The Effect of Foreign Exchange Receipts on Imports of Less Developed Countries

Theoretical and empirical studies of aggregate import behavior generally show the flow of imports to be determined chiefly by aggregate economic activity and by import prices relative to prices of domestically produced substitutes. For many less developed countries, however, this relationship is questionable because of the effects of trade and exchange restrictions. For these countries, imports consist largely of producer goods—capital equipment, maintenance items, and imported components—and there are no adequate domestic substitutes. If restrictions are used to limit imports, there will be a tendency for imports to determine output, rather than the reverse, particularly in the manufacturing sector.

Abstract

Theoretical and empirical studies of aggregate import behavior generally show the flow of imports to be determined chiefly by aggregate economic activity and by import prices relative to prices of domestically produced substitutes. For many less developed countries, however, this relationship is questionable because of the effects of trade and exchange restrictions. For these countries, imports consist largely of producer goods—capital equipment, maintenance items, and imported components—and there are no adequate domestic substitutes. If restrictions are used to limit imports, there will be a tendency for imports to determine output, rather than the reverse, particularly in the manufacturing sector.

Theoretical and empirical studies of aggregate import behavior generally show the flow of imports to be determined chiefly by aggregate economic activity and by import prices relative to prices of domestically produced substitutes. For many less developed countries, however, this relationship is questionable because of the effects of trade and exchange restrictions. For these countries, imports consist largely of producer goods—capital equipment, maintenance items, and imported components—and there are no adequate domestic substitutes. If restrictions are used to limit imports, there will be a tendency for imports to determine output, rather than the reverse, particularly in the manufacturing sector.

In addition, indices of import prices are typically based on foreign supplier prices, and therefore the price effects of trade and exchange restrictions imposed by the importing country are omitted. For many less developed countries, these effects are very important relative to changes in supplier costs, so that the major part of the influence of relative prices on imports is overlooked. Even if some part of the price effects of restrictions is measurable and is included in the relative price variable,1 there is a problem for estimation; to the extent that all changes in trade and exchange restrictions are positively correlated, which is likely, the omission of part of the price effects necessarily results in positive bias in the estimates of the price elasticity. In such cases the extent to which foreign and domestic goods can be substituted is overrepresented.2

This study presents an alternative approach to the import behavior of less developed countries, based on foreign exchange receipts. A conceptual basis is established for a behavioral relation between a country’s imports and its exchange receipts, as a special case of balance of payments adjustment. A model of reserve behavior is then introduced to determine how the response to short-run imbalance is divided between changes in reserves and in imports. Finally, the import-exchange equation is estimated for a number of less developed countries. The empirical results are found to be generally consistent with the hypothesized behavior.

The balance of payments approach to import behavior is shown to rest on a distinction between flows that is not unlike those categories which have elsewhere been called “autonomous” and “accommodating.” 3 To some extent this involves a simplification, even for less developed countries. In exchange for the simplification, however, one can avoid the problems associated with the standard import function. In addition, adoption of the import-exchange approach in multicountry trade models makes it possible to show the effects of “respendings” of foreign exchange that follow from exogenous changes in countries’ receipts—such as an allocation of SDRs, general adoption of tariff preferences, use of the International Monetary Fund’s oil facility, or the swings in economic activity in the industrialized countries—so that the international repercussions of these events can be more accurately assessed.

I. Theoretical Basis of the Foreign Exchange Effect

The notion that less developed countries’ imports are determined by their foreign exchange receipts is found in the literature in connection with (1) the behavior ascribed to less developed countries in world trade models,4 (2) respendings of foreign exchange by less developed countries in studies of the effects of changes in the flow of U. S. foreign aid,5 and (3) the foreign exchange constraint in the two-gap programming models of economic growth.6 The justification for the relationship is usually that demand for foreign exchange exceeds supply at the existing exchange rate, and the stock of reserve assets is small. In these circumstances, if export earnings fall or if capital inflows are reduced, the authorities have little choice other than to tighten restrictions on imports in the short run; similarly, the restrictions on imports may be eased if export receipts or capital flows increase.

Arguments of this type attribute unwarranted significance to excess demand for foreign exchange, because restrictions may be used even when the exchange rate equals its longer-run equilibrium value, and such arguments also ignore the possibility of financing imports out of reserves in the short run. In addition, the existing studies do not consider how the hypothesized import-exchange relation is to be reconciled with the standard macroeconomic import function. It is appropriate, therefore, to begin by indicating the theoretical case for a behavioral relation between imports and foreign exchange receipts.

balance of payments adjustment

The nature of the import exchange relation can be illustrated by an extreme example of a system of exchange control. Licenses to purchase foreign exchange, at par, are issued by the authorities at no cost to a queue of importers, precisely as fast as the foreign exchange becomes available. (Changes in import demand appear as changes in the length of the queue but have no effect on actual imports.)

In the above example, the influence of foreign exchange receipts on imports (that is, on the foreign exchange value of imports) is complete, precise, and immediate. In practice, the effect of receipts on imports is not so exact. Many of the policies used to influence imports are of the “cost” type, rather than quantitative policies, and therefore are less direct and less flexible—such as tariffs, surcharges, advance-deposit requirements, exchange license fees, exchange rate changes, shifts of commodities among the free-rate and administered-rate segments of the exchange market, and so on. Indeed, some countries have eschewed administrative policies almost entirely, relying on fiscal and monetary instruments to achieve external balance. All of these policies result in some lag between a change in exchange receipts and in expenditures. In addition, the relation may be inexact on account of error in estimating the needed amount of policy change. Finally, even when the authorities rely on a comprehensive exchange control system, there are likely to be slippages between receipts and imports. The authorities may dip into reserves to spare producers a sudden, sharp cutback in imported inputs; symmetrically, they may increase reserves by allocating only a portion of current receipts to satisfy current demand. Importers, meanwhile, may stockpile their licenses in anticipation of greater shortages in the future.

Thus, two implications for the import-exchange relationship follow: (1) the assumption that imports equal receipts is an oversimplification; imports are a function of current and lagged receipts, with the length and stability of the lags dependent on the type of policies used for external balance; (2) viewed in the context of the spectrum of trade and exchange controls that countries use, the relation between imports and exchange receipts is seen to be an aspect of balance of payments adjustment.7 The policy changes that account for a relation between receipts and imports are made in response to imbalance in the external sector. It follows that the import-exchange relation is not confined at the conceptual level to less developed countries, nor is it applicable only to countries relying heavily on direct, quantitative controls; conceptually, it is a general phenomenon.

There is an important difference among countries, however, in the extent to which they rely on changes in imports for external adjustment. For less developed countries it is more likely to be true that the supply of exportables is price inelastic in the short run, the aid inflow is determined largely by the decisions of donor governments, foreign private direct investment is responsive to longer-run profit expectations, and factor-income payments and loan repayments to foreigners are contractual and fixed. Under these conditions, imports play a relatively important role in attaining short-run balance, because this flow is responsive to the policy tools that the authorities use, while flows other than imports tend to be exogenous in relation to these policies.

This is a fairly special case. For countries in general, both external disturbances and effects of government adjustment policies are spread out over more or less all the items in the international accounts. Thus, while for all countries there tends to be a behavioral relation between exogenous disturbances and endogenous offsetting changes brought about by the authorities, in general the two types of change do not confine themselves so neatly to certain subsets of items in the international accounts. The exogenous changes cannot be observed as distinct from the endogenous changes. The usefulness of the proposed approach is thus restricted to countries in which this distinction can be well approximated.

exchange receipts and the standard import function

In the abstract example above of the import-exchange relation, imports were determined solely by flexible quantitative restrictions. The familiar formulation—imports as a function of aggregate income and relative prices—is not contravened, however. By standard economic reasoning there is an implicit scarcity price of foreign exchange that varies directly with excess demand. This will tend to be reflected in the domestic market prices of imported goods and in the prices of domestic products which have a large import content. If one could measure the scarcity price, the standard formulation would be a sufficient explanation of import behavior, irrespective of exchange control. The two models—the standard function and the relation based on exchange receipts—would in effect coincide.

