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
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.
APPENDIX I Background to the Model in Section V
The building blocks of the extended model in Section V are reproduced below:
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
The roots of the system are determined by
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
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
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
Under a pegged nominal exchange rate regime, the authorities determine
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
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).
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
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
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:
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):
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.
Dornbusch, Rudiger, “Expectations and Exchange Rate Dynamics,” Journal of Political Economy (Chicago), Vol. 84 (December 1976), pp. 1161–76.
Dornbusch, Rudiger, “PPP Exchange-Rate Rules and Macroeconomic Stability,” Journal of Political Economy (Chicago), Vol. 90 (February 1982), pp. 158–65.
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.
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).
Patinkin, Don, Money, Interest, and Prices: An Integration of Monetary and Value Theory, 2nd ed. (New York: Harper & Row, 1965).
Rodrik, Dani, “Should the Developing Countries Peg to a ‘Real’ Basket of Currencies?” (unpublished; Washington: International Monetary Fund, 1984).
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 xt follows a random walk if xt = xt-1 + vt where vt 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
This stable process implies a tendency for the real exchange rate to converge to its long-run equilibrium rate,
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
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
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
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
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:
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.
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.