Many opponents of quantitative controls on the flow of international capital have argued that such controls may work in the short run, but that in the long run economic agents in an otherwise open economy will find ways to evade them. This paper formalizes the notion of the long-run ineffectiveness of quantitative capital controls by using a framework in which economic agents can evade the controls if they are willing to incur some costs.

This framework contrasts with most other economic models of capital controls, which assume that the controls either introduce a constant (relative or absolute) differential between the yields in domestic and foreign capital markets or effectively stop all capital movements.^{1} By maintaining a yield differential or stopping all capital flows, capital controls are effective in these models, even in the long run. The central theme of this paper, however, is that capital controls are not perfect in reality and are likely to be circumvented if the incentive is great enough. Even if circumventing or evading capital controls is a costly activity, some capital flows are likely to occur in response to a yield differential. To the extent that the flows that do occur despite controls have some feedback effect on the yield differential, moreover, these flows would tend to reduce or even eliminate the yield differential in the long run, other things being equal. One might then observe a yield differential that declines over time, even when the regulations used to control the movements of capital are not changed. Modeling explicitly the way in which capital controls can be circumvented is thus of central importance in describing either the effects of imposing capital controls or the dynamic adjustment of financial market conditions after various disturbances while capital controls are in effect.

In developing an analysis of capital controls it is important to distinguish between quantitative controls on capital flows and controls that are based on differential tax treatment. Controls of the latter type usually involve the use of required reserve ratios or withholding taxes and in general apply not to *flows* of capital but rather to the entire *stocks* of particular types of assets outstanding. Such controls might therefore be able to sustain a constant yield differential between domestic and foreign capital markets as long as stocks of both types of assets (those under control and those free from controls) remain outstanding.^{2}

It should be emphasized at the outset that this paper will not consider controls based on the differential tax treatment of different securities; rather, the concern is mainly with the types of quantitative controls that have been employed in the European Monetary System (EMS). The two EMS members that still have such capital controls in place are Italy and France. The Italian capital controls have been designed to eliminate or reduce the profitability of portfolio investments abroad for residents.^{3} Because exporters and importers of goods and services could circumvent regulations on portfolio investments by changing the terms of payment on their respective contracts, however, strict regulations have also been imposed on the terms that exporters can give their foreign clients and the time intervals within which export receipts must be converted into lire. Similar restrictions apply on the import side. Nevertheless, in an otherwise open economy, where imports of goods and services account for 30 percent of gross national product and where each year millions of tourists cross national frontiers, it is very difficult to control all of the various channels through which capital can be exported. It has therefore been argued that capital controls in a country such as Italy (or France) cannot maintain a constant interest rate differential over the long run.

This argument is borne out by the behavior of the differentials between the regulated domestic interest rates and the unregulated offshore or Euro-interest rates on deposits denominated in lire. As indicated by Figure 1, the experience since 1980 shows in this respect that during periods of “calm” in the EMS—that is, when no realignment was expected—the Euro-lira rates have been very close to corresponding domestic Italian interest rates, despite the presence of capital controls.^{4} When realignments were expected, however, the Euro-interest rates stayed for several months considerably above the domestic Italian rates. (Immediately before realignments, the difference between the two interest rates often exceeded 10 percentage points.) Similarly, Figure 2 shows that the Euro-interest rates on French franc deposits have deviated considerably from corresponding domestic French interest rates only during the periods preceding EMS realignments. The actual interest rate differential that often has been used as an indicator of the severity of capital controls should therefore be regarded as a function not only of the severity of the controls, but also of the nature of the “disturbances” that are affecting the economy and of the time the economy has had to adjust to those disturbances (see Ito (1983) and Otani and Tiwari (1984)).

Figure 1. Effects of Capital Controls in Italy

Note: The variable depicted is *IT.SERW*, the difference between covered (in Italian lire) Eurodeposits and domestic interest rates in Milan (see Appendix I).

Figure 2. Effects of Capital Controls in France

Note: The variable depicted is *DIF.32W*, the difference between French franc Euro-interest rates and domestic interest rates in Pans (see Appendix I).

The analysis in this paper also disputes the common argument that, when controls apply only to capital outflows and not to capital inflows, the potential for massive capital inflows could prevent domestic interest rates from ever exceeding corresponding off-shore rates. The flaw in this argument is that private operators who take the future into account might not transfer funds to the domestic market if they perceived that domestic interest rates were only temporarily above off-shore rates. In particular, if they expected future domestic interest rates to be below off-shore rates, and if controls imply that future capital outflows would be costly, it might not be optimal for them to transfer funds to the domestic market and later incur the costs of transferring them back to the off-shore market. If future off-shore rates were expected to be very high relative to domestic rates, it is even possible that capital outflows could take place during periods in which off-shore rates were below domestic rates. The results of this paper therefore suggest that, even with a given enforcement mechanism in place that is designed to impede capital outflows, the observed interest differential might be positive or negative and might vary considerably over time. Actual interest rate differentials are thus not an accurate measure of the effects of quantitative capital controls. This forward-looking characteristic of capital flows has important consequences for the immediate effects of anticipated future policies. An expansionary monetary policy that is anticipated would thus lead to capital outflows and rising domestic interest rates even before this policy materialized.