This coincidence obtains whether or not administrative control is the only tool used for adjustment. For example, when they desire to decrease imports, the authorities may undertake contractionary macro-economic policies, reducing income in order to make the demand for imports equal to the amount allowed by exchange receipts, or they may undertake policies to reduce the domestic price level and thus reduce import demand. More typically countries change the restrictiveness of import controls (cost-type and/or quantitative), according to whether aggregate income and prices of domestic and foreign goods are changing in such a way as to implement or to frustrate the goal of external balance.

Thus, as a first approximation the sum of the effects on imports of income and correctly measured relative prices is determined by exchange receipts, because of the “external budget” constraint. Income and relative prices, in turn, determine imports. Therefore, the two models of import behavior are not inconsistent. Rather, the import-exchange model is a reduced form equation, which results from substituting the relation between true relative prices and external balance into the standard import function (and similarly for income). In this way imports can be expressed in terms of observable explanatory variables even when changes in relative prices occur largely in the form of changes in restrictions.

It follows, however, that explanatory variables from the structural equations may not be mixed in the reduced form equation. To include both the flow of receipts and the relative price level that it engenders, however incompletely measured, amounts to double-counting of causal factors. This is also true of receipts and income, to the extent that external balance is allowed to influence demand management policies. Since exchange reserves are substitutable for receipts (as will be specified below), it also follows that there is a logical error in using the level of reserves in the standard import function as a proxy for the stringency of controls.8

Inclusion of income or relative prices in the exchange-based import equation is equally objectionable. It might be argued that the authorities, influenced by the “length of the queue” (that is, by the level of excess demand, where the definition of “demand” excludes the influence of all restrictions), will grant some constant percentage of import license applications, so that the standard explanatory variables ought to appear in the exchange-based model. However, in a situation of very large and changeable rates of domestic inflation and relatively fixed exchange rates, the magnitude of import demand indicated by income and measurable relative prices is highly arbitrary. Apart from a desire to smooth fluctuations in imports in order to minimize disruptions in production and consumption, it is not rational on economic grounds to suppose that the authorities are influenced by the length of the queue. They cannot seek simultaneously both to curb excess demand and to satisfy it.

Income and measurable relative prices do retain an influence on imports that is independent of external balance during the lapse of time between a change in receipts and the induced change in restrictions. However, unless they coincide with the direction of balance of payments policy, these changes in the standard variables must eventually be offset and their collective independent effect on imports is therefore transitory.

the basic assumption

For the purposes of this study a three-way categorization is imposed on international flows. “Foreign exchange receipts” (F) is defined as the sum of flows that are effectively exogenous in relation to the external balance policies of the authorities. More accurately, this subset should be called “net” exchange receipts, since it is made up of gross exogenous receipts less gross exogenous payments. The sum of all other flows, excepting imports, is defined as the “change in reserves” (AR), which is therefore endogenous. The change in reserves corresponds to financing of payments imbalance. As used here, reserves is a net concept rather than the gross concept often encountered; it may include assets and liabilities in addition to those meeting strict criteria of liquidity and convertibility. Changes in imports correspond to adjustment. It follows that the balance of payments identity may be written 9

Mt+ΔRtFt.(1)

Prima facie one suspects that in the case of developed countries almost all flows are substantially endogenous, and that F is therefore a nearly empty subset. To explain imports of developed countries on the basis of exogenous net receipts would consequently not be very promising.

exogenous and endogenous flows

Even for less developed countries, the three-way categorization described above is a simplification. Clearly, the model will be more satisfactory in describing the hypothesized behavior the more true it is that the disaggregation permitted by published balance of payments data results in either wholly exogenous or wholly endogenous flows and the more one is successful in discriminating between them.

It is not possible to determine exogeneity or endogeneity with an internal statistical test.10 Therefore the assignment of flows has been made on the basis of extraneous information, primarily published data on short-term borrowing by central banks 11 and International Monetary Fund consultation reports on individual countries. Very roughly, this assignment of flows is as follows: a country’s reserves are defined here to include its holdings of gold, convertible foreign exchange and SDRs, and its reserve position in the Fund,12 plus net bilateral payments- agreement balances, less its use of Fund credit and short-term borrowing by the central bank. Exogenous receipts therefore include export earnings, official grant aid, and other net current account receipts (except for imports, c.i.f.), net long-term private and official capital inflows, net short-term private inflows and official inflows to nonmonetary institutions (loans directly to the central government or its development agencies), and net errors and omissions. Changes in the net foreign assets of commercial banks are counted as endogenous if (during the sample period) the central bank acquired them through nationalization, forced commercial banks to lend it foreign exchange, or induced capital flows for balance of payments purposes by changes in domestic monetary policy (even though these latter flows are exogenous to the extent that they are influenced by monetary conditions in the lending countries). Otherwise, changes in net foreign assets of commercial banks are counted as exogenous, as though they are made up wholly of short- term commercial credit needs of domestic exporters and importers. When closing of the central bank’s foreign exchange window forced foreign suppliers to extend credit (“commercial arrears”), the flow was counted as endogenous, that is, as a decrease in net reserves. Exceptions to the above illustrative distinction between reserve changes and receipts are indicated in a Statistical Annex containing detailed country notes (available from the author on request).

The time series for exogenous net receipts and endogenous reserve changes corresponding to these definitions may only approximate the intended conceptual distinction between cause and effect. Since export earnings may respond somewhat to exchange rate changes, even in the short run, or to changes in aggregate demand policies subordinated to the goal of external balance, they may therefore not be perfectly exogenous. To take a second example, the inflow of medium-term capital received by the central government following an episode of debt rescheduling to refinance former short-term liabilities of the central bank is likely to vary with the balance of payments needs of the recipient, contrary to the assumption of exogeneity.

To the extent that the basic assumption is not fulfilled, there is a problem for estimation. The problem is well illustrated by analogy with a simple model of national income determination. Let the consumption function be represented by C = f(Y), where C is consumption and Y is personal disposable income. By the national accounts identity this expression may be rewritten as C = f(C + I), where I is autonomous expenditure. Since the import exchange equation may be written as M = f(F), and therefore by the balance of payments identity, M = f(M + ΔR), the analogy appears to be exact. As is well known, if the consumption function is estimated with ordinary least-squares, simultaneous-equations bias will affect the parameter estimates because I alone is exogenous and C + I will not be independent of the stochastic term. However, in the case of the import exchange equation, the variable F itself is exogenous and therefore simultaneous-equations bias in this sense will not occur, despite the fact that F is identically equal to the sum of imports and the change in reserves. The problem occurs if endogenous flows are erroneously included in F instead of in ΔR. The analogous problem in the case of the national income model occurs if measured I includes flows that are not wholly exogenous. For example, if changes in inventories are determined by anticipated growth in the economy, this flow is exogenous; but to the extent that inventories change in response to unanticipated changes in current sales, these changes are endogenous. It is therefore unclear whether the change in inventories is to be counted as part of I or part of C.13

In the simple case where M = f(F), the addition of an exogenous flow to an incomplete measure of receipts tends to increase the explanatory power of the model, if the model is an appropriate description of behavior; measured F is brought closer to its true value, the magnitude that actually determines imports. On the other hand, if an endogenous flow is incorrectly added to receipts, the resulting time series will vary less than true receipts, because the included component of reserves will tend to offset part of the exogenous variation. If the apparent explanatory power of the model is consequently higher for a particular sample, that result is misleading. By making measured F less variable, the incorrectly included endogenous flow changes the observed behavior from that which the model purports to represent to something simpler. The difference in the coefficient of determination (R2) is attributable to this change rather than to more accurate measurement of the response of truly endogenous to truly exogenous variables.14

