property and to be uncontrollable by the authorities; its variability is determined by the nature of the uncertainty in the system. Shocks to the demands for and the supplies of goods are shown to have cumulative effects on inflation, the variance of which increases over time—in some instances, without bounds. In this example, instability in the inflationary process tends to lead to instability in real exchange rates.

The second example (Section III) extends the first exercise to include both traded and nontraded goods and studies the role of financial markets under real exchange rate rules. Whereas inflation remains difficult to control and again has a random-walk property, its behavior is more complex; potentially explosive behavior can occur depending on the speed at which the prices of nontraded goods adjust. The example also demonstrates how under a real exchange rate rule the money supply is able to adjust passively through the balance of payments and, hence, why the inflationary process cannot be anchored through a domestic credit target.

The third example (Section IV) focuses on the implications that stickiness in the formation of expectations of inflation has for the inflation process and applies the natural-rate hypothesis to exchange markets. The authorities are assumed to set the nominal exchange rate on the basis of the expected inflation rate of the private sector and with a view to offsetting shocks that change the real exchange rate. As in previous examples, the inflationary process may have a random-walk property; in this example, rapidly increasing inflation may emerge when the targeted real exchange rate of the authorities is above the equilibrium real exchange rate.

The fourth example (Section V) considers some differences in the behavior of inflation in response to nominal shocks under flexible exchange rates and under real exchange rate rules, in a model of overshooting that derives from Dornbusch (1976). Under flexible exchange rates, nominal exchange rates can jump in response to nominal disturbances; under real exchange rate rules, however, no such jumping can occur. Real exchange rate rules can then lead to instability of the inflation process.

The final example (Section VI) considers whether a sustained policy of sterilizing the monetary inflows associated with intervention in the foreign exchange market can allow the authorities to control inflation while following a real exchange rate rule. Sterilization is shown to lead to instabilities in the system under general conditions, suggesting that this policy is infeasible. Concluding comments are presented in the last section, and two appendices elaborate details of the examples given in Sections V and VI.

I. Real Exchange Rate Rules and Determination of the Price Level

The issues raised in this paper fall into the area of monetary theory and the determination of the price level, rather than in the area of real theory with its emphasis on determination of the relative prices of goods. This section addresses several theoretical issues that arise with regard to the determination of the price level and how monetary policy can tie prices down. The section provides a background for the examples contained in the remainder of the paper and illustrates why the authorities will tend to lose control over the price level or the inflationary process when following real exchange rate rules.

It is convenient to begin with a dichotomized economic system that has a “real” and a “monetary” part.⁷ In such a system, the real variables—the relative prices of goods, real incomes, real expenditures, and the like—are determined independently of the level of nominal variables by equations such as those given by

\begin{matrix} \begin{matrix} q_{i}^{d} (\frac{P_{1}}{P_{m}}, \frac{P_{2}}{P_{m}}, \dots, \frac{P_{m}}{P_{m}}, E) \\ = q_{i}^{s} (\frac{P_{1}}{P_{m}}, \frac{P_{2}}{P_{m}}, \dots, \frac{P_{m}}{P_{m}}, E) i = 1, m . \end{matrix} & (1) \end{matrix}

Here there are assumed to be m goods, and equation (1) represents the equilibrium condition for the ith good in terms of equality between the demand for and supply of that good. Demands and supplies depend in general on all relative prices (P_i/P_m) and on real factor endowments (E). With m goods there are at most m - 1 independent equilibrium conditions of the form given by equation (1), and these conditions can be regarded as giving rise to equilibrium relative prices, as functions of exogenous variables such as factor endowments, according to

\begin{matrix} \frac{P_{i}}{P_{m}} = \frac{P_{i}}{P_{m}} (E); & \begin{matrix} i = 1, (m - 1) . & (2) \end{matrix} \end{matrix}

In this system a scaling up or down of all nominal prices by the factor K (a reform in which a zero is added to, or taken off, all prices) has no effect on any real demand or supply.

Absolute prices are determined on the monetary side of the economy, as given by

\begin{matrix} M V = P Y, & (3) \end{matrix}

where M is the stock of money (the unit of account for the nominal prices, P_i - P_m), V is velocity, Y is the real volume of transactions, and P is a price index that is homogeneous of degree one in the money prices of the m goods. With V and T given by the real side of the economy, equation (3) determines the price level (index) if the authorities set the money supply.⁸

In this system a doubling of the money stock leads to a doubling of money prices while leaving all real variables unchanged.⁹ In other words, money is neutral or is a veil as regards determination of the real variables of the system. Setting the money supply is not, of course, the only kind of monetary policy that is possible in such a system; monetary policy could, for example, aim to stabilize the price level, with the money stock then being determined endogenously.

In a system described by equations (1)-(3), it is interesting to speculate about how the price level would be determined if the authorities did not set the money supply or try to stabilize prices. From the equations it is apparent that such a policy raises difficulties. By assumption, real behavior is independent of the absolute price level and depends only on relative prices and on endowments. The set of equations given by equation (1) cannot therefore give a solution for the price level (one level is as good as any other). Nor can equation (3) determine absolute prices, since the authorities are assumed not to set the money supply or price level.

The price level is clearly indeterminate in this case. If the model under consideration describes an economy in which the authorities are not concerned with nominal variables, such a statement does not take one very far. The price level will obviously be at some level, and in that sense will have been determined. The important point is that, at whatever level prices have been determined, the model cannot predict what that level will be and at what point the price level may have escaped control by the authorities.

In essence, our argument on the implications of real exchange rate rules for prices and for inflation in the long run is based on similar considerations. To be less abstract, assume a small economy with its own money, with a real side described by equation (4), and with a monetary side given by equation (5):

\begin{matrix} d ({SP}^{*} / P, Y, E) = s & (4) \end{matrix}

\begin{matrix} M V = P Y . & (5) \end{matrix}

The economy is assumed to produce a single domestic good, and there is a single foreign good; velocity and real income are assumed to be determined independently of nominal variables when all nominal variables are flexible (see footnote 9).

There are three nominal variables in this model economy: P (the price of domestic output), S (the domestic currency price of foreign exchange), and M (the domestic money supply). If the authorities do not set M, P, or S but instead set the real exchange rate (the ratio of SP* to P), it is interesting to consider how the price level is determined. When the authorities intervene in the foreign exchange market so as to peg the real exchange rate, the money supply will change either through intervention in the foreign exchange market (ΔF) or through intervention in domestic financial markets (ΔC). At any moment, the money stock can thus be written as

\begin{matrix} M = C + F . & (6) \end{matrix}

A policy of pegging the real exchange rate and setting domestic credit (C) clearly does not lead to the price level being tied down by the authorities, since the money supply can change through the balance of payments.¹⁰ A real exchange rate rule and a domestic credit target are therefore insufficient for the authorities to anchor prices.

The discussion thus far raises several specific issues that will be covered in the examples that follow. First, it is widely believed that in many economies nominal variables are neutral only in the “long run,” a belief that casts some doubt on the usefulness of an analysis built on long-run results.¹¹ The examples of the paper, however, are all formulated in the “short run,” with some kind of temporary stickiness in prices or in expectations that allows for nominal variables to be nonneutral. The tendency of economies to display longer-run neutrality is sufficient, as it turns out, to rehabilitate the usefulness of long-run results and to give rise to issues of price level determination when there is no exogenous nominal anchor to control prices.

Second, the indeterminacy of the price level in the long run under real exchange rate rules occurs because of the insufficiency of domestic credit to control prices when the money supply can vary endogenously through the balance of payments. It is interesting to consider whether the authorities will be able to control prices by switching from domestic credit to monetary targets when following real exchange rate rules. This is the subject of the second and fifth examples of the paper (in Sections III and VI, respectively); in the latter example it is shown that the sterilization of monetary inflows through the balance of payments, which is implied if one is to have a real exchange rate rule and a money supply target, typically leads to an instability in the system that makes sterilization infeasible over long periods.

Finally, at many points in the paper we use the terms “indeterminacy,” “uncontrollability,” and “instability.” Some differences between these terms should be noted. By prices or inflation being indeterminate we mean that an economic model cannot reveal what their long-run values will be; this is the case under real exchange rate rules with domestic credit targets. By a variable being uncontrollable we mean that the authorities will not be able to influence its value systematically. By a system being unstable we mean that it will not converge (in an expected-value sense) to a long-run equilibrium position. A general point to be made is that in some of the examples we find that inflation may exhibit explosive behavior. This finding should not be interpreted to mean that inflation will in practice explode when a real exchange rate rule is followed. If such explosive behavior is indicated, in general it should be interpreted as implying an inconsistency in a policy mix that will be resolved in one way or another. Volatile behavior of inflation is one kind of resolution; a modification of the policy setting is another.