To begin to formalize these arguments, Section I of the paper presents a model of how operators use resources in their efforts to obtain arbitrage profits. It is shown how this activity might eliminate the interest rate differential over time and how the interest rate differential and capital flows are linked in the short run. Section II then presents a simple macroeconomic model that incorporates the relationship between capital flows and interest rate differentials and provides a feedback mechanism from the capital flows to the interest rate differential, which leads to a stable equilibrium. In the context of this model, the main effects of capital flows are confined to the money market. The speed of adjustment of the interest differential is shown to depend on a parameter that characterizes the costs imposed on agents by the capital controls and a parameter that characterizes the demand for money.

Section III analyzes the implications of incomplete market separation for the degree of autonomy of monetary policy. It shows that in this framework the “offset coefficient” is a function of both time and the speed of adjustment calculated in the previous section. The immediate (impact) offset coefficient might be quite low, but the long-run offset coefficient always equals (minus) unity. This section also argues that the magnitude of the arbitrage flows that are caused by a monetary policy that aims to keep domestic interest rates low depends on the degree of persistence of such a policy. A policy that sustains and is expected to sustain a permanent interest differential might lead to arbitrage flows that are ten to twenty times larger than the flows induced by a transitory policy. Section IV discusses the effects of anticipated future monetary policy and shows how capital outflows might occur even if current domestic interest rates are above current international interest rates. Section V contains some concluding remarks.

## I. A Model of Capital Controls and Evasive Activity

Assume that the domestic interest rate on riskless, domestic currency loans is equal to *r _{t}* and that the rate on Eurodeposits (also in domestic currency, riskless, and for the same maturity) is equal to

*i*Any operator who could obtain a loan in the domestic capital market and then invest the proceeds in the Euromarket would make a riskless arbitrage profit equal to

_{t}*y*–

_{t}(i_{t}*r*, where

_{t})*y*indicates the amount of the loan and thus the scale of arbitrage activity.

_{t}^{5}

The scale of arbitrage activity is interpreted as a cumulative *stock* of funds that has been allocated toward earning arbitrage profits. It is assumed that a private operator may incur costs in transferring capital abroad, and that once he has succeeded in transferring this capital he does not incur any costs in simply rolling over his previous position to continue to make the arbitrage profit *y _{t–1}(i_{t} –* r

_{t}), but only incurs additional costs if he tries to transfer more capital.

Capital controls are more often used to restrict capital outflows (for example, in Italy and France) than to restrict capital inflows (for example, in Germany in the 1970s). It might, therefore, be more appropriate to assume that private operators incur costs only in transferring capital out of the country. Even if capital controls are designed only to restrict outflows, however, it might not be costless for private agents to repatriate capital, since the domestic authorities are often suspicious that this capital might have been previously exported illegally. Indeed, a number of countries have used special incentives to induce private agents to repatriate capital. The formal analysis in this paper, therefore, proceeds under the assumption that the costs of transferring capital are symmetric; that is, they apply to transfers of capital in both directions. But the formal analysis of this paper could also be interpreted as applying to a situation in which the costs of transferring capital are asymmetric (that is, in which they apply only to capital outflows) and international interest rates are, on average, above domestic interest rates.^{6} This has been the case in Italy and France and is likely to be true in other cases as well because governments usually use capital controls to keep domestic interest rates low relative to international interest rates. The question whether capital controls lead to symmetric costs is therefore irrelevant for the results of this analysis. The discussion is related, however, to the experience of France and Italy and will, therefore, proceed under the assumption that international interest rates usually exceed domestic rates, so that *y _{t}(i_{t} – r_{t})* represents an arbitrage profit rather than a loss.

The costs of transferring capital discussed informally so far are captured formally by an adjustment cost function g(∆_{y},), where ∆*y _{t}* ≡

*y*and both

_{t}y_{t–1,}*g’ > 0*and

*g” >*0. The latter condition assumes that the marginal cost

*(g’)*of transferring capital is increasing. Such a condition seems reasonable if one considers the two principal channels through which capital can be transferred abroad: physical movements of cash, and leads and lags. Physical movements of cash might involve increasing marginal costs if the potential fine is a proportion of the attempted transfer that is increasing with the size of the transfer; this has been the case in Italy. Leads and lags would also involve increasing marginal costs because importers and exporters can operate only with a limited flow (their regular trade transactions), and lengthening the delay with which they pay their foreign bills is increasingly more difficult to justify to the authorities enforcing the controls.

^{7}

Given these adjustment costs and arbitrage opportunities, a profit–maximizing operator in the capital market will maximize the expected discounted sum of future profits, which are given by

where *A* ≡ 1/(1 + ρ) is the discount factor (p is the discount rate) for future profits.^{8} Because this paper is not concerned with the effects of surprises or risk, it is assumed that agents have perfect foresight; therefore, the expectations operator has been suppressed. The Euler equation for this problem is

Equation (2) implies that the capital flows (∆y_{t}) are not only a function of the present interest rate differential (*i _{t}*—77), but also of expected future interest differentials. An important consequence of this relationship is that equation (2) might hold even if the present interest rate differential is negative; that is, if the domestic interest rate is above the off-shore interest rate. If future interest rate differentials are expected to be large relative to present interest rate differentials, ∆y

_{t+1}would be large relative to ∆y

_{t}, and the right-hand side of equation (2) might be negative. In this case capital outflows might take place today, even if the domestic interest rate exceeds the off-shore interest rate. It might be optimal for private operators to transfer capital abroad because the instantaneous loss they make today might be more than offset by future gains attributable to the future positive interest rate differentials and the savings in adjustment costs they can obtain by distributing their activity more evenly over time.