Of greater interest are the consequences of incorrectly distinguishing flows in the full model (developed below). In that case the effects of incorrect specification cannot be demonstrated in terms of R2 because of somewhat greater complexity. It is possible, however, to derive expressions for bias in the reduced form coefficients in terms of relationships among subcomponents of receipts and of the change in reserves. In the absence of a priori information on the direction of these relationships among disaggregated flows, it is plausible to assume that components of ΔR are positively intercorrelated, while components of F are uncorrelated. The former assumption is adopted on the grounds that the assets and liabilities making up net reserves tend to be substitutes. The latter assumption is not necessarily true in all cases but is typically true of the exogenous components most likely to be misclassified. On the basis of these assumptions, it can be shown that incorrectly counting an exogenous flow as endogenous results in reduced form estimates which are unbiased or in which the direction of bias is ambiguous. Incorrectly counting an endogenous flow as exogenous necessarily results in bias in one of the reduced form coefficients (see Appendix I).

empirical applications

There are several possible research strategies:

(1) If the goal is to evaluate the approach itself, relative to other hypotheses or for its own sake, then the definitions of receipts and reserves should correspond as closely as possible to what is exogenous and endogenous from the point of view of balance of payments adjustment. The appropriate definitions generally require disaggregated balance of payments data, however, which are available only on an annual basis for most countries. As a consequence, the samples for this alternative tend to be small and to extend over a long period of time in relation to quarterly data. The coefficient estimates are less stable for these reasons.

(2) If high priority is given to the stability of the estimated functions, then the definition of reserves may be narrowed (that of receipts broadened) so that quarterly data are available. An example is “international reserves,” from International Financial Statistics, net of “use of Fund credit.” The “line” between capital and reserves is thereby moved further down the balance of payments accounts, in relation to the first alternative. The resulting time series are also considerably more accessible. (With data for imports and the change in reserves, receipts can be derived algebraically from the balance of payments identity.) This alternative is therefore more feasible if the model is to be estimated for a large number of individual countries. However, it amounts to counting changes in short-term central bank liabilities and certain other items as exogenous capital flows even when there is evidence that they are part of the endogenous response to imbalance, a departure from the basic assumption. The coefficient estimates are therefore biased to some extent. (One can achieve these same economies in data by moving to the other definitional extreme, defining receipts to be comprised solely of export earnings and counting all other flows as endogenous. However, parameter estimates based on these definitions were frequently found to be unreasonable.)

(3) If the goal is forecasting, one may choose a narrower definition of receipts than either of the above—exports, foreign aid, and long- term private capital, for example. Estimates of this magnitude for forecast periods are more easily obtained than estimates of the alternative aggregates.

The first of the above three alternatives has primarily been followed in this study. Estimates corresponding to these definitions of reserves and receipts are hereinafter termed “preferred.” Results corresponding to the alternative definitions indicated in (2) and (3) have also been obtained, however, in order to see what difference these variations produce in the empirical results. They are presented and discussed in a Statistical Annex (available from the author on request).

II. The Adjustment Model

On the basis of the discussion in Section I, imports would be specified as a linear function of current and past values of foreign exchange receipts:

Mt=a+Σi=onbiFti+ui.(2)

In a general way this equation allows for the lags and imprecisions suggested in Section I. The lags will tend to be stable if the authorities use a given set of external balance policies consistently during the sample period. However, the equation takes no explicit account of reserve behavior.

One way of expressing this reservation is in terms of omitted variables. Since imports and the change in reserves are linearly dependent by the balance of payments identity, equation (2) implies that there are no important determinants of reserve behavior other than exchange receipts. If reserve behavior involves variables in addition to present and lagged F, then equation (2) is less adequate than an equation containing them. If the omitted variables are not independent of F, the coefficient estimates of equation (2) will be biased.

Consider what type of reserve behavior is implied by equation (2) in the simple case in which there is no trend in F. On average, M = a + b F (where bbi). It follows from the balance of payments identity that there will tend to be a change in the average level of reserves equal to (1–b)F=a per period. Unless [(1 – b)Fa] this implies a continuing growth or decline in the stock of reserves, which is not plausible since F is constant. Secondly, with long-run reserve behavior interpreted in this way there will also be short-run reserve variation equal to the residuals in equation (2), roughly speaking. Since the mean of the errors, e^t, will equal zero, it is reasonably implied that in the short run reserves are used to finance a series of transitory surpluses and deficits, but it is not reasonable that this type of behavior should occur without regard to the level of actual reserves. In fact, it is likely that when a sequence of imbalances have the same sign there will be a stronger effort on the part of the authorities to restore reserves to some “normal” level.15 Because of these deficiencies, the import- exchange equation is derived below in the context of an explicit model of reserve behavior.

the allocation function

In theoretical work on the demand for international reserves it is common to assume that, in the short run, behavior of the authorities is dominated by the goal of restoring reserves to some desired long-run level.16 Clearly this view is incomplete. If reserve maintenance were the only consideration, the requisite amount of current exchange receipts would simply be set aside to make up the reserve deficiency and the remaining portion of receipts would be allocated to imports (unless receipts were less than the shortfall). The variability of receipts would be passed on entirely to imports. The stock of reserves would not have the function commonly attributed to it of smoothing adjustment to external imbalance.

Accordingly, it is assumed here that the authorities have two goals related to external balance in the current period. First, they wish to restore the stock of reserves to a desired level (R*t), which requires

ΔRt=R*tRt1

and, secondly, they wish to smooth imports, which may be written as

Mt=M*t.17

Since the balance of payments identity requires, at the same time, that the sum of imports and the change in reserves equal receipts, the two goals will generally be in conflict and the actual outcome will be a compromise.

Let it be assumed that the authorities’ response to imbalance is efficient; that is, they allocate current exchange receipts between imports and reserves in such a way that it is not possible to achieve both goals more closely. Thus, the situation in which the authorities add to already excessive reserves at the expense of inducing a larger negative deviation in imports is ruled out, as is the situation in which reserves are drawn down below their desired level in order to finance a sharp and temporary glut of imports.

In Appendix II it is demonstrated that the two assumed goals, on condition that the response of the authorities is efficient, place limits on the allocation of current receipts between imports and reserve changes. A linear allocation function satisfying those limits has the form:

ΔRtFtM*t=(1γ)+γ[R*tRt1FtM*t],0<γ<1.(3)

The denominator on both sides of equation (3) corresponds to the difference between actual receipts and the amount necessary to smooth imports. The numerators of the left-hand and right-hand sides measure the actual and the desired changes in reserves, respectively. The limits require that the slope of the function be positive and lie between zero and one, and that the function pass through the point (1, 1). If it is linear, an efficient allocation function has only one parameter.

Multiplying both sides of equation (3) by FtM*t and substituting for ΔRt in the balance of payments identity—equation (1)—yields

Mt=(1γ)M*t+γ[Ft(R*tRt1)],(4)

a form which is convenient for interpretation. If γ is very nearly equal to unity and therefore (1 –γ) is very small, M* will not have much effect on actual M. An amount which is nearly equal to the reserve shortfall is “deducted” from current F in order to correct the shortfall at once, and the balance of receipts is spent on imports in the current period, despite the fluctuation that may result. Conversely, if γ is nearly equal to zero, the desire to smooth imports dominates the allocation of current receipts and only a small weight is given to the level of imports consistent with restoring reserves.

It is possible to carry the analysis a step further. Consider the assumption that the costs of discrepancies between actual and desired levels of reserves and of imports are quadratic.18 This implies that there are positive costs attached to excessive, as well as deficient, levels of imports and reserves, that costs increase more than proportionally with the discrepancy, and that the costs of excesses are symmetric to the costs of deficiencies. It can be shown that this assumption is a sufficient condition for the linearity of the allocation function. The quadratic cost function may be written as

Ct=a(MtM*t)2+b(RtR*t)2.(5)

Minimizing equation (5) with respect to Mt and Rt, subject to the balance of payments identity, yields equation (4) exactly, if γ =b/(a + b).19 It follows that the allocation function will satisfy the general bounds implied by the two assumed goals for any set of non-negative costs. For example, the larger the cost of a reserve shortfall is relative to an import contraction, the larger is b relative to a and the closer is γ to unity. This is consistent with the above discussion, since, as γ comes closer to unity, the portion of current receipts allocated to making up the reserve shortfall becomes larger and the amount expended in preventing a dip in imports becomes smaller.