II. Stochastic Shocks and the Inflationary Process

A policy that adjusts the nominal exchange rate according to inflation differentials can have important implications for the stability of the price level and inflation. Assume that information on prices is reported with a one-period lag. If world inflation is zero, then the rule for adjusting the exchange rate is assumed to be given by

\begin{matrix} {\tilde{s}}_{t} = {\tilde{p}}_{t - 1} + u_{t}, & (7) \end{matrix}

where s is the logarithm of the nominal exchange rate, expressed as the domestic currency price of one unit of foreign currency; ${\tilde{s}}_{t}$ is defined as ${\tilde{s}}_{t} \equiv s_{t} - s_{t - 1}$ ; and P_t is the logarithm of the general price level (accordingly, ${\tilde{P}}_{t - 1}$ is inflation in period t - 1); and u_t represents a random term assumed to have a mean of zero, which may be due to imperfect information about prices. In this case the “true” inflation rate would be ${\tilde{P}}_{t - 1}$ , whereas the authorities perceive it to be ${\tilde{P}}_{t - 1} + u_{t}$ ; u_t could also represent any one-step devaluations the authorities may undertake in trying to affect the real exchange rate.¹²

The domestic nominal price of a single traded good (the price level) is assumed to adjust slowly to divergences between the (logarithm of the) actual real exchange rate, s_t - p_t, and its long-run equilibrium level, $\bar{z}$ , which is assumed to be constant. (This assumption is not essential for the conclusions, which depend only on the long-run equilibrium real exchange rate being determined independently of monetary variables.) Inflation then follows

\begin{matrix} {\tilde{p}}_{t} = φ (s_{t} - p_{t} - \bar{z}) + v_{t} + m, & \begin{matrix} φ > 0. & (8) \end{matrix} \end{matrix}

Here φ is a positive constant; v_t is a disturbance that follows a random walk, as given by v_t - v_t-1 = e_t; and m could represent the equilibrium inflation rate or the inflation rate targeted by the authorities.¹³ Equation (8) implies that the change in the inflation rate is governed by

\begin{matrix} {\tilde{p}}_{t} - {\tilde{p}}_{t - 1} = φ ({\tilde{s}}_{t} + {\tilde{p}}_{t}) + e_{t} . & (9) \end{matrix}

Substituting equation (7) for s_t in equation (9) yields the following expression for the current inflation rate, ${\tilde{p}}_{t}$ :

\begin{matrix} {\tilde{p}}_{t} = {\tilde{p}}_{t - 1} + (e_{t} + φ u_{t}) / (1 + φ) . & (10) \end{matrix}

The important implication of equation (10) is that the inflation rate in any period is equal to the inflation rate in the last period plus a composite disturbance term. This disturbance will be denoted by w_t, where w_t ≡ (e_t + φu_t)/(1 + φ). Whenever equation (8) accurately describes the price-formation process, equation (10) implies that the authorities will not be able to control inflation when they are adjusting the nominal exchange rate according to the rule described by equation (7): inflation will follow a random walk, and successive disturbances will have cumulative effects on inflation. Moreover, there will be no convergence of the actual inflation rate, ${\tilde{p}}_{t}$ , toward its equilibrium or target rate, m. ¹⁴

If the exchange rate rule was introduced at time zero, current inflation can be written as

\begin{matrix} {\tilde{p}}_{t} = {\tilde{p}}_{0} + Σ_{j = 1}^{t} w_{j} & (11) \end{matrix}

or, by using equation (8), as

\begin{matrix} {\tilde{p}}_{t} = φ (s_{0} + p_{0} - \bar{z}) + v_{0} + m + Σ_{j = 1}^{t} w_{j} . & (12) \end{matrix}

Equations (11) and (12) together imply that the inflation rate that existed at the time the exchange rate rule was implemented will have a tendency to persist. A one-step devaluation in any period over and above ongoing domestic inflation will tend to raise the inflation rate in all future periods: if during any period the authorities devalue by an additional 1 percent (that is, in addition to the nominal depreciation needed to offset inflation differentials), inflation in all future periods will, on average, rise by φ/(1 + φ) percent. The random-walk property of the inflationary process comes about in this example because there is no exogenous nominal anchor for the price level or inflation; the inflation rate therefore will not tend to settle down to any steady-state level, and shocks will have the cumulative effects outlined.

Equation (12) does not necessarily imply that there will be accelerating inflation; it does, however, suggest that the authorities cannot control inflation under a real exchange rate rule and that the variance of inflation may increase over time. The variance of the inflation rate depends on the process governing the composite disturbance term w_t. If e_t and u_t are distributed independently over time, each with mean of zero and variance of var(f) and var(u) respectively, the variance of the inflation rate increases without bounds over time. The variance (conditional upon current information) of the inflation rate at any time T in the future is given by

\begin{matrix} var ({\tilde{p}}_{T}) & = & var (v) + T [var (w)] \\ = & var (v) + T [var (e) + φ^{2} var (u)] / {(1 + φ)}^{2} . \end{matrix}

As time progresses, this variance clearly goes to infinity, which might be called the worst case. If w_t follows a more convenient process, the variance of inflation will initially increase and then approach a steady-state level. Assume that w_t follows

w_t = bw_t-1 + x_t, 1 > b > 0,

where x_t is distributed independently over time with variance var(x_t). The variance of the inflation rate at time t can then be written as

var ({\tilde{p}}_{t}) = var (v) + Σ_{j = 0}^{t} b^{j} var (x) .

In this case the variance initially increases; it will, however, reach a steady-state level equal to

var ({\tilde{p}}_{\infty}) = var (v) + (\frac{1}{1 - b}) var (x) .

The purpose of real exchange rate rules is frequently to keep the real exchange rate constant.¹⁵ A real exchange rate rule, such as that given by equation (7), that is based on past inflation rates might not, however, achieve a constant real exchange rate it inflation becomes highly variable. In the context of the present example, the real exchange (denoted by q_t = s_t - p_t) follows

\begin{matrix} q_{t} = q_{t - 1} + \frac{1}{1 + φ} (u_{t} + e_{t}) . & (13) \end{matrix}

Equation (13) implies that if the real exchange rate rule is implemented by using past inflation rates as in equation (7), the real exchange rate follows a random walk and thus is itself unstable.¹⁶ There is no tendency then for the real exchange rate to converge to its long-run equilibrium $\bar{z}$ .

This illustrative case shows that, given our price-formation structure, rules that adjust the nominal exchange rate according to inflation differentials imply that the variability of the inflation rate is increased and that the inflation rate is not controllable by the authorities. Contrast this situation with that of a conventional fixed or nominal crawling-peg exchange rate policy. If the authorities aim for an inflation rate of m, they could set a rate of devaluation of m percent per period for the crawling peg (since world inflation is assumed to be zero). This policy can be written formally as

\begin{matrix} {\tilde{s}}_{t} = m + u_{t} . & (14) \end{matrix}

The inflation rate is then governed by

\begin{matrix} {\tilde{p}}_{t} = {\tilde{p}}_{t - 1} / (1 + φ) + m φ / (1 + φ) + (e_{t} + φ u_{t}) (1 + φ) . & (15) \end{matrix}

Equation (15) implies that the inflationary process is stable under a crawling peg; indeed, the expected steady-state inflation rate implied by equation (15) is equal to m. ¹⁷ The central difference between this exchange rate regime and the real exchange rate regime described by equation (7) is that the crawling peg involves the authorities setting an exogenous nominal rate of devaluation.

Under the real exchange rate rule the authorities have no target for the nominal exchange rate, which is indexed on last period’s inflation rate.

III. The Inflationary Process with Nontraded Goods

The example in this section concentrates on the implications of differences in the behavior of the prices of traded and nontraded goods for the nature of the inflationary process under a real exchange rate rule. The exchange rate rule in this example is given below, where we allow for nonzero inflation in the rest of the world and abstract from random variations in the rate of devaluation:

\begin{matrix} {\tilde{s}}_{t} = {\tilde{p}}_{t - 1} - π . & (16) \end{matrix}

Here π is a fixed rate of world inflation. In this example the change in the general price level or consumer price index (CPI), ${\tilde{p}}_{t}$ , is defined as a weighted average of the prices of traded and nontraded goods, with respective weights of 1 - α and of α. It is assumed that the domestic price of tradables is determined directly by the exchange rate and world market prices; this assumption implies that the change in the price of traded goods is equal to the change in the exchange rate plus world inflation. CPI inflation is then given by

\begin{matrix} {\tilde{p}}_{t} = α {\tilde{p}}_{n, t} + (1 + α) ({\tilde{s}}_{t} + π) . & (17) \end{matrix}

The change in the price of nontraded goods is assumed to be determined by the sum of two effects. The first represents adjustments to deviations of the real exchange rate from its long-run equilibrium level, as in the first example; the second represents the inflationary forces that would change the price of nontradables even if the real exchange rate were at its long-run equilibrium level. It is assumed that these inflationary forces can be expressed in terms of past and current changes in the general price level; they then capture effects that might come from the indexation of wages and from expectations that are based on past price changes. The change in the price of nontraded goods can be written formally as

\begin{matrix} \begin{matrix} P_{n, t} & = & φ (p_{i, t - 1} + s_{t - 1} - P_{n, t - 1} - \bar{z}) \\ + ψ {\tilde{p}}_{t - 1} + (1 - ψ) {\tilde{p}}_{t}, \end{matrix} & (18) \end{matrix}

where p_{i, t} is the price of traded goods, $\bar{z}$ is the long-run equilibrium real exchange rate, and ψ represents the relative weight of past inflation in expectations about nontraded-goods inflation. A value of zero for ψ indicates no expected change in the real exchange rate; if the real exchange rate is at its equilibrium value, a value of unity for ψ implies that expectations are based only on past inflation.

The link between inflation and financial markets is captured by a simple money demand function of the form

\begin{matrix} m_{t}^{d} = p_{t} - ε (r + {\tilde{p}}_{t}) = p_{t} - ε {\tilde{p}}_{t}, & (19) \end{matrix}

where the real interest rate, r, is assumed to be constant and, in what follows, is set equal to zero; $m_{t}^{d}$ represents the logarithm of the demand for nominal money balances; and ε is the semi-elasticity of the demand for money with respect to the nominal interest rate $(R = r + {\tilde{p}}_{t})$ . (For simplicity and illustrative purposes, it is assumed that expected inflation as of period t is equal to inflation during period t.) The money market is assumed not to be continually in equilibrium; it is instead assumed that money holdings adjust by a fraction of the discrepancy between money demand and the money balances that existed at the beginning of each period:

\begin{matrix} m_{t} - m_{t - 1} = {\tilde{m}}_{t} = λ (m_{t}^{d} - m_{t - 1}) . & (20) \end{matrix}

The balance sheet of the central bank implies that changes in the money supply can originate either from domestic credit expansion, ΔDC, or from increases in reserves, ΔR:

\begin{matrix} {\tilde{m}}_{t} ≅ \frac{Δ M_{t}}{M_{t}} = \frac{Δ D C_{t}}{M_{t}} + \frac{Δ R_{t}}{M_{t}}, & (21) \end{matrix}

where M_t represents the stock of nominal money (variables indicated by lowercase letters are in logarithms).

