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I have benefitted greatly from discussions on earlier drafts of the paper with Peter Clark. I am also grateful to Warren Coats, Jr., Ichiro Otani, Andres Gluski, George Tavlas, Yuzuru Ozeki, and Dallas Batten for helpful comments and suggestions.
Available empirical studies suggest that the adoption of the floating rate regime has not reduced the global demand for official reserves appreciably, although it led to some shift in the demand in the early 1970s. For this point, see, for example, Williamson (1976) and Lizondo and Mathieson (1987).
In this paper, reserves are defined as foreign assets held by a country’s monetary authorities and do not include those held by financial institutions. The latter, however, can be an important supplement to official reserves to the extent that they can finance other items in the balance of payments in response to, certain policy actions, e.g., an increase in domestic interest rates.
Expenditure-switching policies are generally excluded from discussion because of the difficulty in quantifying the adjustment costs stemming from the use of such policies. The use of direct control measures on international trade is also excluded because of their adverse effect on resource allocation.
The causes of fundamental disequilibrium can be numerous, reflecting both domestic and external disturbances, e.g., exogenous shifts in relative prices, foreign demand, and domestic production and demand.
Part of external disequilibrium could also be financed through recourse to external borrowing, and the extent to which monetary authorities of a country hold reserves to meet fundamental disequilibrium will depend on the availability and terms of external borrowing. The importance of external borrowing to alleviate the cost of external adjustment is analyzed by Martin and Selowsky (1988).
This point was also stressed by Clark (1970) and E. Claassen (1975), in which the speed of adjustment is treated as an endogenous variable that is determined along with the optimal reserve stock. However, their optimal conditions for the speed of adjustment differ from those derived in this paper because of the different specification of the economic cost of external adjustment. This point is explained in more detail below.
It might be noted that the appropriateness of the marginal propensity to import as a proxy for the marginal cost of adjustment has not necessarily been supported by empirical studies, as the coefficient of this variable generally gives the wrong sign in regression equations.
This point, namely, that incorporation of the possibility of fundamental disequilibrium into the analysis would require an inter-temporal model, is also stressed by Williamson (1973) in his comments on Niehans (1970) who explored implicitly an intertemporal optimizing approach in connection with the discussion of the utility of reserves. An interesting attempt is also made by Martin and Selowsky (1988) to specify the cost of adjustment in a dynamic framework.
In what follows, the excess demand for foreign exchange refers to the excess demand for foreign exchange by the private sector (or the overall balance of payments deficit) unless otherwise indicated.
Strictly speaking, the demand for official reserves must be analyzed in relation to expected future disturbances, not in relation to those of the past. But the size and duration of future disturbances could perhaps be gauged, as a rough approximation, by examining past disturbances that are manifested in changes in official reserves. On this point, see, for example, Triffin (1961).
Olivera (1969) also assumes a normal distribution as an approximation of the density function of the excess demand for foreign exchange in his discussion of the optimal demand for official reserves.
The empirical evidence concerning the stochastic nature of changes in official reserves has been mixed and further investigation is needed. For example, Kenen and Yudin (1965) observed that monthly changes in official reserves in selected 14 countries during 1958-62 displayed a significant serial correlation and stressed that the balance of payments in the short run should also be described as a Markov process rather than a simple random walk variable. The existence of a serial correlation was also stressed by Archibald and Richmond (1971), although they argued that the serial correlation was rather characterized by heteroskedasticity. On the other hand, Streeter (1970) found that, using quarterly and annual data for the period of 1958-67, there was virtually no support for the autoregressive hypothesis and strong evidence for the normality hypothesis. On this latter point, see Williamson (1973).
It is assumed that there are no speculative capital outflows in response to the emergence of fundamental disequilibrium and consequent possible declines in official reserves.
It should be noted that the nominal values of these aggregates are equal to the real values, because domestic prices are assumed to be exogenously set at a constant level under the assumption of a small country.
In what follows, macroeconomic variables, such as income (or output) and expenditure, refer to their expected values unless otherwise indicated.
In general, these adjustment measures will include exchange rate policy, although the extent of the recourse to this policy will depend on the nature and causes of such disequilibrium. It should be noted that the adequacy of official reserves will be substantially influenced by the degree of exchange rate flexibility pursued by the monetary authority, but this issue is not discussed in this paper.
Namely, the length of the adjustment period is equal to T periods.
These assumptions imply that the monetary authority envisions a certain adjustment strategy over a definite time period which includes its assessment of optimal policies and their likely economic impact on the balance of payments.
The size of θ will depend partly on the type and extent of external adjustment policies implemented by the monetary authority and the economy’s supply elasticity in response to these measures. The assumption that θ is less than unity is made to keep the model dynamically stable.
The key assumption for the derivation of E[x] and V[x] is that the excess demand for foreign exchange is serially uncorrelated. Under this assumption, E[x] and V[x] are given by:
E[x] = E[x0] + … + E[xT-1]
V[x] = V[x0] + … + V[xT-1]
Substituting E[xt] = (1 - γt)μ and V[xt] = σ2 into the above equations gives:
E[x] = μ(T - γT(T - 1)/2)
V[x] = Tσ2
Noting T = 1/γ, these give the formulae presented in the text.
This assumption differs from the standard stochastic approach in which reserve depletion is assumed to induce the adoption of external adjustment policies. The importance of the role of external borrowing in meeting possible reserve depletion, however, has recently been recognized in Dooley, Lizondo, and Mathieson (1989). As noted in the text, the scope for market borrowing by highly indebted countries are now limited, and they will have to rely more on official sources, including Fund credit. It should also be noted that external borrowing in this context refers to “compensatory” borrowing by monetary authorities, which will be registered below the line and will not affect the capital account. Needless to say, such external borrowing would be undertaken when signs of possible reserve depletion emerge rather than after reserves have actually been depleted.
More realistically, the marginal cost of external borrowing (i) could be assumed to be a positive function of the amount of external borrowing (x-R).
This feature reflects that the random variable x is a compound random variable which is composed of T independent random variables xt. For this point, see the definition of x given in (6).
This specification of the potential cost of reserve depletion is based on the specification of “depletion penalty” developed by Arrow, Harris, and Marschak (1951) in the discussion of optimal inventory policy.
The partial differentiation of (12) gives the following first order condition to minimize the total cost associated with reserve holdings.
Noting that F(R) depends on γ, μ, and σ2, the first order condition is rewritten as (11) in the text. The second order condition is satisfied because F′(R) = f(R) is always positive. A detailed mathematical appendix is available on request.
The positive sign of the partial derivative of R with respect to σ2 assumes (R-λ) > ϵ.
The negative sign of the partial derivative of s with respect to ρ assumes T < 1/ρ.
The first order condition for the minimization of (14) is given by:
(1+ρ)(1-θ)μ((1+ρ)T-1-Tln(1+ρ))/(ρ2T2(1+ρ)T) - (j2/J1)σ2where T = 1/γ.
The second order condition and the impact of changes in the major explanatory variables on the speed of adjustment is given by:
2(1+ρ)T - 1 - (Tln(1+ρ)+1)2 > 0.
In this connection, it is worth noting that official reserves held by oil-importing countries increased substantially following the rises in oil prices in the 1970s, which created a major fundamental disequilibrium in the balance of payments in these countries.