The interpretation of γ in terms of relative costs yields a further analytical result. Since reserves are defined broadly and on a net basis in the intended application of the model, it seems natural to allow for differences in cost according to the type of reserve instrument. A deficiency of credit with the Fund (large outstanding drawings), for example, might be expected to induce a smaller curtailment of current imports than a deficiency of foreign exchange. It can be shown, however, that this distinction is logically irrelevant for the specification.20 From the point of view of providing the foreign exchange needed to offset a reserve deficiency, it takes as much import reduction to increase Fund credit by one unit as it does to increase foreign exchange assets by one unit.

There may be objections to the assumption of quadratic costs. It is clear that reserve excesses have positive costs, and it is plausible that these costs will increase more than proportionally with the excesses. This follows from the supposition that the larger the excess is, the shorter is the period of time that it will be held—and therefore the less favorable the yield.21 It is also reasonable to assume that the cost of a shortfall of reserves is positive and that it increases more than proportionally with the shortfall. However, a priori, one might well expect the costs of deficient reserves to be larger than the costs of excesses—rather than equal to them, as is implied by a quadratic cost function. As the level of reserves falls, the authorities are induced to borrow; decreases in net reserves are effected by increases in reserve liabilities rather than by decreases in reserve assets. The interest charges are likely to increase with the amount borrowed as an offset to lenders’ risks. In the extreme, the supply of borrowed reserves tends to become highly inelastic. Further credit will be granted only with conditions on the borrower’s internal and external policies,22 or the borrower will be forced to devalue or to default on outstanding obligations—alternatives which frequently involve considerable political cost. Taken together these financial and political costs may well be greater than the costs of correspondingly “medium” to “large” excesses.23

With regard to import fluctuations, the assumption of a quadratic cost function is subject to the same reservation. The costs of import fluctuations are related to the adjustments in production and consumption that are induced.24 The costs will increase more than proportionally with the fluctuations if there are increasing marginal rates of substitution of domestic for foreign goods. In the case of a reduction in imports, for example, the economy will first give up foreign goods for which there are relatively good domestic substitutes; the larger the reduction is, the more imperfect are the substitutes that must be used. The presumpion of nonproportional costs is strengthened to the extent that producers and consumers hold inventories of foreign goods25 and to the extent that restrictions fall first on capital goods and then on imported inputs and spare parts.26 Conceptually, the costs of import fluctuations are quite symmetric as between excesses and shortfalls, but in practice the costs of adjusting to higher than average imports need not be borne. Unlike cutbacks, production and consumption will not be forced into line with a glut of foreign goods. Rather, the goods will simply be stored, involving much smaller costs. In principle, the foreign exchange to pay for them could be stored at even less cost, but this is generally prohibited because it reduces the control of the authorities over expenditure (and even if it were not prohibited, it would be unattractive to producers because of the greater risk that the authorities could not honor the exchange licenses).

These arguments do not prove that departures of reserves and imports from desired levels involve asymmetric costs; the question is in part an empirical one. While it would be preferable to allow for asymmetric costs in the specification, this leads to enormous algebraic complexity; 27 therefore, the actual cost curves are approximated by quadratic functions throughout this study. The possible error in this approximation is mitigated because in a given period MtM*t and RtR*t will always have the same sign (as shown in Appendix II). Thus, if the true cost of a reserve shortfall is understated by the assumed quadratic form, the cost of the import deficiency (which must necessarily occur at the same time) will also be understated. This reduces the error with respect to the allocation of receipts between them.

nontransitory disturbances

In the static Clark-Kelly model, all balance of payments disturbances are transitory, and fundamental disequilibrium does not occur.28 The problem is reduced to one in which the authorities hold reserves against disturbances which are self-correcting; in the end all cancel out, whether the authorities adjust much or little and whether their reserve stock is large or small.

Clearly it would be desirable to drop the assumption of transitory disturbances, but this attempt quickly leads to serious difficulty. To illustrate, suppose that for a given country the flow of net exchange receipts appears to show a positive trend, with random fluctuations about the trend. In this case, it does not seem likely that the authorities will wish to accumulate reserves so as to offset the trend permanently. Countries are unwilling and/or unable to let their reserves change by indefinitely large amounts in the short run. This intuitive argument suggests that it is the fluctuations about trend that require adjusting or financing.

But if the trend reverses itself at a point in time, then what appeared to be long-run growth becomes a medium-term cycle. The “trend” is eventually seen to be part of a relatively longer fluctuation, a peak which the authorities might well wish to smooth through accumulation and then reduction of reserves. This negates the intuitive case for ignoring the trend.

The problem is that the distinction between systematic and random components in exchange receipts cannot be made unconditionally, but it can only be made relative to a given period of time. It follows that it is logically impossible to speak rigorously of optimal behavior in a dynamic setting unless one has foreknowledge of the parameters of a virtually infinite distribution of disturbances. Anything short of that amounts to circumscribing the problem more or less arbitrarily. Nevertheless, the authorities involved must and do make decisions regarding how much of a current imbalance is to be financed and how much is to be adjusted.

The alternative chosen here requires a more modest amount of information at the cost of being optimal in a more limited analytical sense. It is assumed first that the authorities utilize a concept corresponding to “permanent” or “long-run” exchange receipts (F*). This magnitude serves as the norm by which the exogenous disturbance is measured; (FtF*t) is defined as the ex ante imbalance in international payments. Consequently, “desired” imports (M*), which in the balance of payments context means perfectly smoothed imports, is specified to be given by the condition that M* = F*.29 In fact, F* may change somewhat from period to period. Thus, the simplification implicit in the concept of long-run receipts is that part of the actual variation in imports is ignored in assessing the trade-off between the variability of imports and deficient or excessive reserves.30

Secondly, it is assumed that the authorities estimate F* from recent historical data, in a manner reflecting the notion that the future is likely to be similar to the past in some degree. If Ft tends to remain constant over several periods, then it is taken to be the long-run level of receipts. But if Ft changes, the change in receipts influences the authorities’ view of the extent to which current receipts are representative of long-run receipts, in a positive or negative direction according to whether change is generally expected to continue or to be reversed in future periods. Explicitly, it is assumed that31

F*t=Ftλ(ΔFt).(6)

A positive value of λ corresponds to the judgment that the current change in receipts is likely to be transitory, while a negative value corresponds to the judgment that the current change will tend to continue. A large absolute value of λ implies that the authorities believe the change is likely to accelerate, or that they have a long time horizon, or both; the converse holds for a small absolute value. The value of λ is taken to be exogenous to the model developed here and is assumed constant over the sample periods.

Expectations hypotheses are most often applied to a very large group of economic agents, such as a nation’s consumers or producers. Individually these agents are likely to have little knowledge of the specific causes of change in, say, “permanent income,” and therefore may reasonably be assumed to rely heavily on actual past changes in order to distinguish transitory from permanent components of change. Central bankers in less developed countries, on the other hand, who are likely to have a somewhat more adequate knowledge of the causes of change in their external receipts and the duration of those factors, will have less need to place reliance on the indirect method of observing the change in current and past values. As a consequence the values of F* used by them in preparing their foreign exchange budget for the next year may be more accurate than the values estimated implicitly by the model.

desired net reserves

Since the import-exchange equation is to be fitted with time-series data for individual countries, factors that are important in explaining differences among countries’ average reserve holdings, but that are unlikely to change much over time for a single country, may be ignored—for example, the marginal propensity to import and the opportunity cost of reserves.