Equations (19)–(21) imply that a rise in prices has to be associated with an increase in the stock of money, which can come about either through domestic credit expansion or through the balance of payments. Because real exchange rate rules typically have been implemented in conjunction with a limit on domestic credit expansion, only the balance of payments channel is considered here. Moreover, since the most volatile item in the balance of payments is typically capital flows, capital flows are likely to be the balance of payments account that adjusts to satisfy shifts in money demand, at least in the short run.

A crucial issue that has arisen in some countries that have followed real exchange rate rules is whether capital flows have caused inflation or vice versa. In the context of real exchange rate rules and the example we have constructed, inflation is determined independently of capital flows and of all other financial variables; capital flows serve only to increase the available money balances necessary to satisfy a higher demand for money that is due to price level increases.

This conclusion would not be affected if excessive money growth had an independent inflationary impact on nontraded-goods prices. To take this effect into account, equation (18) could be rewritten as

\begin{matrix} {\tilde{p}}_{n, t} = φ (R E_{t - 1} - \bar{z}) + ψ {\tilde{p}}_{t - 1} + (1 - ψ) {\tilde{p}}_{t} + γ (m_{t} - m_{t}^{d}), & (18 a) \end{matrix}

where RE_t-1 is the real exchange rate and $R E_{t} \equiv p_{i, t} + s_{t} - p_{n, t}$ . The term $γ (m_{t} - m_{t}^{d})$ represents the independent effect of money on nontraded-goods inflation. Using equations (19) and (20) allows us to rewrite equation (18a) as

\begin{matrix} \begin{matrix} {\tilde{P}}_{n, t} & = & φ ({RE}_{t - 1} - \bar{z}) + ψ {\tilde{p}}_{t - 1} + (1 - ψ) {\tilde{p}}_{t} \\ + γ [γ Σ_{i = 0}^{t} (p_{t - i} - ε {\tilde{p}}_{t - 1 - i}) {(1 - λ)}^{i} - (p_{t} - ε {\tilde{p}}_{t - 1})] . \end{matrix} & (18 b) \end{matrix}

Equation (18b), like equation (18), contains only expressions in terms of the general price level, the price of nontradables, and the exchange rate; it can thus be solved for the current inflation rate as a function only of past inflation, in a similar way as solving equation (18). The result, however, is more complicated because in this case inflation becomes an infinite-order difference equation. Note that rising inflation in general has an ambiguous effect on money demand and, hence, the capital account; whereas higher prices raise the nominal demand for money, higher expected inflation reduces real money demand. In the analysis of the paper, the former effect is assumed to dominate. Because equation (18b) has an infinite-order distributed lag, it is not possible to determine the stability of the resultant process for inflation in general; equation (18b) does, however, imply that the authorities cannot control inflation.

The adjustment process that satisfies the increased demand for nominal balances that is the result of an increasing price level is not specified here. Such an adjustment process does not in general have to be based on perfect capital mobility.¹⁸ One possibility would be to use the balance-sheet identity that the change in reserves, ΔR_t, is the sum of the current account and the balance of capital movements. The current account might then be a function of the real exchange rate, and net capital movements could be a function of the interest rate differential (adjusted for expectations about exchange rate changes). Because the real exchange rate rule implies that prices and the exchange rate follow an autonomous process, the only variable that is free to adjust to induce the required flow of reserves (at a given rate of domestic credit expansion) is the interest rate. Sudden capital inflows might then happen because the inflationary process set in motion by the real exchange rate rule leads to a higher demand for nominal balances, a demand not satisfied by domestic credit expansion.¹⁹

These points can be illustrated formally by noting that inflation is determined by the system of equations (16) through (18). These give rise to a homogeneous,²⁰ second-order difference equation of the form

\begin{matrix} \begin{matrix} [1 - α (1 + ψ)] {\tilde{p}}_{t + 1} + [(φ - 2) + 2 α (1 - ψ)] {\tilde{p}}_{t} \\ - [α (1 - ψ) + (φ - 1)] {\tilde{p}}_{t - 1} = 0, \end{matrix} & (22) \end{matrix}

with roots ρ₁ and ρ₂, where

\begin{matrix} ρ_{1} = 1, & ρ_{2} = 1 \end{matrix} - \frac{φ}{1 - α (1 - ψ)} .

The unitary root is analogous to the random-walk property found in the first example (Section II); any disturbance to the inflation rate has a tendency to show up in all future inflation rates. Inflation is thus unstable in the sense that there is no anchor in the form of a steady-state inflation rate to which the system would eventually settle down. The second root indicates that inflation might be explosive and could exhibit fluctuations. Explosive fluctuations will occur if the second root is smaller than -1; that is, if φ > 2[1 - α(1 - ψ)].²¹

The solution for the current inflation rate can be written as

\begin{matrix} {\tilde{p}}_{t} = A_{1} + A_{2} ρ_{2}^{t}, & (23) \end{matrix}

which shows that inflation and the price level depend on initial conditions, as given by A₁ and A₂, and on the second root, ρ₂. Because money demand is also a function of the price level and inflation, money demand can be expressed in terms of the same initial conditions and the behavior of the second root:

\begin{matrix} m_{t}^{d} = p_{0} + \underset{i = 0}{Σ} \ln (A_{1} + A_{2} ρ_{2}^{i}) - ε (A_{1} + A_{2} ρ_{2}^{t}) . & (24) \end{matrix}

The behavior of the real exchange rate implicit in this system is somewhat different from that in the first example. Using the system of equations (16)-(18) allows the CPI-baseil real exchange rate, denoted by q_t ≡ p_{i, t} + s_t - p_{n, t}, to be expressed as follows:

\begin{matrix} q_{t} (ψ + \frac{1 - α}{α}) = (ψ + \frac{1 - α}{α} - \frac{φ}{α}) q_{t - 1} + \frac{φ}{α} \bar{z} . & (25) \end{matrix}

Equation (25) implies that there is a steady-state real exchange rate that is equal to the equilibrium real exchange rate, $\bar{z}$ , and that the real exchange will tend to settle down to this equilibrium value as long as the second root in the system (equation (22)) above is larger than - 1.

Given the partial adjustment process (equation (20)). money demand determines the evolution of the money supply. If domestic credit expansion is limited, the implication is that the balance of payments adjusts to changes in money demand. Indeed, using equations (20) and (21) allows the balance of payments to be written in terms of past and current values of the demand for money:

\begin{matrix} \frac{Δ R_{t}}{M_{t}} ≅ - \frac{Δ D C_{t}}{M_{t}} + \tilde{λ} Σ_{i = 0}^{t} m_{t - 1}^{d} {(1 - λ)}^{i - 1} . & (26) \end{matrix}

Because money demand is determined by the evolution of prices as in equation (24), equation (25) shows that the balance of payments and, thus, changes in reserves (sterilized intervention is not considered here) are also influenced by prices when the authorities follow a real exchange rate rule.²² The large capital inflows experienced by some countries that have followed real exchange rate rules cannot necessarily be viewed as inflationary. Instead, as in the example above, these flows might be seen as the consequence of the high inflation rates that are caused by the real exchange rate rules. The increases in the price level brought about through these rules lead to a higher nominal demand for money, which in turn is satisfied through the balance of payments, when domestic credit expansion is limited,

IV. The Inflationary Process with Flexible Prices and a Surprise Supply Function: An Applicaton of the Natural-Rate Hypothesis

The preceding two examples have featured economies in which some prices are sticky. In the example of this section, prices are assumed to be flexible, whereas expectations are assumed to adjust adaptively or sluggishly. The example represents an application of the natural-rate hypothesis to exchange markets, and it is shown how maintaining the real exchange rate away from its full equilibrium (or natural rate) requires either continually rising or falling inflation.

Consider an economy that produces a single good that is an imperfect substitute for foreign output. The authorities set the nominal exchange rate so as to maintain a constant real exchange rate, a policy that requires them to adjust the exchange rate not only for inflation differentials, but also for shocks that affect the equilibrium real exchange rate.²³

The supply and demand functions for domestic output are assumed to be of the form

\begin{matrix} y_{t}^{s} = α [p_{t} - E_{t - 1} (p_{t})] + \sum_{t}^{s} & (27) \end{matrix}

\begin{matrix} y_{t}^{d} = β (s_{t} - p_{t}) + Σ_{t}^{d}, & (28) \end{matrix}

where all variables are measured in logarithms. Foreign prices are constant and have been set equal to unity, and all parameters are defined to be positive; $Σ_{t}^{d}$ , $Σ_{t}^{s}$ denote real shocks to supply and demand, respectively, that are assumed to have a mean of zero. According to equation (27), supply depends on the gap between the actual and expected price levels, and on shocks as given by $Σ_{t}^{s}$ ; according to equation (28), demand depends on the price of foreign relative to domestic output (the real exchange rate) and on $Σ_{t}^{d}$ . The authorities are assumed to have a domestic credit target, and we do not explicitly consider financial markets in this example. Money balances are assumed to adjust passively through the balance of payments, as in the examples in Sections II and III.

It is convenient to add and subtract P_t-1 to and from the right-hand side of equation (27). With the real exchange rate given by r_t = s_t - p_t, equations (27) and (28) can be rewritten as

\begin{matrix} y_{t}^{s} = α [{\tilde{p}}_{t} - \underset{t - 1}{E} ({\tilde{p}}_{t})] + Σ_{t}^{s} & (27 a) \end{matrix}

\begin{matrix} y_{t}^{d} = β r_{t} + \sum_{t}^{d} . & (28 a) \end{matrix}

The rule for setting the nominal exchange rate is assumed to keep the real exchange rate constant at the level obtaining in period zero (r₀); this assumption requires that the authorities adjust the nominal exchange rate according to their perception of the expected inflation rate of the private sector and in response to shocks that alter the real exchange rate.²⁴ Under these conditions, the evolution of inflation is described by

\begin{matrix} {\tilde{p}}_{t} = \underset{t - 1}{E} ({\tilde{p}}_{t}) + β / α r_{0} + 1 / α (Σ_{t}^{d} - Σ_{t}^{s}) . & (29) \end{matrix}

For simplicity, inflation is measured here by changes in the price of domestic output rather than as a weighted average of changes in the prices of domestic and foreign goods.