^{9}

The view of the effects of quantitative capital controls proposed here, therefore, implies that even if a country only has controls that restrict capital outflows and no restrictions on capital inflows, one might sometimes observe that domestic interest rates were above corresponding off-shore interest rates. Even if capital controls function only against outflows, private operators value capital they have already brought abroad not only at the present interest rate; they also take into account future interest rates because they know that it would be costly for them to transfer capital abroad rapidly if interest rate differentials change in favor of off-shore markets.

A private operator has to take i_{t}, and *r _{t}* as given, but a stable general equilibrium can exist only if there is some feedback from

*y*, to (i

_{t}–

*r*because equation (2) implies that capital outflows will stop if

_{t})where the subscript *ss* refers to a steady-state value. Equation (3) implies that if there is a permanent increase in the international interest rate—that is, if *i _{ss}* rises—the domestic interest rate has to increase by the same amount if the economy is to reach a new stationary equilibrium. In this sense, capital controls would be ineffective against permanent shocks.

The complete macroeconomic model that describes how the stationary equilibrium is attained is described in Section II. Whatever the details of this model, equation (3) must hold at the stationary equilibrium. Equation (3) says that, at the steady state, the marginal cost of transferring an infinitesimal additional amount of capital abroad, *g*’(0), has to equal the marginal benefit, which is equal to the interest differential (i_{ss} – r_{ss}) multiplied by (1 + ρ)/ρ, since the flow of additional benefits accrues for the entire future. This relationship implies that if the marginal cost of increasing the arbitrage activity by a small amount is zero around the stationary equilibrium—that is, if g’(0) = 0—the steady-state interest rate differential must also equal zero. The data on the differential between Euro-interest rates and domestic interest rates for French franc and lira deposits, as presented in Figures 1 and 2, suggest that this is indeed the case for these two currencies; over the long run, the interest rate differential seems to disappear. A particular functional form of the adjustment-cost function that would yield this result is given by

where Φ indicates the severity of the capital controls. This specific functional form will be used in the remainder of the paper because it yields a linear solution.^{10} With quadratic adjustment costs, the solution for *y _{t}* becomes

Equation (5) again illustrates the point that capital outflows (positive values of *y _{t})* might occur even if the domestic interest rate is higher than the off-shore interest rate. With quadratic adjustment costs, i

_{t}<

*r*could occur if ∆y

_{t}_{t+1}/∆y

_{t}(that is, the proportional rate of change in capital flows) exceeds

*A*.

Most macroeconomic models that incorporate the concept of limited capital mobility have assumed that capital flows are a function of only the current interest differential. In contrast, the present formulation emphasizes that capital flows should be a function of present and future (expected) interest differentials. This can be seen by solving the difference equation (5) forward:

Equation (6) implies that capital flows today depend on the present value of present and future discounted interest differentials. (The discussion in Section IV will show that this implication has important consequences for the effects of anticipated future policies.)

The quadratic formulation of the adjustment costs also implies that, at the steady state, the interest rate differential has to disappear. Because equation (4) implies that *g* ‘(0) = 0, it follows from equation (3) that

if the Euro-interest rate is constant at *i*. This result implies that if capital controls were reinforced in such a manner that Φ increases, this increase would have no effect on the steady state, and interest rates would still be equalized across markets. In this framework the domestic interest rate is therefore determined in the long run exclusively by the foreign interest rate. A similar result has been obtained by Edwards (1985) and Edwards and Khan (1985), who assumed that, because of capital controls, domestic interest rates respond to changes in international interest rates with some delay according to *r _{t} =* θ[i

_{t}–

*r*. Their formulation also implies that in the long run the two interest rates converge. The cost-of-arbitrage model developed in this paper, therefore, yields some microeconomic foundation for the parameter θ. The main difference between the formulation in these two papers and that in the present model is that with optimizing agents the solution is forward looking and not an adjustment with respect to the past. This point will become relevant in the discussion of the effects of anticipated future policies below.

_{t–1}]## II. The General Equilibrium

This section describes the general equilibrium model that captures the feedback from the capital flows to the interest rate differential. This feedback is assumed to occur through the effect of capital flows on the domestic money market, which determines the domestic interest rate, *r _{t};* the Euro-interest rate,

*i*, is assumed to be exogenous.