It is assumed first that the major factor affecting change in the desired level of the reserve stock of an individual country, over time, is change in the variability of ex ante imbalance (FtF*t). It is also assumed that the level of long-run receipts (F*t) is a reasonable proxy for the standard deviation of imbalances—that is, it is assumed that the larger the volume of net receipts is, the larger is the dispersion of imbalances about their long-run level. Finally, the function is assumed to be linear. The equation for desired reserves may be written:

R*t=α0+α1F*t.(7)

Since F*t=M*t, the assumptions imply that desired reserves vary with a smoothed measure of imports. In the theoretical literature the point has been made emphatically that reserves are held not to pay for imports but to finance discrepancies between imports (or, more generally, payments) and receipts. This supports the first of the above assumptions. However, whether the variability of imbalances grows with the volume of receipts is an empirical question, and the existing evidence is mixed. Ex post evidence generated by this study, presented below in the empirical section, is also slightly mixed but in general is consistent with the assumption. The literature contains some indications of scale economies in reserve holdings but even if that phenomenon should be demonstrated unambiguously, the linear form assumed here may be taken as an approximation.32

There is little doubt as to the general reasonableness of the desired reserves function thus specified, but it is noticeably ad hoc. A theoretical link has now been well established between the level of desired reserves and the speed of adjustment of reserves (γ in equation (3), above).33 If a country chooses a slower speed of adjustment to reserve shortfalls, it must concomitantly hold a larger stock of reserves on average; the two are not independent. Nevertheless, in the presence of nontransitory disturbances, one cannot show the relation between them analytically without assuming some distribution for FtF*t.34

shifts in the parameters

The notion that the authorities have in mind a desired level of reserves and that departures from it lead them to take corrective action is not accepted by all writers.35 One of the arguments is that objectives other than external balance may impinge on the level of reserves, and that the degree of conflict among objectives, as well as the compromise with regard to the reserve target, may vary from period to period. The argument is valid in that a simple hypothesis regarding desired reserves may not explain very much of the observed variation. For this reason developed countries are excluded from the present study, and considerable effort is devoted to isolating the flows used for financing in order to come as close as possible to the magnitude to which the authorities do react. However, the claim that the authorities may ignore the level of reserves clearly goes too far.

A second argument against the concept of a desired level of reserves is that the level may change without regard to underlying balance of payments factors. To cite an extreme example, the Indian authorities planned to use a portion of that country’s reserves, swollen by World War II and the Korean conflict, to finance capital expenditures budgeted for the first five-year plan, but the deficits never materialized. There were similar intentions for the second five-year plan, but in this instance the reserve loss in the first 18 months of the plan exceeded by several times the amount of decrease planned for the full five years. The authorities restored only part of the unintended decrease, apparently adjusting their “desires” to a lower level of average reserves. This type of event leads some observers to suppose that the level of reserves is not so important as abrupt changes in the level.36 The position taken in the present study is that this hypothesis is a secondary consideration, not the primary one. A low level of average reserves implies large costs in the form of price distortions and interruptions in production and consumption dependent on foreign goods, however imperfectly or belatedly these costs are reflected in policy.

If shifts in the equation for desired reserves are ignored in the import- exchange model, the parameter estimates will be biased and unstable; it will be difficult to know what is being estimated. But if the parameter shifts are allowed, an element of judgment is involved. The hypothesized concept of desired reserves may be “empirically favored” by excusing it from explaining large changes which are assessed to be extraneous.37 The error in doing so is reduced if one sets up criteria for exogenous shifts ex ante and is unswerving in applying them. Accordingly, special allowance has been made in this study for changes of two types. The first type is a hypothesized change in official preferences between the smoothing of imports and short-run development finance or consumption, because of a political event such as a war, a change of government, or the implementation of a new development plan. The most common example is the very large reserve decreases of many countries immediately after World War II. A wartime export boom had occurred, while imports, both of consumption goods and of replacement parts and new machines, were unavailable. To this pent-up demand were added, in some cases, new nationalistic desires to buy out foreign corporate owners, to industrialize rapidly, and to engage in formal development planning. When the loss of observations is not large, this type of change is handled simply by making the sample for estimation begin after reserve losses had forced the authorities to take corrective measures. When the break occurs later in the sample of available data, the parameters are allowed to shift at the time the change takes place.

The second type of shift allowed occurs when the authorities decide to change the basic nature of their system of trade and payments restrictions. It is convenient to think in terms of three prototypes: (1) a freely fluctuating rate, which requires minimal reserves and produces a very fast speed of adjustment, (2) thoroughgoing exchange control (quotas administered by way of licensing, with mandatory surrender of receipts) and/or frequent changes in cost-type restrictions (shifts of commodities among multiple rates, changes in mixing formulae for surrender of receipts, occasional devaluations of some of the rates, changes in tariffs, surcharges, taxes, and advance deposits), which require more reserves and result in a somewhat slower adjustment speed, and (3) indirect, macroeconomic measures (monetary and fiscal policies). It should be noted that existence of the administrative machinery required for quantitative and cost-type restrictions is not of itself significant, but only the actual use, for purposes of adjustment, of frequent changes in these policies has significance.

Detailed discussions of the shifts hypothesized for individual countries are given in the Statistical Annex (available from the author on request). Those resulting in substantial changes in the parameters are presented in the empirical section, below. A change of either type, of political goals or of the underlying external adjustment mechanism, is assumed to require simultaneous shifts in all the structural parameters except λ (the parameter relating to the authorities’ estimate of long-run exchange receipts). This is done out of respect for the logical relation between the level of desired reserves and the speed of adjustment, and is done at some cost in this study, since the number of observations in one or the other subsample is generally quite small (about half a dozen) relative to the three parameters to be estimated. When all the evidence is considered, the performance of the model is seen to be weakest with respect to desired reserves, especially the estimates of α1, in spite of the effort to discover the existence and dates of extraneous institutional changes and allow for them.

the complete model

Including the balance of payments identity, the model consists of these five equations, as discussed above:

Mt+ΔRtFt(1)
ΔRtFtM*t=(1γ)+γ[R*tRt1FtM*t](3)
M*t=F*t(p.656)
F*t=Ftλ(ΔFt)(6)
R*t=α0+α1F*t(7)

Solving equation (3) for ΔRt, substituting in equation (1), and then solving for Mt, one obtains

Mt=(1γ)M*t+γ[Ft(R*tRt1)].(4)

Obversely, the model could be solved with the change in reserves as the dependent variable, although imports are emphasized in this study.

Substitution from equations (6) and (7) for the unobservable variables in equation (4) yields

Mt=γα0+γRt1+(1γα1)Ft(1γγα1)(λ)ΔFt.(8)

Let the reduced form equation for estimation be written as

Mt=c0+c1Rt1+c2Ft+c3ΔFt+ut.(9)

It follows by inspection that the model is exactly identified. The structural parameters are given by

λ=c3c1c2γ=c1α1=1c2.38c1(10)

In equations (8) and (9), the intercept of the desired reserve function is also identified (α0 = – c0/c1). However, in general there are no stock data corresponding to the definitions of reserves used below. From the identity

Rt1Rb+Σb+1t1ΔRi

where b is some base year, it is seen that equation (8) can be rewritten with the unknown quantity included in the constant term:

Mt=[γRbγα0]+γRt1+(1γα1)Ft(1γγα1)(λ)ΔFt(11)

where

Rt1Σb+1t1ΔRi.

Equation (11) is the form used for estimation.39 The difference (Rbα0) is identified but not its individual terms.

When an exogenous event is hypothesized to cause a shift in the parameters of the adjustment function and desired-reserves function, equations (4) and (7) become

Mt=[1(γ+ΔγDt)]M*t+(γ+ΔγDt)[Ft(R*tRt1)](4)
R*t=(α0+Δα0Dt)+(α1+Δα1Dt)F*t(7)

where Dt is a dummy variable. Since Dt=Dt2, after substituting from equations (6) and (7') equation (4') becomes

Mt=γα0+γRt1+(1γα1)Ft(1γγα1)(λ)ΔFt+Dt[(Δα0γ+Δγα0+ΔγΔα0)+ΔγRt1(Δα1γ+Δγα1+ΔγΔα1)Ft+(Δγ+Δα1γ+Δγα1+ΔγΔα1)(λ)ΔFt)].(8)

By inspection, the structural parameters are seen to be overidentified by one, (The parameter λ does not change.) Therefore, equation (8') was estimated subject to the implicit constraint on the parameter estimates.40

III. Empirical Results

Tables 1 and 2 contain estimates of the import-exchange equation for eight countries. These are the preferred estimates—that is, in each case the distinction between exogenous and endogenous flows, in the form of the definitions employed for reserves and receipts, corresponds as closely as published data will allow to the available institutional knowledge about the flows used for financing and the flows beyond the influence of the government’s external balance policies. A detailed description of the respective definitions for individual countries is given in the Statistical Annex (available from the author on request), along with alternative estimates resulting from definitions based on more easily obtainable data or definitions more amenable to forecasting.