The real exchange rate ruling in period zero is given by

\begin{matrix} r_{0} = (α / β) [{\tilde{p}}_{0} - \underset{t - 1}{E} ({\tilde{p}}_{0})] + 1 / β (Σ_{0}^{s} - Σ_{0}^{d}) . & (30) \end{matrix}

According to equation (29), the evolution of inflation is related to the behavior of expectations and to the level of the real exchange rate in period zero; it also depends on the nature of the shocks to demand and supply.

The behavior of inflation is considered under the assumption that expectations of inflation are sticky or adaptive; specifically, expectations are assumed to evolve according to equation (31), where θ is a positive parameter lying between zero and unity:

\begin{matrix} \underset{t - 1}{E} ({\tilde{p}}_{t}) = θ {\tilde{p}}_{t - 1} + (1 - θ) {\tilde{p}}_{t - 2} . & (31) \end{matrix}

Equation (31) represents a kind of adaptive expectations mechanism; equations like it have been used to proxy expected inflation in many Phillips curves. When θ=1, the implication of equation (31) is that expectations are static and that expected inflation is equal to the ongoing inflation rate; in general, expected inflation is a weighted average of inflation in periods t - 1 and t - 2.

Substituting equation (31) into equation (29)—and using equation (30) to eliminate r₀—gives rise to an inflation equation of the form

\begin{matrix} \begin{matrix} {\begin{matrix} \tilde{p} \end{matrix}}_{t} & = & θ {\tilde{p}}_{t - 1} + (1 - θ) {\tilde{p}}_{t - 2} + [{\tilde{p}}_{0} - \underset{t - 1}{E} ({\tilde{p}}_{0})] \\ + 1 / α (Σ_{0}^{s} - Σ_{0}^{d}) + 1 / α (Σ_{t}^{d} - Σ_{t}^{s}) . \end{matrix} & (32) \end{matrix}

According to equation (32), inflation follows a second-order difference equation. The general solution to equation (32) can be written in the form

\begin{matrix} {\tilde{p}}_{t} & = & A_{1} {(1)}^{'} + A_{2} {(θ - 1)}^{'} \\ + \frac{[{\tilde{p}}_{0} - {θ p}_{- 1} - (1 - θ) {\tilde{p}}_{- 2}] t}{(2 - θ)} \\ + [stochastic terms], & (33) \end{matrix}

where A₁ and A₂ are arbitrary constants, and the roots of the difference equation are unity and (θ - 1).

To consider the nature of the inflationary process implied by equation (33), consider the case in which expectations are static and, hence, θ=1. With reference to either equation (32) or (33), it can be seen that in this case inflation follows a random walk around a trend. The trend is determined by the nature of the shocks to demand and supply and by the difference between inflation in the initial and earlier period $({\tilde{p}}_{0} - {\tilde{p}}_{- 1})$ :

\begin{matrix} {\tilde{p}}_{t} & = & {\tilde{p}}_{t - 1} + [({\tilde{p}}_{0} - {\tilde{p}}_{- 1}) + 1 / α (Σ_{0}^{s} - Σ_{0}^{d})] \\ + 1 / α (Σ_{t}^{d} - Σ_{t}^{s}) . & (34) \end{matrix}

The solution to equation (34) can be written as

\begin{array}{l} {\tilde{p}}_{t} = {\tilde{p}}_{0} + ({\tilde{p}}_{0} - {\tilde{p}}_{- 1}) t + \frac{1}{α} Σ_{i = 0}^{t} (Σ_{i}^{d} - Σ_{i}^{s}) \\ t = 1, 2, 3, \dots . & (35) \end{array}

Equation (35) illustrates that, depending on whether the real exchange rate held constant is above or below its “full” equilibrium value, exploding or imploding inflation may result.²⁵ The intuition behind this statement is straightforward: if the authorities are maintaining the real exchange rate above equilibrium, it is necessary that actual inflation stay ahead of expected inflation. Because expected inflation, by assumption, catches up to actual inflation, inflation must be continually rising in order to hold the real exchange rate constant. More generally, with θ not equal to unity, the solution in equation (33) again has a random-walk property in which one root is equal to unity; the other root, however, is negative and lies between zero and unity. Under these conditions, the inflationary process has a more complex structure, and oscillations may occur. The particular process that inflation follows will depend on the nature of the shocks to demand and supply ( $Σ_{t}^{d}$ , $Σ_{t}^{s}$ ).

The kind of “accelerationist” argument developed in this example may help to explain why inflation has often risen sharply when real exchange rate rules have been followed. If initial devaluations are so large as to move the real exchange rate above its full equilibrium level (overdepreciation), inflation must then continually rise if the real exchange rate is to be held constant. The argument, of course, is an application of the natural-rate hypothesis, which has often been applied to labor markets, to the implications of holding the real exchange rate away from its natural or full equilibrium rate.²⁶

V. The Inflationary Process in a Model of Overshooting

The example in this section illustrates an important difference between the effects of nominal shocks under flexible exchange rates and those under a real exchange rate rule. It has been shown that under a flexible exchange rate the nominal exchange rate may “overshoot” in response to nominal disturbances when goods prices adjust slowly and capital is perfectly mobile (Dornbusch (1976)). In this section real exchange rate rules are shown to exclude such overshooting and in so doing may contribute to instability in the price level. The rationale for this result is that with flexible exchange rates the nominal exchange rate typically must “jump” to make the system stable—in more technical terms, it jumps to the stable saddle path that leads to a new steady state with a finite price level. With a real exchange rate rule, however, the nominal exchange rate can no longer jump and cannot, therefore, lead the economy to a new equilibrium. Real exchange rate rules, as opposed to fixed, predetermined nominal exchange rates, may also fix the real exchange rate; these rules therefore close other channels that might move the economy toward equilibrium.

The instability that may be caused by real exchange rate rules is illustrated here by two models. The first is kept as simple as possible to show the source of instability. The second model is somewhat more complex and takes into account a number of different effects; it arrives, however, at similar conclusions. Both models are in continuous time and abstract from the timing issues contained in the first two examples of the paper (in Sections II and III).

Model 1

The first model consists of two equations that describe, respectively, the demand for money and the balance of payments. Money demand is given by

\begin{matrix} m = α p + (1 - α) s - ε [α D (p) + (1 - α) D (s)] . & (36) \end{matrix}

All variables are expressed as deviations from their respective trend values. The general price level is given by a weighted average of the prices of domestic goods, p, and the prices of foreign goods, s (the exchange rate), when the foreign currency prices of foreign goods are normalized to unity. The notation D() designates the right-hand time derivative operator; that is, D(p) = dp/d (time). The definition of the real exchange rate rule is assumed to imply that D(p) = D(s), but this assumption does not imply that in this model goods markets are perfectly integrated; it is only the real exchange rate policy that makes this part of the economic system behave as if the law of one price held. The real exchange rate rule is assumed to fix the real exchange rate—that is, $p - s = \bar{q}$ —and this assumption implies that money demand can be rewritten as

\begin{matrix} m = α q + s - ε (s), & (37) \end{matrix}

where s is the rate of change in (the logarithm of) the exchange rate.

The second building block of the model is the link between the balance of payments and the money supply:

\begin{matrix} D (m) = β [\bar{r} - r^{*} - D (s)] . & (38) \end{matrix}

The right-hand side of equation (38) is the capital account; it is assumed that the real exchange rate that is fixed by the authorities leads to a balanced current account.²⁷ Capital inflows are an increasing function of the differential between a domestic interest rate, $\bar{r}$ , that is assumed to be fixed and an exogenous foreign interest rate, r*, that is adjusted for the expected change in the exchange rate. Capital flows are assumed to be affected negatively by the expected rate of depreciation of the nominal exchange rate; hence, in this example capital is assumed to be less than perfectly mobile. Capital flows translate into changes in the money supply, since it is assumed that the authorities keep domestic credit constant.

The real exchange rate rule does not allow the exchange rate to jump; equations (37) and (38) therefore represent an unstable system of two differential equations with two predetermined variables: the money supply, m, and the exchange rate, s.²⁸

The reason for the instability can be found by inspecting the money demand function (equation (37)). The only variable in this equation that can react to a change in the money supply that is due to an increase in domestic credit is the rate of depreciation: a decrease in money leads to a higher expected and actual rate of depreciation.²⁹ This higher rate of depreciation then leads to capital outflows (or just to lower capital inflows), which in turn reduce the money supply further and thus require an even higher rate of depreciation. This instability occurs even if there is no capital mobility; that is, even if β = 0. In such a case the money supply is constant, but a negative money shock will still require a faster rate of depreciation. The faster rate of depreciation has to be accompanied by a faster rate of inflation because the real exchange rate rule specifies that the rate of depreciation has to be equal to the rate of inflation. The faster rate of depreciation then leads to a higher price level in the future and, thus, to an even lower real money stock; a lower real money stock in turn leads to an even higher rate of depreciation so that equilibrium in the money market can be maintained.

The model thus far does not take into account a variety of channels that might move the economy toward long-run equilibrium even under a real exchange rate rule. These channels include the effects of changes in income, which may influence money demand and prices, and the effects of changes in the interest rate, which may influence money demand and capital flows. The second model does take such effects into consideration and shows that the instability problem remains, although it is no longer a necessary feature of the specification.