_{t}The assumption that the Euro-interest rate is exogenous may appear unusual because Euro-interest rates are usually thought of as being determined by the market. It is exactly this fact, however, that is being used here. In the Euromarkets, covered interest parity seems to hold precisely. This implies that, given the deutsche mark interest rate, the interest rate on Eurodeposits in domestic currency has to be equal to the sum of the deutsche mark interest rate and the forward discount on the domestic currency. The forward discount in turn is related to the expected rate of depreciation of the domestic currency. But if the home country—for example, Italy—is in the EMS, the expected rate of devaluation, and thus the forward discount, is determined by the probability of a realignment if the domestic currency is at or near its lower intervention limit. For the purpose of this paper, the EMS is therefore treated as a system of fixed exchange rates, which can be adjusted from time to time by the participating governments. Hence the forward discount on the domestic currency is exogenous in the sense that it is determined by the expectations of the public about the likely actions of the authorities.^{11}

Formally, covered interest parity implies that

where *i _{t}, _{DM}* is the Euro-interest rate on deutsche mark deposits,

*F*the forward exchange rate, and

_{t}, is*S*is the spot exchange rate, with both exchange rates expressed in terms of domestic currency per deutsche mark. The Euro-interest rate on deposits in domestic currency, i

_{t}_{t}, is thus exogenous because the interest rate on deutsche mark deposits is determined in the German market and the forward discount

*(F*is determined by the authorities.

_{t}/S_{t})The domestic interest rate, *r _{t}*, however, is assumed to respond to the conditions in the domestic money market. The equilibrium in the domestic money market is determined by money demand and supply. Money demand is given by a simple function:

where λ represents unity divided by the semi-interest-rate elasticity of money demand; *m _{t}* is the natural logarithm of the nominal money supply,

*m*and

_{t}= In(M_{t});*p*is the natural logarithm of the general price level. Income does not appear as a separate determinant of money demand in equation (8) because it is assumed to be exogenous. It will be shown later that the results would not be affected if this assumption were dropped.

_{t}Capital flows influence the domestic interest rate because they influence the monetary base. If it is assumed for simplicity that the multiplier is equal to unity, then the money supply is equal to the monetary base, which in turn is given by the sum of domestic credit and net foreign assets of the central bank:

where C represents domestic credit, which is exogenously determined by the central bank; and *F _{cb, t}* represents the net foreign assets of the central bank, which are equal to the difference between the economy’s overall net foreign assets,

*Ft*, and the net foreign assets of the private sector,

*F*.

_{p, t}The model of capital controls and evasive activity developed in the previous section can now be used to determine the path of the net foreign asset position of the private sector, *F _{p, t}*. Because outflows of private capital correspond to an increase in the net foreign asset position of the private sector, by implication the variable

*y*used to describe the capital flows or arbitrage activity in the previous section corresponds to

_{t}*F*in this section.

_{p, t}^{12}The evolution of the net foreign assets of the private sector is thus given (see equation (5)) by

The evolution of the net foreign asset position of the economy, *F _{t}*, reflects the time path of the current account, which is assumed to be a function of the terms of trade and of the difference between the actual and the desired net foreign asset position of the economy,

*F*:

_{t}where *s* represents the natural logarithm of the nominal exchange rate. Normalizing the foreign price level to unity *(s – p _{t})* thus represents the terms of trade or real exchange rate. As mentioned above, the EMS is treated here as a system of fixed exchange rates, and

*s*is therefore assumed to be constant. The results of the analysis would not be affected, however, if the authorities fixed a predetermined, nonconstant path for the nominal exchange rate. For the purpose of this analysis, it is sufficient to assume that the exchange rate is determined outside the model. In equation (11),

*F*represents the target or desired level of foreign wealth of the economy, and the βs are positive constants.

^{13}

The model can be closed by using a conventional sticky-price adjustment formula that assumes that inflation is related to excess demand, which in turn is related to the terms of trade or real exchange rate:

The system of equations (8)–(12) describes the path of the slowly adjusting variables *p _{t}, F_{t}, F_{p, t}*, and the domestic interest rate,

*r*, as a function of the exogenous forcing variables i,

_{t}*F, s*, and C. The solution to the system is recursive in that equation (12) determines the path of the price level,

*p*. Given this path of the price level, equation (11) determines the path of the net foreign asset position of the economy,

_{t}*F*The variables

_{t.}*p*and

_{t}*F*are thus exogenous to the money-market equilibrium as determined by equations (8)-(10), which can be written in one equation as

_{t}^{14}

Equation (13) can be treated as a single second-order, nonlinear difference equation in *F _{P, t}* with the roots

where *M* represents the steady-state nominal money supply. It is apparent from equation (14) that this equation has one unstable and one stable root. Because operators in the financial markets would not expand their arbitrage activity indefinitely if the forcing variables in equation (14) were constant, it can be assumed that the domestic interest rate maintains the economy on the stable path and that the unstable root can be eliminated from the solution.

Because the (stable) root, Λ_{2}, determines the speed at which the system would converge to the steady state, equation (14) shows that the speed of adjustment is a function only of the parameters that describe the financial markets, ρ and λ/Φ. It can also be shown from equation (14) that the stable root is a decreasing function of λ/Φ. Because λ is equal to unity divided by the semi-interest-rate elasticity of money demand, by implication the speed at which the equilibrium is reached is inversely related to the semi-interest-rate elasticity of money demand. Intuitively, this means that the equilibrium, which implies *i _{t} = r_{t}*, is reached faster if even small capital inflows have a large effect on the domestic interest rate. The same result also implies that an increase in the restrictiveness of the capital controls—that is, an increase in Φ—leads to a slower adjustment.