In selecting countries for application of the model, an effort was made to include examples of external balance policies both with much and with little reliance on administrative controls,41 and to achieve

Table 1.

Reduced Form Coefficients: Preferred Definitions of Receipts and Reserves1

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R2 = coefficient of determination; D-W = Durbin-Watson statistic; SEE = standard error of the estimate (in millions of U.S. dollars); M= mean of the dependent variable (value of imports, in millions of U.S. dollars); for the number of observations, see Table 2. The numbers in parentheses are standard errors. For the variables to which the coefficients apply, see Section II, the complete model.

The shift dummy equals 1 in the shorter subperiod (see Table 2).

Coefficients of dummy variables equal to 1, in 1957 for Burma and in 1959 for Colombia. See the discussion in the Statistical Annex (available from the author on request).

These are not true reduced form coefficients; see footnote 40 of the text. Moreover λ, which was estimated directly. is omitted here but w presented in Table 2.

Table 2.

Structural Coefficients: Preferred Definitions of Receipts and Reserves1

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The numbers in parentheses are large sample standard errors.

See Section III, desired reserves and the variability of disturbances.

some geographical dispersion. Countries appearing to present data problems were avoided, however, as were those affected by periods of military conflict. While petroleum exporters may provide an interesting application of the model, particularly of the extreme case in which imports may be used relatively little for adjustment, these countries do not account for a very large part of the trade of less developed countries and have certain atypical characteristics; therefore, petroleum exporters have been excluded and other countries have been used to illustrate the situation in which little reliance is placed on trade and exchange controls. Because of these criteria, no countries from the Middle East and Africa are included in this study.

long-run exchange receipts

In the model, F*t has a smoothing function, mechanically speaking, since it is a moving trend of current and expected future values of receipts.42 If the authorities expect that on balance the current change in F will continue in the same direction, smoothing requires that F* lead F (that is, change in anticipation of it), and λ < 0; if they expect the current change to be temporary, smoothing requires that F* lag F and λ > 0. There is no a priori argument as to the correct sign of the coefficient; that is an empirical question. The estimates in Table 2 are positive and therefore imply the expectation that absolute values of period-to-period change are large relative to the overall trend. One can state, however, that the estimate for Thailand lies just outside the reasonable range. Being greater than unity, it implies swings in F* greater than those in F; imports are implicitly being “smoothed” toward a norm that varies more than actual receipts, and the effort is pointless. The fault may lie in the specification, however. If, in the extreme, a country experienced a period of fluctuations with no trend, followed by a period of trend with no fluctuations, it would be unreasonable to assume λ to be stable over the sample comprised of the two subperiods. Five of the eight estimates of λ are greater than twice their standard errors, and a sixth is nearly twice.43

the speed of reserve adjustment

It was demonstrated theoretically that efficient response to external imbalance requires that λ fall between zero and unity. Values outside this range imply an excessive increase in reserves achieved at the expense of an unwanted cutback in imports, or a glut of imports financed out of already deficient reserves. The estimates in Table 2 conform to the theoretical limits, with the exception of Chile in the earlier sub- period (an estimate that is more than twice its standard error as well as of the wrong sign), and India in the earlier subperiod (an estimate very close to the theoretical range).

Only one of the nonperverse estimates is twice as great as its standard error. However, this outcome does not necessarily indicate that the model is weak; it could just as well be re-expressed in terms of the other part of the interval—that is, γ' = (1 – γ)—in which case six of the estimates would exceed their standard errors by three times or better. By the nature of the problem it is as reasonable to compare this coefficient with unity as to compare it with zero in judging its significance.

Some of the results are questionable, however, on the basis of a more casual criterion. The closer γ is to unity, the more reserve adjustment takes precedence over import smoothing; and the converse is true for γ close to zero. In the case of countries relying little on controls for external adjustment (El Salvador and Thailand), a small value of γ is to be expected. It is consistent with the lags inherent in the type of policy used and the volume of average reserves thus required. But the estimates of γ for Argentina and Colombia are unexpectedly low in view of the small average reserves of these countries. Strictly speaking, the theory does not support this kind of comparison between countries. One would need to allow systematically for differences in the type of exchange regime (differences in lags), in the variability of ex ante disturbances, and in the relative magnitudes of a and b (the costs of departures of reserves and imports from their desired levels). It may be that, in Argentina and Colombia, the import deviation required for balance was generally in the negative direction and the costs in terms of idle productive capacity and interruptions in large public investment projects were very large, so that the low estimates of γ are plausible.

desired reserves and the variability of disturbances

Estimates of α1 the slope of the desired reserve function, are the least stable of the three structural parameters. In no case in Table 2 is the estimate twice as large as its standard error.

The negative estimates of α1 have the wrong sign if the assumptions underlying the specification of the desired reserve function are correct. In equation (7), α1 is specified to be the coefficient of F*, which in turn is assumed to be a proxy for the standard deviation of the disturbances (FtF*t). It is possible to test this assumption in an ex post fashion. For each country, time series of F*t and FtF*t were computed, using the estimated value of A. Second, estimates of the standard deviation of FtF*t were computed from three-period moving samples.44 The time series of estimates of the standard deviation was used as the left-hand variable and values of F*t as the right-hand variable, in a linear regression. The coefficient of F*t in this regression and its t value are reported in the column headed “Proxy” in Table 2. The results support the assumption, since seven of the eight coefficients are positive, five significantly so, indicating that F*t tends to be directly correlated with the variability of the disturbances. The test is a limited one in that it demonstrates no more than internal consistency; the estimate of λ used in the test involves the prior assumption that the proxy is correct. But the test is not meaningless in the sense that it cannot contradict the assumption; the outcome for India provides an example.

In the case of India the test results indicate that as F*t increases, the variability of external imbalances decreases, while the corresponding estimates of α1 indicate that as F*t increases, the level of desired reserves decreases. This is quite consistent with the theory, while inconsistent with the proxy assumption. The ratios of these three coefficients to their standard errors are in the neighborhood of unity—not utterly negligible—and the estimates of α1 are of reasonable magnitude in absolute value. It may not be universally true that the variability of imbalance varies directly with the volume of receipts.

Excluding those estimates of α1 from the shorter subperiods of the two divided samples (which are based on extremely few observations) and those having the wrong sign, the remaining estimates tend to vary directly with the proxy coefficient; excluding Burma and Thailand, the simple correlation coefficient is 0.97. Therefore, the range of estimates of α1 over the countries studied may in part represent differences in the variability of countries’ ex ante imbalances.

The size of α1 is also influenced by the trade-off between average reserves and import fluctuations. Without a general theoretical framework one cannot set theoretical limits on the size of α1 nor systematically judge the size of the estimates. In the least, however, it does not seem plausible that α1 can be greater than unity in the long run, for this implies a desired stock of reserves larger than annual imports, while in fact less developed countries have generally held a smaller stock.

By this criterion the estimate for Burma lies substantially outside the reasonable range.

goodness-of-fit statistics

The performance of the model in the case of countries relying little on restrictions (El Salvador, Thailand and, marginally, China) is apparently superior to its performance for other countries, on average (see Table 1). There are two explanations for this result, but they are not mutually exclusive. First, the economic difference between the two groups of countries is not confined to exchange regimes. The countries relying little on controls are also small and have relatively large external sectors. It is conceivable that, for this reason, the attention of their authorities to imbalance in the external sector is relatively more systematic, even though their policies are less direct. The other countries may have ignored the external constraint to a greater degree, in the sense that the process of external adjustment is less regular and a model of their responses leaves more variation unexplained, despite the fact that they employ policies that are intrinsically more capable of effecting precise and prompt adjustment.