Model 2

The extended model contains four equations. The first describes capital flows as a function of the difference between the (expected) rate of depreciation and the interest rate differential. The equation is modified, however, to account for the hypothesis that it is foreign capital that is attracted by the covered interest rate differential. This presumption implies that the domestic currency value of the capital flows and, hence, the induced change in money have to be multiplied by the exchange rate. Capital flows are then determined by

\begin{matrix} D (m) = β [r - r^{*} - D (s)] + s . & (39) \end{matrix}

The money demand function is modified to take into account income and interest rate effects:

\begin{matrix} m = α \bar{q} + s - ε D (s) - λ r + ψ y^{d}, & (40) \end{matrix}

where y^d represents aggregate demand or income, and Ψ is the income elasticity of money demand. Money demand is also influenced by the domestic nominal interest rate, r, which is no longer assumed to be fixed. Spending, y^d, is determined by the real exchange rate, potential output, y, and the real interest rate:

\begin{matrix} y^{d} = φ (s - p + \bar{u}) + γ \bar{q} - σ [r - α D (p) - (1 - α) D (s)] . & (41) \end{matrix}

Because the real exchange rate is fixed by the real exchange rate rule, the first term on the right-hand side of equation (41) is constant and can be set equal to zero. The real exchange rate rule also implies that D(s) = D(p); equation (41) can then be rewritten as

\begin{matrix} y^{d} = γ \bar{y} - σ [r - D (s)] . & (42) \end{matrix}

Prices are assumed to follow a Phillips-curve relationship; their rate of change is a function of the divergence between actual and potential output:

\begin{matrix} D (p) = π (y^{d} - \bar{y}) . & (43) \end{matrix}

The extended model is thus given by equations (39)—(40) and (42)-(43), This second model determines the lour endogenous variables: income, y^d the interest rate, r; the change in the money supply, D(m); and the rate of inflation, D(p). which has to equal the rate of depreciation, D(s), because of the real exchange rate rule. Details of the solution can be found in Appendix I, where it is also shown that even this extended model, which takes into account the interaction between goods and financial markets, is in most cases unstable.³⁰ This is again a corollary of the principle mentioned in the introduction: with a real exchange rate rule, there is no anchor for the price level and, thus, for inflation.

VI. An Economy with a Capital Market Not Integrated with the Rest of the World: The Implications of Sterilization

In none of the examples considered does the possibility of sterilizing the monetary consequences of intervention in the foreign exchange market change the result that prices or inflation will be uncontrollable under a real exchange rate rule. There is a widespread perception, however, that sterilization might give rise to the possibility of controlling prices in the short run, provided that the degree of capital mobility is not too high. In the following example the validity of this perception is considered in the context of a model in which there is zero capital mobility and, hence, maximum scope for sterilization. It is demonstrated that a consistent policy of attempting to offset the monetary implications that intervention in the foreign exchange market has for prices or for the money supply gives rise to an instability in the system that is reflected in either unstable current accounts or foreign assets. The sustainability of sterilization is therefore questionable. The results are obtained under private sector expectations that are assumed to be consistent with the attainment of policymakers’ goals. As such, the results are derived under conditions that are particularly favorable to the success of sterilization.³¹ Because of the complexity of the model assumed, it is easier to work in continuous time and in a deterministic framework than to allow for stochastic elements. The results are general, however, and in qualitative terms can be compared with those of the earlier examples.

The structure of the model is the same as in the first example (Section II) in the sense that there is a single domestic good. There is also a domestic bond, however, which is not traded internationally and the return on which can move independently of international interest rates. A balance of payments (or current account) equation is also added to the model, and there are assumed to be no private capital transactions. With D used for the right-hand time derivative operator and with all variables other than interest rates measured in logarithms, the model consists of three equations describing the evolution of the endogenous variables (equations (44)-(46)) and a real exchange rate rule (equation (47)). For ease of exposition, time subscripts have been omitted.

Inflation:

\begin{matrix} Dp = π [α_{0} + α_{1} (s - p) - α_{2} (R - {DP}^{E}) + α_{3} (M - p) - \bar{y}] + {Dp}^{E} . & (44) \end{matrix}

Current account:

\begin{matrix} DF = β_{0} + β_{1} (s - p) + β_{2} (R - {Dp}^{E}) - β_{3} (M - p) + ρ F . & (45) \end{matrix}

Money supply (equals money demand):

\begin{matrix} \begin{matrix} M = θ C + (1 - θ) F = λ_{0} - λ_{1} R + p, & θ \in (0, 1) . \end{matrix} & (46) \end{matrix}

Real exchange rate rule:

\begin{matrix} s - p = constant = 0. & (47) \end{matrix}

Equation (44) describes a Phillips curve, with deviations of actual from expected inflation depending on the deviation of output from its potential level. The deviation of output from potential in turn depends positively on the deviation of the real exchange rate (s - p) from its equilibrium level, negatively on the deviation of the real interest rate (R - Dp^E) from its equilibrium level, and positively on real wealth (m - p) deviations (real money balances).³² For simplicity, the model abstracts from endogenous movements in output; introducing such movements would complicate the model without changing its substantive conclusions. Equation (45) describes the current account and. hence, the evolution of foreign assets held by the monetary authorities, given intervention in the foreign exchange market. The trade account component improves both as competitiveness increases and as real interest rates rise; it deteriorates as real wealth (real money balances) increases. The current account also depends on the interest payments on the outstanding net debtor position of the country, ρF.³³ Equation (46) describes equilibrium in the money market and, hence (by Walras’s law), in all financial markets. The domestic money supply, M, is divided between domestic assets, C, and foreign assets, F, held by the monetary authorities. The nominal demand for money is assumed to vary directly with the price level and to fall as the interest rate (on bonds) rises.³⁴

In a pegged exchange rate regime, the monetary authorities set the nominal exchange rate, S, and domestic credit, C, and let the private sector determine the real exchange rate, S - P, and, through the balance of payments, the money stock. With S = S₀ and C = C₀, it is straightforward to verify that in the long run, when Dp = Dp^E = 0 = DF, the real part of the system is independent of nominal variables. A doubling of the exchange rate at a constant stock of domestic credit leads to a doubling of the money supply and the price level, leaving the real exchange rate, the real interest rate, and the nominal interest rate unchanged.

Under a flexible exchange rate regime, the authorities set the money supply and let the nominal exchange rate and price level be determined endogenously, with no change in international reserves. Under this regime it is straightforward to verify that a doubling of the money supply leads to a doubling of prices and the exchange rate in the long run, while leaving all real variables unchanged. In the long run the authorities can set only the exchange rate or the money supply independently in this model. Given a level for either of these variables, there is one and only one value for the other that is consistent with long-run equilibrium.

But what about the short run when a real exchange rate rule, such as that given by equation (47), is being followed? Is it possible for the monetary authorities to peg the real exchange rate (s - p), which requires that they intervene in the exchange market to support whatever nominal exchange rate is forthcoming, while at the same time controlling either the money supply or prices? To consider this question, equation (47) specifies that the real exchange rate is held constant—for simplicity, at zero.³⁵

Holding Inflation and Prices Constant Under a Real Exchange Rate Rule

To maximize the chances of success for this policy, it is assumed that the private sector believes that the policy is feasible; it is assumed, therefore, that the expected inflation rate of the private sector is equal to the inflation rate targeted by the authorities, which is zero.

Under the conditions of following a real exchange rate rule and trying to hold inflation constant, the authorities have only one instrument to use: domestic credit. (The nominal exchange rate is linked to the price level to hold the real exchange rate constant.) Domestic credit can influence inflation because it can influence real interest rates and, hence, the deviation of output from its potential level. By the assumptions that there is zero capital mobility and that expectations of inflation are constant, the authorities are assumed to have complete leverage over real interest rates.

To determine the implications of the assumed policy rule, set s - p = Dp = Dp^E = 0 in equations (44)-(46) and also set p = 0, leading to the following system:

\begin{matrix} α_{0} - α_{2} R + α_{3} [θ C + (1 - θ) F] = 0 & (44 a) \end{matrix}

\begin{matrix} DF = β_{0} + β_{2} R - β_{3} [θ C + (1 - θ) F] + ρ F & (45 a) \end{matrix}

\begin{matrix} θ C + (1 - θ) F = λ_{0} - λ_{1} R . & (46 a) \end{matrix}

Starting from a full equilibrium, consider the implications of an autonomous fall in the demand for domestic goods at the expense of foreign goods (d α₀ <0,d β₀>0).³⁶ Instantaneously, and before foreign assets have time to change through the trade account, the authorities must expand domestic credit to push down real interest rates sufficiently to eliminate deflationary pressure. Although it appears that the monetary authorities have succeeded in controlling prices, there are further adjustments to be considered. An increased demand for foreign goods, lower real interest rates, and a higher money supply (because of a higher C) cause the trade account to deteriorate, leading to a loss of foreign assets. This weakening external position tends to reduce the money supply and to create incipient deflationary pressure.

In this model the only way for the authorities to avoid such pressure is through 100 percent sterilization of monetary outflows: every unit decrease in F is offset by an equal increase in C. From inspection of equations (44a)-(46a), the problem with this policy is apparent (see also Appendix II). Whereas inflation is kept at zero and the interest rate remains constant, the trade account never moves back into balance. Under these conditions the authorities are faced with sterilizing a given current account deficit indefinitely; in the process, they will have to buy increasingly greater quantities of bonds. Such a situation is unstable either because the supply of bonds is limited or because foreign exchange reserves eventually go to zero.³⁷ Another problem with such a policy can be seen by solving equations (44a)-(46a) for the current account (that is, DF):

\begin{matrix} \begin{matrix} DF & = & β_{0} - β_{3} λ_{0} \\ + [β_{2} + β_{3} λ_{1}] [α_{0} + α_{3} λ_{0}] {[α_{2} + λ_{1} α_{3}]}^{- 1} + ρ F . \end{matrix} & (48) \end{matrix}

Equation (48) shows that the current account deteriorates at an increasing rate because of the effect of interest payments. This result also implies that the authorities do not control the current account if they try to keep the real exchange rate constant and, at the same time, try to control inflation. This situation is in sharp contrast to one of the purposes of real exchange rules, which is to control the current account. The loss of control over the current account arises in the present context because the current account is not determined exclusively by the real exchange rate and the authorities lose control over the other factors that determine the current account as they try to control simultaneously the price level and the real exchange rate.