## III. Implications for the Degree of Autonomy of Monetary Policy

The degree of autonomy of national monetary policy in a regime of fixed exchange rates has often been discussed in terms of the so-called offset coefficient. This coefficient measures by how much any given (unanticipated) change in domestic credit is “offset” or neutralized by capital flows. Without capital controls (and if domestic and foreign assets are perfect substitutes), this offset coefficient should be equal to unity because in this case (fixed or predetermined exchange rates, no capital controls, and perfect substitutability between assets) the domestic interest rate (and thus money demand) are fixed by the foreign interest rate, so that the central bank cannot control the money supply. Capital controls have been used by several countries precisely because such measures allow the central bank to influence the domestic interest rate even if the exchange rate is fixed.

This section shows that, in the framework proposed here, the offset coefficient is a function of time and goes to unity in the long run. The result that the offset coefficient is larger in the long run than in the short run has been rationalized in the literature by assuming a partial adjustment in money demand (and sometimes in money supply)—see, for example, Claasen and Wyplosz (1982) and the references cited therein. In this framework, a similar result is obtained because capital controls slow down the capital inflows attracted by the interest rate differential.^{15}

The offset coefficient can be calculated by computing the change in *F _{p, t}*—that is, the capital outflows—induced by an unanticipated increase in domestic credit by ∆

*C*from

*C*to

*C*’ The difference equation that determines the time path of

*F*can be written as

_{p, t}^{16}

where Λ is the stable root in equation (14) and *F _{p, ss}* is the steady-state stock of private assets abroad, which is determined by the steady-state equilibrium condition on the money market:

Equation (16) implies that, if there is an unanticipated increase in domestic credit of *∆C* at time zero and if the system was initially at its steady state, the capital outflows (denoted by *∆F _{p, t})* caused by the increase in domestic credit are given by

which implies that the offset coefficient, given by 1 Λ ^{t}, is an increasing function of time and goes to unity in the long run. The impact offset coefficient is given by 1—∆. The size of the offset coefficients thus depends on the parameters that determine the speed of adjustment of the difference equation in *F _{p, t}*. As discussed in the previous section, this speed of adjustment, or ∆, depends only on ρ and

*λ/*Φ. An increase in the severity of capital controls—that is, an increase in Φ—would lead to a lower offset coefficient; capital controls would therefore increase the degree of autonomy of domestic monetary policy in the short run. But whatever the degree of short-run autonomy for monetary policy, this framework also implies that in the long run the offset coefficient goes to unity.

Another way to measure the degree of autonomy of monetary policy would be to calculate the amount of capital outflows that the central bank would have to sterilize if it wished to keep domestic interest rates below international interest rates. Such a policy has been suggested for countries with a large public sector debt burden. The argument for capital controls in this case is that they would lead to lower interest payments on the (domestic) public sector debt and thus would help to limit the fiscal deficit. The framework presented here suggests that such a policy would lead to large capital outflows. The magnitude of the outflows would depend not only on the size of the interest differential that the authorities wish to maintain, but also on the time span for which the authorities wish to maintain the interest differential.

The difference in the magnitude of the capital outflows in response to temporary and permanent interest rate policies can be calculated directly from equation (5), If the authorities maintain an interest rate differential of *i _{t}—r_{t} = D* for only one (the current) period (a transitory policy), capital outflows are given by

*(i*—r

_{t}_{t})/Φ =

*D/Φ*. But if the authorities maintain the same interest differential for the indefinite future (a permanent policy), capital outflows are given by (D/Φ)[(1 + ρ)/ρ]. The difference in the effects of transitory and permanent policies is thus given by the factor (1 + ρ)/ρ. If p, the rate used by arbitrageurs to discount future profits, is equal to 10 percent, this factor is equal to 11. This implies that a permanent policy of maintaining domestic interest rates below international interest rates would lead to capital outflows that are eleven times as large as the capital outflows induced by a transitory policy. With ρ = 5 percent, the magnification factor for a permanent interest rate policy would be equal to 21.

## IV. Effects of Anticipated Future Monetary Policy

The analysis in the previous section has shown that an unanticipated increase in domestic credit can at least reduce domestic interest rates for some time before it is offset by capital outflows. An anticipated future increase in domestic credit, however, would have quite different effects. As shown by equation (6), capital outflows depend on the present value of future interest differentials; this relationship implies that an anticipated future increase in domestic credit that will lower domestic interest rates at some point in the future has to lead to capital outflows the moment that the increase is anticipated. In turn, until the increase in domestic credit materializes the domestic money supply has to decline and domestic interest rates have to rise.

The forward-looking nature of the arbitrage opportunities can, therefore, lead to the seemingly paradoxical situation that capital outflows exist despite capital controls and despite domestic interest rates that are above international interest rates.^{17} By how much capital flows react to the news about the future increase in domestic credit depends on how much time is expected to pass before the increase in domestic credit materializes. The precise amount of the initial capital flows can be calculated from the requirement that the rate of capital outflow is at a maximum during the period in which the increase in domestic credit actually occurs. Between the time the news about the future increase in domestic credit arrives and the time the increase materializes, capital outflows have to accelerate because during this period the domestic interest rate is above the international interest rate; in other words, capital flows have to be increasing as shown by equation (5). When the increase in domestic credit materializes, the domestic interest rate drops below the international interest rate, and capital flows start to decline.