The second explanation is that in the case of countries avoiding restrictions, more flows may be endogenous (although not in the sense of being subject to administrative control). For example, in El Salvador coffee producers require a substantial amount of seasonal credit. In the early years of the sample they obtained this from commercial banks in New York. A series of subsequent external surpluses led to lower interest rates domestically, and producers borrowed from domestic commercial banks instead, resulting in a substantial capital outflow. At a later time El Salvador incurred several annual deficits in succession and the capital from New York flowed back in, cushioning the shortfall in total exchange receipts as domestic producers resorted to foreign credit lines again. While an attempt has been made to include such flows as part of the change in net reserves (in this case, by including net foreign assets of the commercial banks, through which the foreign credit was channeled), it is not certain that all such flows have been successfully identified, if only because in an economy without controls many flows tend to be “somewhat endogenous.” To the extent that the distinction achieved is imperfect and some endogenous components are included with net exogenous receipts (the former offsetting part of the true variation of the latter) the explanatory task of the model may be reduced. However, the structural coefficient estimates will for the same reason correspond less well to the behavior that the model purports to represent, and they will be biased (see Appendix I).

One of the Durbin-Watson statistics in Table 1 is very low, namely that for India. In this case if the observation for 1970 is omitted from the sample, the Durbin-Watson statistic increases to 1.9 because of that change alone; the R2 also improves and the coefficients increase slightly relative to their standard errors. The alternative results are given in the Statistical Annex, which is available from the author on request. An obvious hypothesis regarding that year is that India treated its first allocation of SDRs differently from other exchange receipts, contrary to assumption. However, the other countries received SDRs as well, except for China and Thailand, and these have more reasonable Durbin- Watson statistics.

parameter shifts

A specification in which the structural parameters of the model were allowed to shift, because of a hypothesized once-for-all change extraneous to the model, was estimated for five countries. In two of these cases the shift was judged significant (Chile and India) and in three cases it was not (Argentina, Burma, and China). The judgment was made on the basis of the F test; however, since in these cases the regression model is nonlinear, the F test does not apply, strictly speaking. It remains intuitively appealing relative to the other arbitrary criteria one might devise, but no claim of statistical significance is made.45

The shift in the structural parameters for Chile corresponds to a change from reliance on restrictions to the use of relatively frequent changes in the exchange rate, approximating free fluctuation. The estimated change in γ has the right sign on the basis of the supposition that the latter adjustment mechanism is faster, although the level of γ has the wrong sign in the former subperiod. On the same basis the change in α^1 has the wrong sign, since it implies greater additions to desired reserves with faster adjustment and is unreasonably large. Here the model is hampered by the extent to which the change in the policy used for external adjustment is itself attributable to persistent payments difficulties, so that the earlier period is characterized by recurring under- adjustment and the latter by compensation, a belated restoring of reserves. Only with much longer samples could one be sure the coefficient magnitudes typical of restrictions and rate fluctuations had been isolated, as opposed to a transition between the two.

This reservation also applies to Argentina (a country for which the shift was judged to be insignificant), although the change in regime was from restrictions to indirect macroeconomic policies. The alternative results for Argentina (in the Statistical Annex) show that while the increase in α1^ is positive, which is the expected sign, the magnitude of α1^ in the second subperiod is greater than unity. That is too large to be reasonable in the long run. It is likely that the implied increase in reserves is partly a temporary offset to the unintended decreases of the earlier period. Only in the case of China (for which the shift was also rejected) are the signs and the magnitudes of the changes in both structural parameters reasonable, although they are not large relative to their standard errors. In this case, noticeably, the change from a period of restrictions to one of indirect external adjustment policies came gradually. The change in regime was thus a continuation of a trend rather than an abrupt correction of a large and persistent imbalance.

In the case of India the change in the estimate of γ has the wrong sign, although the earlier estimate is based only on five observations. The change in α1^ is hard to interpret, since the level of that parameter is less than zero in both subperiods. If the negative signs are reasonable (which is conceivable according to the discussion above of the proxy test), the change means that the rate of decline in desired reserves in relation to the decline in the variability of disturbances is lessened. This also implies initial reserve caution rather than the long-run value of α1 that would be expected to accompany the decision to reduce the level of desired reserves.

For Burma, while the hypothesized shift makes no substantial difference in the overall power of the model, the corresponding estimates (reported in the Statistical Annex) are more easily interpreted than those resulting from specifying no shift (reported in Table 2). The institutional change in this case is related to a government decision to subsidize home consumption of exportables. As a consequence of that policy, foreign exchange receipts fell sharply during the latter part of the sample—by 60 per cent, comparing 1964 and 1970 levels. Therefore the positive estimate of α1 reported in Table 1 corresponds both to reserves rising with receipts during earlier years, and to reserves falling with receipts during later years. This is reasonable except for the size of α1^ (2.6). If a shift is allowed, the value of α1^ for the earlier subperiod is approximately unity and for the latter subperiod is 2.8. The former value is more reasonable as a measure of long-run behavior. The latter implies that, while reserves were declining in the latter subperiod, the desired stock was increased to a more conservative level relative to the variability of receipts. As was the case for Chile and Argentina, this estimate of α1 cannot be interpreted as long-run behavior; it seems, instead, to measure transitory behavior.

IV. Conclusion

This paper describes an effort to explain and to measure the behavioral relation between imports and foreign exchange receipts of less developed countries. That such a relationship exists has long been hypothesized casually in the literature, an important idea in light of the flaws inherent in the standard import function when applied to these countries. The paper presents the theoretical case for that relationship and indicates its place in relation to existing theory. A rational model of short-run response to external imbalance is developed, on which is based the specification of the import-exchange equation.

The reported empirical findings are broadly consistent with the hypothesized behavior. For the eight countries tested, estimates of the speed of adjustment of reserves (γ) fall in the theoretical range with two minor exceptions. The implicit assumption as to how the authorities discriminate between permanent and transitory payments disturbances results in estimates of λ which are also reasonable, with one exception. In the case of desired average reserves—the estimates of α1—the empirical results are less strong; two are unreasonably large and none is twice its standard error. It appears to be the case that the available time series are too short to provide stable estimates of the long-run behavior underlying this aspect of the model. One finds some episodes of large expenditure of reserves extending over several successive years, followed by compensatory reserve husbanding, and of very conservative reserve accumulation behavior coincident with the initiation of new policies. The model is based on long-run economic relationships and leaves some shorter-run variation unexplained.

The import-exchange equation is proposed as a substitute for the standard import function. It is attractive because it does not require measurement of the price effects of import and exchange restrictions and because it is free of the overstatement of the power of the standard model that may result from the probably strong influence of imports on output and income. It will be especially useful in a multicountry context, since it is capable of showing the initial and feedback effects on trade of changes in global foreign exchange flows.

APPENDICES

I. Consequences for Bias of Departures from the Basic Assumption

The model, with variables in deviation form, may be written

Mt=c1Rt1+c2Ft+c3Ft1+ut

where γ = c1 as in equation (9), but λ = c3/(c3 + c2c1) and α1 = (1 – c2c3)/c1 because Ft and Ft–1 have been substituted for ΔFt.

Case I

An exogenous capital flow (Kt) is incorrectly counted endogenous. Relative to the correct specification, K is implicitly subtracted from F in current and past periods. The negative value of K is added to ΔR (by convention, Kt >O implies a decrease in reserves). Therefore, the stock (S) to which K is the corresponding flow is subtracted from the stock of reserves appearing in the correct model. The expression in terms of flows for S is:

St=S0+Σi=1tΔSi=S0+Σi=1tKi

(where the prime on S0 denotes that the average value of S during the sample period has been subtracted from the value of the stock in the period preceding the first sample observation). It follows that the incorrect specification may be written as

Mt=b1(Rt1St1)+b2(FtKt)+b3(Ft1Kt1)+vt.(1)

The correctly specified model may be written in a parallel fashion as

Mt=c1(Rt1St1)+c2(FtKt)+c3(Ft1Kt1)+c1St1+c2Kt+c3Kt1+ut.