Holding the Money Supply Constant Under a Real Exchange Rate Rule

In the previous example, inflation and prices remain constant while the policy rule is in place. The money supply initially contracts and then remains constant. In a regime in which the money supply is always held constant, it is straightforward to verify that the system again is unstable.³⁸

Consider a decrease in the demand for domestic goods similar to that assumed above. From equations (44)-(47) it is apparent that, at the instant of the shock, prices are fixed so that financial equilibrium with a given money supply ties down the interest rate. Prices then start falling over time, tending to lower the nominal demand for money and to reduce the trade account by increasing real wealth. With the nominal money stock held constant by means of sterilization, the domestic interest rate tends to fall. Although this fall in the interest rate tends to lessen deflationary pressures, it leads to further deterioration in the trade account and to additional sterilization.

Again there is no tendency for the current account to settle down to zero. Price deflation will, however, tend toward zero, and in this sense holding the money supply constant stabilizes inflation (apart from temporary deviations). Similar problems as under an inflation target clearly arise with respect to the sustainability of the policy.

These points can be seen formally by solving equations (44)-(46) for DF and DP:

\begin{matrix} D P = π {α_{0} + λ_{0} [α_{3} - (α_{2} / λ_{1})] + (M_{0} - p) [α_{3} + (α_{2} / λ_{1})]} & (49) \end{matrix}

\begin{matrix} D F = β_{0} + β_{2} λ_{0} / λ_{1} - (M_{0} - p) [β_{3} + (β_{2} / λ_{1})] + ρ F . & (50) \end{matrix}

The first equation implies that the price level will eventually settle down to a steady-state level. The current account, however, is again unstable. As the price level goes toward its steady-state level, the trade account deficit goes toward some constant, and interest payments on accumulated deficits then lead to an increasing current account deficit. The system of equations (49) and (50) implies again that the authorities have lost control of the current account, although they keep the real exchange rate constant. By attempting to sterilize the monetary consequences of a real exchange rate rule, they lose control over the factors that influence the current account.

There are, of course, important senses in which the results obtained in this example are “special,” and one therefore would not want to take the specific characteristics of adjustment in each case too seriously. There is a general point already mentioned, however, that transcends the specifics of the model. It is that a policy of following a real exchange rate rule and trying to control the money supply or prices (or both) is likely to be unsustainable; control at some point will break down. Thus, although it would be possible to question particular characteristics of the model—for example, that there are no wealth effects when there is 100 percent sterilization—it is easy to demonstrate that, if wealth effects attributable to public bonds do exist, instability appears elsewhere in the system.³⁹ Indeed, the existence of wealth effects from sterilization in conjunction with a real exchange rate rule often serve to lead to instability in the real interest rate and current account.

The example considered in this section was intended to be the most favorable to following a real exchange rate rule and sterilizing. If one moves in the direction of allowing for some capital mobility and allows expected inflation to vary, both of these factors would tend to reduce the leverage of domestic credit on real interest rates. Both would tend, therefore, to increase the volume of bond sales necessary to influence real interest rates and, hence, would make the eventual collapse of the policy mix inevitable in time. The policy mix considered is in general unsustainable, and in this important sense demonstrates the infeasibility of following a real exchange rate rule and having a money supply or inflation target.

VII. Conclusions

This paper has examined the consequences of real exchange rate rules for the inflationary process in the context of a variety of different models. The models were designed to capture and describe the different ways in which the functioning of economies is affected by stickiness in prices or by expectations of inflation when real exchange rate rules are followed. Whereas these examples do not cover all the conceivable situations that may be encountered, they all do suggest that the monetary authorities may no longer be able to control inflation if they set the nominal exchange rate according to a real exchange rate rule and that, if the authorities do try to control inflation, they will tend to lose control of another important economic variable. Moreover, the examples suggest that under certain conditions exploding inflation may be the result when a real exchange rate rule is followed.

The source of this potential instability can best be understood by using the fundamental insight of the monetary approach to the balance of payments: that monetary and exchange rate policies are two equivalent, but mutually exclusive, ways to determine inflation in the long run (Frenkel (1976)). Given this fundamental relationship between monetary and exchange rate policy, a real exchange rate rule is essentially a policy of full monetary accommodation: any shock to the price level is “validated” 100 percent through the exchange rate and, by way of the balance of payments, through the money supply.

It might be argued that this accommodation is not immediate because the feedback from the exchange rate to the money supply is given by the balance of payments, which might react only slowly to exchange rate movements. Recent developments in some countries that follow real exchange rate rules suggest, however, that very high inflation rates might emerge even within relatively short periods of time.

Apart from the question of how fast the potential instability manifests itself in actual inflation rates, it has also been argued that the authorities might neutralize all feedback through the balance of payments by a policy of sterilized intervention. It is in general recognized that sterilized intervention is a viable policy only for the short run, but it has been suggested that this short run might be long enough for practical purposes. The example presented in Section III of this paper, however, suggests that sterilized intervention may have no effect on inflation even in the short run. In the context of that example, sterilized intervention would produce only a temporary monetary disequilibrium without having any effect on inflation in the short or the long run. The example in Section VI suggests that successful sterilization might lead to instability in variables other than prices.

All the examples in the paper reach the result that the authorities may lose control over the inflationary process when following a real exchange rate rule. The example in Section IV in particular, however, implies that whether the targeted real exchange rate is above or below the equilibrium rate has important implications for whether inflation will be expected to increase or decrease, and for the likely course of the balance of payments. In situations in which the real exchange rate is overdepreciated, inflation is likely to rise and the balance of payments to improve. Conversely, when the real exchange rate is overappreciated, deflation—accompanied by deterioration of the balance of payments—is the likely outcome.

The principal conclusion of the paper can therefore be restated as follows: widely accepted principles about the general long-run properties of economics imply that under a real exchange rate rule the authorities no longer control the price level, and that inflation might become unstable. Recent events in some countries that have adopted real exchange rate rules suggest that the potential instability in inflation might manifest itself quite rapidly.

APPENDIX I Background to the Model in Section V

The building blocks of the extended model in Section V are reproduced below:

\begin{matrix} D (m) = β [r - r^{*} - D (p)] + p & (51) \end{matrix}

\begin{matrix} m = α \bar{q} - ε D (p) - λ r + ψ y^{d} & (52) \end{matrix}

\begin{matrix} y^{d} = γ \bar{y} - σ [r - D (p)] & (53) \end{matrix}

\begin{matrix} D (p) = π (y^{d} - \bar{y}) . & (54) \end{matrix}

Equations (51), (52), (53), and (54) correspond, respectively, to equations (39), (40), (42), and (43) in Section V; D(s) does not appear in the system described here because the exchange rate policy implies that D(s) = D(p). To analyze the stability of the inflationary process under these conditions, it is necessary to reduce the system of equations (51)-(54) to two differential equations in m and p. Equations (53) and (54) can be used to solve for the interest rate, r, to yield

\begin{matrix} r = \frac{γ - 1}{σ} \bar{y} + D (p) [(σ π - 1) / π σ] . & (55) \end{matrix}

Equation (55) can then be used to eliminate r from equation (51):

\begin{matrix} D (m) + β [(π σ - 1) / π σ] D (p) - p = β [\bar{y} (γ - 1) / σ - r^{*}] . & (56) \end{matrix}

This is the first differential equation of the system; to obtain the second, equations (55) and (53) can be used in equation (52):

\begin{matrix} \begin{matrix} m - {ψ / π - ε - λ [(π σ - 1) / π σ]} - p \\ = \bar{q} + \bar{y} [ψ - λ (γ - 1) / σ] . \end{matrix} & (57) \end{matrix}

Denoting the constant terms in equations (56) and (57) by C6 and C7, respectively, this system can be written more compactly as

\begin{matrix} [\begin{matrix} D & D β (\frac{π σ - 1}{π σ}) - 1 \\ 1 & [\frac{ψ}{π} - ε - λ (\frac{π σ - 1}{π σ})] - 1 \end{matrix}] [\begin{matrix} m \\ p \end{matrix}] = [\begin{matrix} C 6 \\ C 7 \end{matrix}] . & (58) \end{matrix}

The roots of the system are determined by

\begin{matrix} D^{2} [\frac{ψ}{π} - ε - λ (\frac{π σ - 1}{σ})] + D [1 + β (\frac{π σ - 1}{π σ})] - 1 = 0. & (59) \end{matrix}

Because this system involves two predetermined variables, p and m, it is unstable even if only one root is positive. It follows that the system is unstable if y [ψ/π - ε -λ(πσ - 1)/πσ]>0 because the negative constant term in equation (59) implies that there have to be two distinct real roots, one negative and one positive. If [ψ/π - ε -λ(πσ - 1)/πσ]<0, however, the system would still be unstable if [1 + p (πσ - 1)/πσ]>0. The implication therefore is that, as long as ψ/π - ε≥0, the system is always unstable. (A sufficient condition for this would be that ε = 0; that is, that money demand depends only on the interest rate and not on inflation.) Note that the stability of the system does not depend on the degree of capital mobility.