It is apparent from equation (13) that changes in the international interest rate, i* _{t}*, are equivalent to changes in domestic credit.

^{18}This implies that unanticipated and anticipated future changes in international interest rates have the same effect on capital flows and domestic interest rates as changes in domestic credit. Deviations from interest rate parity and capital flows can, therefore, be caused not only by domestic monetary policy but also by disturbances in the international financial markets.

## V. Concluding Remarks

This paper has developed a simple model of capital controls in the presence of incomplete market separation and has demonstrated that quantitative controls are not effective in the long run. Although this argument has often been made informally, it apparently has never been formally incorporated into the macroeconomic models that are often used to discuss short-run and medium-run policy problems.

The main conclusion from the framework presented here is that quantitative capital controls could be effective in controlling short-run fluctuations in domestic interest rates, but that they should not be used in attempts to offset permanent shocks and to keep domestic interest rates below international interest rates in the long run. Thus, quantitative controls should be used only to provide some insulation against temporary short-run fluctuations in the economic environment.

The available data on domestic and off-shore interest rates for France and Italy seem to confirm this conclusion to the extent that significant differentials between domestic and off-shore interest rates have appeared only during periods of turbulence in the EMS. During periods of calm in the EMS—that is, when no realignment of the intra-EMS parities has been expected—the interest rate differentials have disappeared.

The framework developed in this paper also implies that the evasion of capital controls or arbitrage activity that is induced by the interest rate differential between domestic and off-shore markets leads to capital flows that are a function not only of the present interest rate differential, but of future interest differentials as well. Thus, capital outflows might occur even if the current interest rate differential is close to zero, since investors take future interest rate differentials into account when they decide where to invest.

The long-run ineffectiveness of capital controls in isolating domestic financial markets from the international economic environment also shows up in the so-called offset coefficient. In this framework the offset coefficient is a function of time: in the short run it might be close to zero, but in the long run it always equals (minus) unity. This finding implies that, under a fixed exchange rate and with capital controls, a given change in domestic credit would only partially be offset through the balance of payments in the short run; in the long run, however, the offset would be complete. Capital controls can, therefore, provide only some temporary autonomy for national monetary policy.

The data used in Figures 1 and 2 of the text were assembled by the Fund’s Research Department; all interest rates are in percentage units per year:

*USD03A* Three-month Euro-interest rate (LIBOR, London interbank offered rate) on U.S. dollar (asked) daily, from DRI FACS (Bank of America, San Francisco, June 1, 1973, 10:00 a.m. PST, Pacific standard time)

*IT.SERW* Difference between covered (in Italian lire) Eurodeposits and domestic interest rates in Milan; weekly, Wednesday observation:

= *R1 when R1* > 0

= *R2 when R1* < = 0 and R2 < 0

=0 when *Rl <* = 0 and *R2 >* = 0

*R1* 400[(1 + USD03B/400) – (ITC00A/ITC03B) – (1 + /ITM03A/400)]

*R2* 400[(l + USD03A/400) – (1 + ITM03B/400)] – (1 + ITM03B/400)]

*USD03B* Three-month Euro-interest rate (LIBOR) on U.S. dollar (bid) daily, from DRI FACS (Bank of America, San Francisco, June 1, 1973, 10:00 a.m. PST)

*ITC00A* Spot Italian lire (U.S. dollars per lira) (asked) daily, from DRI FACS (Bank of America, San Francisco, June 1, 1973, 9:00 a.m. PST)

*ITC00B* Spot Italian lire (U.S. dollars per lira) (bid) daily, from DRI FACS (Bank of America, San Francisco, June 1, 1973, 9:00 a.m. PST)

*ITC03B* Three-month forward Italian lire (U.S. dollars per lira) (bid) daily, from DRI FACS (Bank of America, San Francisco, June 1, 1973, 9:00 a.m. PST)

*ITC03A* Three-month forward Italian lire (U.S. dollars per lira) (asked) daily, from DRI FACS (Bank of America, San Francisco, June 1,1973, 9:00 a.m. PST)

*ITM03A* Three-month Italian interbank rate (asked) daily, from DRI FACS (Bank of America, San Francisco, November 12,1980, 9:30 a.m. PST); TD 13660C was used for the period before November 12, 1980

*ITM03B* Three-month Italian interbank rate (bid) daily, from DRI FACS (Bank of America, San Francisco, November 12, 1980, 9:30 a.m. PST); TD 13660C was used for the period before November 12, 1980

*TD* 13660C Three-month Milan money-market rate (mid-point) daily, from the Fund’s Treasurer’s Department (January 3, 1978)

*DIF. 132W* Difference between French franc Euro-interest rates and domestic interest rates in Paris (TD13260EB – TD13260C); weekly, Wednesday observation

*TD* 13260EB Three-month French franc Euro-interest rate (bid) daily, from the Fund’s Treasurer’s Department (January 3, 1978); London, mid-morning

*TD* 13260C Three-month French interbank rate daily, from the Fund’s Treasurer’s Department (January 3, 1978).