APPENDIX II Background to the Model in Section VI

The model in Section VI (equations (45)-(46)) consists of three equations that can be written in general form as

\begin{matrix} DP = f (\underset{+}{r}, \underset{+}{m}, \underline{R}, \underset{+}{α}) & (60) \end{matrix}

\begin{matrix} DF = g (\underset{+}{r}, \underline{m}, \underset{+}{R}, \underline{β}) & (61) \end{matrix}

\begin{matrix} R = h (\underline{m}) . & (62) \end{matrix}

Expected inflation has been set equal to zero; m is equal to real money balances (C + F)/P; r is the real exchange rate (S/P), and α and β are shift parameters. The real variables of this system (M, r, and R) are independent of nominal variables in the full equilibrium when DP = DF = 0. For simplicity, we abstract in this appendix from the interest payments component of the current account. The full equilibrium can be written as

\begin{matrix} \begin{matrix} \begin{matrix} r = r (α, β) \\ m = m (α, β) \end{matrix} \\ R = R (α, β) . \end{matrix} & (63) \end{matrix}

This equilibrium is assumed to exist and to be unique. Nominal variables in the full equilibrium are determined by noting that, since real variables depend only on real variables, changes in nominal variables from one full equilibrium to the next satisfy

\begin{matrix} θ \bar{C} + (1 - θ) \bar{F} = \bar{M} = \bar{P} = \bar{S} . & (64) \end{matrix}

Under a pegged nominal exchange rate regime, the authorities determine $\bar{S}$ and $\bar{C}$ . From equation (64). this determination is clearly sufficient to determine $\bar{P}$ , $\bar{M}$ , and $\bar{F}$ as well. Under a flexible exchange rate regime, the authorities set $\bar{M}$ (with $\bar{F} = 0$ ). From equation (64), this determination is sufficient also to determine $\bar{P}$ and $\bar{S}$ .

Under a real exchange rate rule, the authorities typically set only the nominal variable C. From equation (64), this determination is not sufficient to determine $\bar{M}$ , $\bar{F}$ , $\bar{S}$ , and $\bar{P}$ .

Note that this indeterminacy arises in the long run, independently of the degree of capital mobility. In the model of Section VI there is zero capital mobility. Two problems potentially arise with the real exchange rate rule: first, it does not tie down prices and the nominal money supply in the long run; second, the real rate that is pegged (r₀) may differ from the full equilibrium rate as given by equation (63), implying that no long-run equilibrium exists.

The examples in the text consider whether the authorities can follow a sustained policy of pegging the real exchange rate and sterilizing. Here, in turn, we demonstrate four propositions.

Proposition 1. In the absence of a real exchange rate rule, the model is stable, and nominal variables are controlled either by the authorities’ setting M or S (but not both).

Without a real exchange rate rule, the dynamics of the system are found by substituting r, m, and R into equations (60) and (61) to give, in deviations from equilibrium,

\begin{matrix} Dp = Dp [\underset{(-)}{(p - \bar{p})}, \underset{(+)}{(F - \bar{F})}] & (65) \end{matrix}

\begin{matrix} DF = DF [\underset{(?)}{(p - \bar{p})}, \underset{(-)}{(F - \bar{F})}] . & (66) \end{matrix}

The only ambiguity here concerns the impact of prices on the trade account; higher prices reduce competitiveness, thus worsening the trade account, but at the same time they tend to improve the trade account by reducing real wealth.

If the competitiveness effect dominates, the system is unambiguously stable. The determinant of the above system is positive, and its trace is negative. A real equilibrium such as that described by equation (63) is reached, and, through the arguments stated earlier, nominal variables are determined if either M or S is tied down.

Proposition 2. With a rent exchange rate rule, long-run equilibrium does not exist unless the real exchange rate that is set by the authorities equals its equilibrium value. Regardless of whether the real rate is in equilibrium, the price level is indeterminate under a real exchange rate rule and a domestic credit target.

The first part of this proposition comes from equation (63)—given α and β, there are by assumption unique values of M and r associated with α and β. Nominal indeterminacy arises, as noted above, because fixing domestic credit and having a real exchange rate target do not determine prices.

Consider the stability of the system under a real exchange rate rule. In linear form, the equations can be written as

\begin{matrix} D p = a [(F - \bar{F}) - (P - \bar{P})] & (67) \end{matrix}

\begin{matrix} D F = b [(F - \bar{F}) - (P - \bar{P})], & (68) \end{matrix}

where a and b are composite coefficients. The determinant of this system is negative; in [p, F] space, the Dp - Df = 0 lines have a 45-degree slope. Neither prices nor foreign assets are determined.

Propostion 3. If the authorities hold the money supply constant by sterilizing foreign assets (dC + dF = 0), the system continues to be unstable under a real exchange rate rule.

With the money supply constant, the equations of the system can be written as

\begin{matrix} D P = - α (P - \bar{P}) & (69) \end{matrix}

\begin{matrix} D F = β (P - \bar{P}) & (70) \end{matrix}

Because the DF equation no longer includes F as an argument, the instability problems alluded to in the text arise; the current account does not settle down to balance. Note that we abstract here from the interest payments components of the current account; when this component is included, as in the text, the current account may change at an increasing rate.

Proposition 4. When public bonds are assumed to be a component of private sector wealth, the instabilities associated with following a real exchange rate rule and holding prices constant may be reflected in instability in some variable other than the current account.

To illustrate tins possibility, consider briefly the following model, in which prices are assumed to be held constant by open market operations, but the real exchange rate is held constant by intervention in the foreign exchange market:

\begin{matrix} D F = a_{1} R - a_{2} (C + F + B) + a_{0} & (71) \end{matrix}

\begin{matrix} D P = 0 = - b_{1} R + b_{2} (C + F + B) + b_{0} & (72) \end{matrix}

\begin{matrix} R = - h_{1} (C + F) + h_{2} B + h_{0} . & (73) \end{matrix}

For simplicity, prices have been set equal to zero, and B denotes private sector holdings of public bonds. The stability of this system can be considered under conditions when open market operations (dC + dB = 0) ensure that prices remain constant, whereas intervention in the foreign exchange market gives rise to DF ≠ 0. Expressing the above equations in deviation from equilibrium form, we obtain one expression for the current account and another for domestic credit (ignoring constants):

\begin{matrix} D F = (\frac{a_{1} b_{2}}{b_{1}} - a_{2}) F^{'} & (74) \end{matrix}

\begin{matrix} d C^{'} = - \frac{1 + \frac{h_{1} b_{1}}{b_{2}}}{h_{1} + h_{2}} \cdot \frac{b_{2}}{b_{1}} d F^{'}, & (75) \end{matrix}

where a prime indicates a deviation from equilibrium. From equation (74) it is apparent that the trade account is not necessarily stable under the assumed policy mix. The reason is clear: the need to hold prices constant calls for the authorities to lower interest rates whenever the trade account is in deficit so as to prevent lower wealth from leading to deflation; lower interest rates can lead to the result that the trade account deficit may never disappear. Note from equation (75) that an unstable trade account will lead to instability in domestic credit and, from the monetary equilibrium condition, to instability in the interest rate. This example does not imply that it is impossible to hold the real exchange rate constant and to have a target for the price level or inflation. It does suggest that one will not in general be assured of being able to achieve both of these objectives simultaneously.

REFERENCES

Dornbusch, Rudiger, “Expectations and Exchange Rate Dynamics,” Journal of Political Economy (Chicago), Vol. 84 (December 1976), pp. 1161–76.
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Dornbusch, Rudiger, “PPP Exchange-Rate Rules and Macroeconomic Stability,” Journal of Political Economy (Chicago), Vol. 90 (February 1982), pp. 158–65.
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Frenkel, Jacob A., “A Monetary Approach to the Exchange Rate: Doctrinal Aspects and Empirical Evidence,” Scandinavian Journal of Economics (Stockholm), Vol. 78 (May 1976), pp. 200–25.
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Frenkel, Jacob A., and Harry G. Johnson, eds., The Monetary Approach to the Balance of Payments” (Toronto: University of Toronto Press, 1976; London: Allen & Unwin, 1976).
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Patinkin, Don, Money, Interest, and Prices: An Integration of Monetary and Value Theory, 2nd ed. (New York: Harper & Row, 1965).
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Rodrik, Dani, “Should the Developing Countries Peg to a ‘Real’ Basket of Currencies?” (unpublished; Washington: International Monetary Fund, 1984).
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Sargent, Thomas J., Macroeconomic Theory (New York: Academic, 1979).
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Mr. Adams, an economist in the Research Department of the Fund, is a graduate of Monash University.

Mr. Gros, also an economist in the Research Department when this paper was written, is now with the Institut de Recherches Economiques, Université Catholique de Louvain, Belgium; he is a graduate of the University of Chicago.

The authors thank their colleagues in the Fund and participants at seminars held in the European Department and the Research Department for helpful comments on earlier versions of the paper.

To limit speculative pressures, implementation of these rules is in general not made public. This paper, therefore, does not refer to specific countries.

The paper therefore considers the monetary rather than real consequences of following real exchange rate rules; Rodrik (1984) and Dornbusch (1982) have discussed some of the real issues associated with these exchange rate rules. The paper deals only with two-sided rules that involve a target for the real exchange rate such that the authorities will devalue if domestic inflation is above world inflation and revalue in the converse case. A one-sided rule, which implies that the authorities will devalue only when domestic inflation is above world inflation, is not considered. Such a rule would be either inoperative or. when it is operative, equivalent to the two-sided rules considered here.

The possibility of sterilization of the monetary inflows that come through the balance of payments and, hence, of complementing real exchange rate rules with targets for money (instead of for domestic credit) is discussed below (Section VI); it is noted that sustained sterilization is usually infeasible when following a real exchange rate rule.

If all prices were perfectly flexible and if purchasing power parity held at all times, the real exchange rate rules we describe would be redundant or impossible to implement. With perfectly flexible prices, the real equilibrium of an economy is determined only by real variables such as fiscal and commercial policy; in such an economy an exchange rate rule that determines only a nominal variable would be unable to affect the real exchange rate. Some stickiness in prices, expectations, or both is necessary for a meaningful analysis of real exchange rate rules.