Capital flows from one market to another can be compared to flows of a liquid between two containers. If capital markets (the “containers”) are open, the “flow” of capital (the “liquid”) between the two containers can be said to be unrestricted; this open flow implies that the liquid must always attain the same level in the two containers; that is, the same rate of return must always prevail in both markets. Capital controls can then be viewed as restricting the flow between the two containers—for example, by connecting the containers with a small pipe. The friction inside the pipe slows down the flow between the two containers, and the liquid may therefore stay at different levels in each for sometime. Eventually, however, the flow through the pipe will equalize the level of the liquid in both containers; that is, the rates of return will eventually be equalized across markets.

The small-country case corresponds to a combination of one very large and broad container with another very small and thin one; outflows from the large container (the rest of the world) to a first approximation do not affect the level of the liquid in the large container but do have a significant effect on the small one (the small country).

In physics, the force opposing the flow of a viscous liquid through a pipe is a function of the viscosity of the liquid, the length of the pipe, and the speed at which the liquid flows (see Van Heuvelen (1982, p. 281)):

where η represents the coefficient of viscosity, *L* the length of the pipe, and v the speed at which the liquid flows through the pipe. This relationship implies that the power, *P* (energy per unit of time), needed to force a liquid through a pipe of length *L* is given by

The adjustment-cost equation proposed in the text of this paper specifies that adjustment costs equal a constant times ∆*y ^{2}* If that constant is equal to 4πηL and the capital flows, ∆y, also represent the velocity at which capital flows occur, the model of adjustment costs presented herein is exactly analogous to the mathematical description of the flow of liquids in physics.

AdamsCharles and JeremyGreenwood“Dual Exchange Rate Systems and Capital Controls: An Investigation,”Journal of International Economics (Amsterdam) Vol. 18 (February1985) pp. 43–63.

AizenmanJoshua A.“On the Complementarity of Commercial Policy, Capital Controls, and Inflation Tax,”Canadian Journal of Economics (Toronto) Vol. 19 (February1986) pp. 114–33.

BaseviGiorgio“Instruments for Preserving Economic Efficiency and International Capital Mobility” in Capital Controls and Foreign Exchange Legislations Occasional Paper (Milan: Euromobiliare, 1985).

ClaasenEmil-Maria and CharlesWyplosz“Controle des movements de capitaux: quelques principes de l’experience francaise” Annales de l’INSEEInstitut National de la Statistique et des Etudes Economiques (Paris) (Nos. 47-481982) pp. 629–69.

DooleyMichael P. and PeterIsard“Capital Controls, Political Risk, and Deviations from Interest-Rate Parity,”Journal of Political Economy (Chicago) Vol. 88 (April1980) pp. 370–84.

DornbuschRudiger“Special Exchange Rates for Capital Account Transactions,”NBER Working Paper 1659 (Cambridge, Massachusetts: National Bureau of Economic Research, July 1985).

EdwardsSebastian“Money, the Rate of Devaluation, and Interest Rates in a Semiopen Economy: Colombia, 1968-82,”Journal of Money Credit and Banking (Columbus, Ohio) Vol. 17 (February1985) pp. 59–68.

EdwardsSebastian and Mohsin S.Khan“Interest Rate Determination in Developing Countries: A Conceptual Framework,”Staff PapersInternational Monetary Fund (Washington) Vol. 32 (September1985) pp. 377–403.

FloodRobert P. and NancyPeregrim Marion“The Transmission of Disturbances Under Alternative Exchange Rate Regimes with Optimal Indexing,”Quarterly Journal of Economics (Cambridge, Massachusetts) Vol. 97 (February1982) pp. 43–68.

FrenkelJacob A. and Carlos A.Rodriguez“Exchange Rule Dynamics and the Overshooting Hypothesis,”Staff PapersInternational Monetary Fund (Washington) Vol. 29 (March1982) pp. 1–30.

FrenkelJacob A. and AssafRazin“The Limited Viability of Dual Exchange Rate Regimes,” NBER Working Paper 1902 (Cambridge, Massachusetts: National Bureau of Economic Research, April 1986).

GiavazziFrancesco and MarcoPagano“Capital Controls and the European Monetary System” in Capital Controls and Foreign Exchange Legislations Occasional Paper (Milan: Euromobiliare, 1985).

IssingOtmar“Der Euro-DM Markt und die Deutsche Geldpolitik” (unpublished; Würzburg, Federal Republic of Germany: University of Würzburg, 1987).

ItoTakatoshi“Capital Controls and Covered Interest Parity,” NBER Working Paper 1187 (Cambridge, Massachusetts: National Bureau of Economic Research, August 1983).

KhanMohsin S. and NadeemUl Haque“Foreign Borrowing and Capital Flight: A Formal Analysis,”Staff PapersInternational Monetary Fund (Washington) Vol. 32 (December1985) pp. 606–28.

OtaniIshiro and SiddharthTiwari“Capital Controls Interest Rate Parity and Exchange Rates: A Theoretical Approach” (unpublished; Washington: International Monetary Fund, May 1984).

StockmanAlan. C and Hernandez D.Alejandro“Exchange Controls, Capital Controls, and International Financial Markets,” NBER Working Paper 1755 (Cambridge, Massachusetts: National Bureau of Economic ResearchOctober1985).