In none of the examples considered do we make allowance for outside nominal assets other than money held by the private sector; under certain conditions (Patinkin (1965)) the existence of nominal public debt can serve to tie prices down, even when real exchange rate rules are followed. We disregard this possibility because most countries do not have targets for nominal public debt held by the private sector, and we believe that any anchoring of the price level through the existence of such assets is unlikely to be of importance in practice (sec Appendix II).

A variable x_t follows a random walk if x_t = x_t-1 + v_t where v_t is white noise. By a variable being described by a random walk, we mean either that it is described by a strict random walk or, if it has a trend, that it follows a random walk around that trend.

The system is dichotomized in the sense that the real variables will be determined independently of nominal variables. Nominal variables, however, will be influenced by real variables (see Patinkin (1965)). Equation (1) represents a full equilibrium; hence, real balance effects are not included in the equation.

If we allow for rational expectations, tying down the current money supply is not sufficient to anchor the price level; in general, the path for the expected future money supply must also be tied down if velocity and, hence, prices are to be anchored.

Strictly speaking, here we require a doubling of the current and all expected future money supplies so that expected inflation and, hence, velocity do not change. In what follows, we abstract from any supernonneutralities associated with changing inflation or monetary growth rates.

Consider an initial equilibrium with domestic credit given by C₀, and with the price of domestic output, the domestic money supply, and the exchange rate given respectively by P₀, M₀ and S₀. Even with domestic credit fixed at C₀, there clearly are an infinite number of possible equilibria in which M, P, and S are scaled up or down equiproportionately, leaving real variables unchanged.

One can never be sure of what is meant by the long run, or of why time lags exist. Informational difficulties may lie at the core of the “short-run” through “long-run” dichotomy (see Sargent (1979)).

In this example we assume that the authorities have a target for domestic credit. Monetary equilibrium is not explicitly considered until the next example, where it is shown how the money supply adjusts endogenously through the balance of payments so as to finance any inflation rate that is forthcoming.

This kind of equation has been widely used in the literature; it could he derived from a Phillips-curve adjustment process applied to the goods markets.

An alternative to the real exchange rate rule, equation (7), is also possible. Consider the implications of a policy that fixes the rate of depreciation of the nominal exchange rate without reference to domestic inflation. Such a policy of a prefixed crawl leads to an inflationary process that is stable and to an expected inflation rate equal to the target rate m in the above model; see the discussion of equations (14) and (15) below.

The following argument also applies if the targeted real exchange rate is not a constant, as long as the path of the targeted real exchange rate is prefixed.

The other examples in this paper show that, under different hypotheses about the implementation of the real exchange rate rule, the resultant real exchange rate might be stable. The resultant inflationary process, however, is always unstable.

The real exchange rate is also stable under a prefixed crawl; under equation (14) it is governed by

q_{t} = \frac{1}{1 + φ} q_{t - 1} + \frac{φ}{1 + φ} \bar{z} + (u_{t}^{'} - v_{t}) / (1 + φ) .

This stable process implies a tendency for the real exchange rate to converge to its long-run equilibrium rate, $\bar{z}$ .

A small country may thus find that monetary policy cannot influence real interest rates in the short or long run. regardless of the degree of capital mobility. In general, its real interest rate can be determined by foreign real interest rates (as under perfect capital mobility); the domestic real interest rate could also be tied down by domestic real factors.

This does not imply that all countries using real exchange rate rules will experience sudden capital inflows. Many of these countries also experience high rates of domestic credit expansion because of slippage in meeting fiscal targets, In these cases, monetization of the fiscal deficit might be enough to satisfy the additional demand for money that is induced by inflation attributable to the real exchange rate rule.

If world inflation changes over time, equation (22) becomes nonhomogeneous, with a particular solution that is a function of time.

Restrictions on the value of the price-adjustment parameter φ can be gained by looking at the behavior of prices under a crawling peg with a fixed rate of depreciation equal to m. Using ${\bar{s}}_{t} = m$ instead of the purchasing-power-parity rule (equation (16)) leads to the following expression for inflation:

{\tilde{p}}_{t + n} + (φ - 1) {\tilde{p}}_{t} = (π + m) φ,

which implies that there is a steady-state inflation rate, equal to π + m, and that the system is stable as long as Φ < 2 (with dampened oscillations if 1 < ϕ < 2).

Sterilized intervention would not make any difference in this framework. Because money demand has to be ratified somehow, sterilized intervention would lead to a change only in the composition of the assets of the central bank, without any effect on the size of the total stock of money (sec Section VI).

In this example we therefore abstract from any instability in the real exchange rate that could come about when following a real exchange rate rule (see Section II).

The nominal exchange rate is adjusted according to

{\tilde{s}}_{t} = \underset{t - 1}{E} ({\tilde{p}}_{t}) + β / α r_{0} + 1 / α (Σ_{t}^{d} - Σ_{t}^{s}) .

To maintain the real exchange rate constant, the authorities need to know how private sector expectations are formed and the nature of the shocks to demand and supply. In the text we investigate the implications of the authorities’ having this information, under conditions when $E_{t - 1} ({\tilde{p}}_{t})$ is related to past inflation. Accordingly, we show how real exchange rate rules that adjust nominal exchange rates according to past inflation can be rationalized not only by information lags, as in the first two examples, but by a particular expectation process as well. There is no suggestion that the assumption that the authorities, have complete information is realistic; it is made for purposes of illustration and to demonstrate the implications of a policy that is able to hold the real exchange rate constant, albeit at a “disequilibrium” level.

The full equilibrium real exchange rate is defined as the rate existing when actual and expected inflation are equal. Consequently, with reference to equation (35). the real exchange rate ruling at t = 0 is a full equilibrium rate if $({\tilde{p}}_{0} - {\tilde{p}}_{- 1}) = 0$ .

As applied to labor markets, the argument is that if unemployment is held below its natural rate, continually rising inflation will occur.

Allowing for a nonzero current account does not in any way affect the conclusions, since a nonzero current account would only add a constant to the right-hand side of equation (38).

The system can be written in matrix form as:

[\begin{matrix} D (s) \\ D (p) \end{matrix}] = [\begin{matrix} 1 / ɛ & - 1 / ɛ \\ - β / ɛ & β / ɛ \end{matrix}] [\begin{matrix} s \\ p \end{matrix}] .

The determinant is equal to zero, implying that the system is unstable: any small shock would drive both the money supply and the exchange rate away from equilibrium.

This type of perverse reaction is well known in the literature (see, for example, Dornbusch (1976)); it can usually be excluded, however, because there is a variable such as the exchange rate that can jump and bring the economy to a stable path. Thus, under a freely floating exchange rate this perverse reaction could not happen.

This conclusion does not depend on the degree of capital mobility or asset substitutability; see Appendix I.

Accordingly, the results suggest that it will not he feasible to complement real exchange rate rules with money supply targets.

It is assumed that money is the only component of private financial wealth: public bonds are treated as an inside asset (see comment in Section VII).

Changes in the net debtor position of the country are financed by the issuance of foreign bonds, which are assumed to be traded only between the (domestic) public authorities and foreigners.

For simplicity, the analysis abstracts from output effects in the money demand function.

Note that if a real exchange rate rule is followed the level of prices is indeterminate in the long run. If P₀ is a solution for prices, so too is p₀ + k, p₀ + 2k, and so on.

This disturbance changes the long-run real exchange rate; hence the real exchange rate the authorities are pegging is a disequilibrium one.

In the case of a shock of opposite sign, foreign exchange reserves might accumulate indefinitely, but in that case the central bank would have to sell bonds to the public in increasing quantities that the public may be unwilling to acquire.

With reference to equations (44)-(46), set (s - p) = (J but, instead of setting DP = 0, set m = M₀. It is still assumed that DP^E = 0.

The lack of wealth effects under total sterilization comes about because real wealth is equal to nominal money divided by prices; public sector interest-bearing debt is not regarded as wealth. In the background of the example is a fiscal policy that holds wealth constant as the economy runs current account imbalances. We do not focus on this policy because our primary concern is with the monetary consequences of real exchange rate rules. See Appendix II.

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IMF Staff papers: Volume 33 No. 3

Author:

International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1986: Issue 003

Publisher:: International Monetary Fund

ISBN:: 9781451972887

ISSN:: 1020-7635

Pages:: 256

DOI:: https://doi.org/10.5089/9781451972887.024

Keywords
I. Real Exchange Rate Rules and Determination of the Price Level
II. Stochastic Shocks and the Inflationary Process
III. The Inflationary Process with Nontraded Goods
IV. The Inflationary Process with Flexible Prices and a Surprise Supply Function: An Applicaton of the Natural-Rate Hypothesis
V. The Inflationary Process in a Model of Overshooting
- Model 1
- Model 2
VI. An Economy with a Capital Market Not Integrated with the Rest of the World: The Implications of Sterilization
- Holding Inflation and Prices Constant Under a Real Exchange Rate Rule
- Holding the Money Supply Constant Under a Real Exchange Rate Rule
VII. Conclusions
- APPENDIX I Background to the Model in Section V
- APPENDIX II Background to the Model in Section VI
REFERENCES

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Abstract

I. Real Exchange Rate Rules and Determination of the Price Level

II. Stochastic Shocks and the Inflationary Process

III. The Inflationary Process with Nontraded Goods

IV. The Inflationary Process with Flexible Prices and a Surprise Supply Function: An Applicaton of the Natural-Rate Hypothesis

V. The Inflationary Process in a Model of Overshooting

Model 1

Model 2

VI. An Economy with a Capital Market Not Integrated with the Rest of the World: The Implications of Sterilization

Holding Inflation and Prices Constant Under a Real Exchange Rate Rule

Holding the Money Supply Constant Under a Real Exchange Rate Rule

VII. Conclusions

APPENDIX I Background to the Model in Section V

APPENDIX II Background to the Model in Section VI

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