Van HeuvelenAlan“Physics: A General Introduction” (Las Cruces: New Mexico State University Press, 1982).

Mr. Gros, an economist in the Research Department when this paper was written, is currently at the Université Catholique de Louvain and the Centre for European Policy Studies in Belgium. He wishes to thank his colleagues in the Fund for discussions and comments that contributed substantially to the development of the paper.

See, for example, Adams and Greenwood (1985), Aizenman (1986), Basevi (1985), Dornbusch (1985), Flood and Marion (1982), and Stockman and Alejandro (1985). Edwards (1985) and Edwards and Khan (1985) present a model in which it is assumed that the effect of capital controls is to lead to a partial adjustment of interest rates. The explicitly optimizing model presented in this paper can be interpreted as yielding a partial justification for the assumption employed in these two earlier papers.

The yield differentials sustained by this type of controls, however, are usually small relative to the yield differentials that are sometimes caused by quantitative controls. For example, the yield differential between domestic interest and Euro-interest rates on assets denominated in deutsche mark is usually below half a percentage point; in particular, Euro-deutsche-mark rates are always inside a corridor around German domestic rates, with the width of the corridor determined by the German reserve requirements (see Issing (1987)). By contrast, the corresponding yield differential on assets denominated in lire has sometimes exceeded 10 percentage points.

In the past it was required that, for each U.S. dollar invested abroad, 50 cents had to be held in a zero-interest lira deposit. Portfolio investment abroad would thus have been profitable only if the foreign interest rate were more than double the Italian interest rate. This regulation has recently been changed by lowering the required amount of the zero-interest deposit to only 15 percent of the portfolio investment abroad.

See Appendix I for descriptions and sources of the data used in Figures 1 and 2. Similar data are presented in Giavazzi and Pagano (1985); see also Claasen and Wyplosz (1982).

The distinction between deposit and loan rates is not emphasized in the remainder of the paper, since the paper considers only situations in which r_{t} is smaller or equal to *i _{t}*. The difference between asked and bid rates is taken into account, however, in the data shown in Figures 1 and 2 on differentials between the Eurodeposit rates and domestic Italian and French loan rates. These charts show that since 1979 domestic French interest rates have almost always been below the corresponding Euro-interest rates. The same is true for the period 1979-83 in Italy.

The reverse would hold for controls against capital inflows. For a precise definition of the term “on average,” see the discussion following equation (6) in this section.

The same assumption of increasing marginal costs is also made in Khan and Ul Haque (1985).

The maximization problem (1) does not contain any *net* asset constraint because the variable for arbitrage activity, y_{t}, does not represent any net position. Frenkel and Razin (1986) emphasize the constraints implicit in the intertemporal budget constraint for the viability of dual exchange rates and, thus, capital controls.

It is implicitly assumed here that borrowing on the off-shore markets is not allowed or, equivalently, that domestic deposit rates are always below Euroloan rates.

It is interesting that the quadratic adjustment cost formula could also be derived from a model that treats capital flows as a liquid that flows from one container (capital market) with a higher level (of interest rates) to another container with a lower level. The law of communicating vessels states that, in equilibrium, the fluid in two connected containers has to attain the same level; that is, interest rates must equalize in the long run. See Appendix II for a more precise development of this analogy.

If the forward discount is equal to the expected rate of depreciation, the forward discount should be equal to the probability of the product of a realignment times the size of the devaluation if a realignment occurs.

In the context of this model there should be no two-way flows of private capital. As long as *r _{t}* is below

*i*, imports of capital would never be profitable for private agents. Note also that the variable

_{t}*y, in*Section I referred to the capital flows effected by an individual, competitive operator; the variable

*F*, represents the market aggregate.

_{p, t}This formulation assumes that the public implicitly capitalizes the returns on central bank foreign assets and treats such assets on their own.

This result would not be affected if money demand were a function of income and if income in turn were determined by the real exchange rate and the net foreign assets of the economy. The additional term that would appear in equation (13) in this case would still act as an exogenous forcing variable. Note that the sticky-price adjustment formula in equation (12) has been used in this paper primarily because it is a standard feature of many macroeconomic models. Assuming flexible prices would lead to similar results, except for the case of a devaluation, for which the assumption of a sticky-price adjustment mechanism would be crucial.

In the literature, a long-run offset coefficient different from unity is usually allowed for by assuming that foreign and domestic assets are not perfect substitutes. This effect is not considered in this paper.

Equation (15) assumes that prices are at the steady-state level *ρ = s* and that the system was initially at a steady state. The general solution for *F _{P, t}* would be

*F*, where

_{p, t}—F_{p, ss}= KΛ^{t}*K*is an arbitrary constant. Evaluated at time zero, this yields

*F*. Because

_{p,0}– F_{p, ss}= K*F*is a slowly adjusting variable, however,

_{P, t}*F*has to be equal to the previous steady-state value, which would be given by equation (16) evaluated with C instead of C’. This implies, therefore, that –∆

_{p,0}*C = K*.

It is assumed that, before the news of the future increase in domestic credit arrives, domestic interest rates are equal to international interest rates.

More precisely, in equation (13) a change in *i _{t}* is exactly equivalent to a change in domestic credit if ∆i

_{t}=

*—*∆λ

*C/M*.