By writing St-1 in terms of flows, and rearranging, one may make the substitution

c1St1+c2Kt+c3Kt1=c2Kt+(c3+c1)Kt1+c1(Kt2+Kt3+)

Both specifications may be written in matrix notation by defining, with dimensions as indicated

δ=[c1,c2,c3];1×3;Y=[(Rt1St1),(FtKt),(Ft1Kt1)];T×3;Z=[c2Kt+(c3+c1)Kt1+c1(Kt2+Kt3+)];T×1.

The true model becomes

M=Yδ+Z+u

while the incorrectly specified model is

M=Yδ+v.(2)

The problem of counting an exogenous flow as endogenous is thereby reduced to the problem of omitting the variable Z. Where δ˜ denotes the ordinary least- squares estimate obtained by regressing M on Y alone, it follows that

δ˜=(YY)1YM=(YY)1Y[Yδ+Z+u].E{δ˜}=δ+[(YY)1YZ].(3)

Thus, the estimate δ˜ is equal to its true value (c1, c2, c3), plus the coefficients that would result from fitting the equation

[c2Kt+(c3+c1)Kt1+c1(Kt2+Kt3+)]=f[(Rt1St1),(FtKt),(Ft1Kt1)](4)

where (Rt–1St–1) may be written (ΔRt–1+Rt–2…–Kt–1Kt–2–…).

Given the assumption that K is uncorrelated with (FK) (see the text discussion, page 647), one concludes: (1) Each of the terms in the hypothetical regressand is uncorrelated with (FtKt) and (Ft–1Kt–1). Therefore b2 and b3 in equation (1) are unbiased estimates of c2 and c3; (2) The term c2Kt in the regressand is uncorrelated with the regressor (Rt–1St–1) because the latter appears with a lag; (3) The remaining terms in the regressand also occur with negative signs in (Rt–1St–1), which implies negative bias in the estimate of c1. At the same time there is a presumption of positive bias because of the relationship between ΔR and K, according to the obverse of the import-exchange equation (see the complete model in Section II of the paper). As a result, the direction of the bias in c1 is ambiguous.

Case II

An endogenous flow (Kt) is incorrectly counted exogenous. The incorrectly specified model may be written as

Mt=d1(Rt1+St1)+d2(Ft+Kt)+d3(Ft1+Kt1)+wt.(5)

Defining X = [(Rt–1St–1), (Ft + Kt), (Ft–1Kt–1)],

the true model may be written as

M=XδZ+u.

Where δ˜ is the vector of coefficient estimates that result from regressing M on X alone, it follows that

E{δ˜}=δ[(XX)1XZ].(6)

The bracketed product is the vector of ordinary least-squares estimates of the coefficients in

[c2Kt+(c3+c1)Kt1+c1(Kt2+Kt3+)]=f[(Rt1+St1),(Ft+Kt),(Ft1+Kt1)].(7)

One concludes: (1) By the assumption in the text that components of the change in reserves are positively intercorrelated, K is inversely correlated with AR, and therefore there is a presumption that K is inversely correlated with F by the obverse of the import-exchange equation. Necessarily K varies positively with itself. Therefore, the direction of bias with respect to the second two regressors—and therefore c2 and c3—is ambiguous. (2) Kt is uncorrelated with the first regressor, unless one assumes K is autocorrelated. (3) The remaining terms in the regressand are inversely correlated with the first regressor by assumption. (By convention, the sign of the endogenous component is reversed when it is counted a capital flow; R + S represents the stock of true reserves, less the stock to which –K is the corresponding flow.) Given the negative sign of [(X’X)–1X’Z], it follows that c1 is biased upward. Accordingly, estimates of λ and γ from a model incorrectly specified in this way will be biased upward; α1 will have negative bias.

II. The Bounds of the Allocation Function

In the text of this paper it was assumed that the authorities have two goals related to the allocation of current exchange receipts.46 First, they wish to restore reserves to their desired level, expressed as ΔRt=R*tRt1. Secondly, they wish to even out fluctuations in imports, expressed as Mt=M*t.47 At the same time, the balance of payments identity requires that the sum of imports and the change in reserves must be equal to receipts, so that the two goals will generally be in conflict and the actual outcome will be a compromise. In addition, it was assumed that the authorities choose an efficient allocation, efficiency having been defined to mean a situation in which it is not possible, by modifying the allocation, to achieve both goals more closely. (An efficient allocation is not unique.)

The limits can be described geometrically in terms of certain ratios,48 constructed as follows: The quantity (FtM*t) is defined as the ex ante excess or shortfall of receipts, since it measures the difference between current receipts and the amount of foreign exchange required to finance desired imports. The change in reserves (ΔRt) is defined to be the ex post excess or shortfall in receipts, that part of an ex ante imbalance which is not “adjusted” by a change in imports. In Chart 1, below, the ratio of the desired change in reserves to the ex ante imbalance is measured along the horizontal axis; the ratio of the ex post to the ex ante imbalance is measured along the vertical axis. In these two ratios, all values except ΔRt are given. In effect the authorities are presented with a point on the horizontal axis, and their response determines the vertical coordinate.

Chart 1.
Chart 1.

Ratios of Desired and Actual Changes in Reserves to the Excess or Shortfall in Foreign Exchange Receipts

Citation: IMF Staff Papers 1974, 003; 10.5089/9781451969344.024.A004

Consider the line aa', parallel to the horizontal axis and one unit above it. Points on aa' must satisfy the equation ΔRt/(FtM*t)=1, which by (1) implies that Mt=M*t. Thus, if the ex ante imbalance is fully absorbed by a change in reserves, the flow of imports equals its desired value; points on aa’ correspond to perfect smoothing of imports. (Points on the horizontal axis itself satisfy ΔRt/(FtM*t)=0, implying that ΔRt= 0, and therefore that Mt = Ft; at such points the current imbalance is fully adjusted by a change in imports and there is no smoothing). Secondly, consider the 45° line (bb'). Points on this line satisfy the equation ΔRt=(R*tRt1), which means that reserves are fully restored to their desired level in the current period (the second goal).

It is a simple matter to show that, for any given point on the horizontal axis, the compromise value of ΔRt chosen by the authorities will be such that the corresponding point is likely to lie in the closed region bounded by adb and b'da' (the shaded region in Chart 1). In the case of an ex ante excess—(FtM*t)>0—the demonstration is as follows: (1) Using inequalities in place of the equalities of the preceding paragraph, it follows that for any point lying above aa' actual imports are less than desired imports.49 (2) Similarly, for any point lying above bb', actual reserves will be greater than desired reserves. (3) Therefore, for any point lying above the broken line adb', the authorities could spend some of the excess reserves to offset the negative deviation in imports, with the result that reserves are brought closer to their desired level and simultaneously imports are made more smooth. (4) For obverse reasons the same result (both goals may be achieved more fully) holds for any point below the broken line bda'. (5) However, in the closed region bounded by aa' and bb', the two goals are in conflict. Reserves can be brought closer to their desired level only at the expense of greater fluctuation in imports; imports can be made more smooth only by way of a greater divergence between actual and desired reserves.

For an ex ante shortfall of receipts—(FtM*t)<0—the inequalities of the preceding paragraph are reversed because of multiplication of both sides by the negative (FtM*t). This leads to the opposite results: For points above aa', imports are now too large; and for points below aa', they are too small; reserves are deficient above and to the left of bb' and too large below and to the right of it. The trade-off between the two goals still occurs in the shaded region shown in Chart 1, however; in the open region bounded by the sides of the obtuse angles, it is always possible to achieve both objectives more closely.

As a first approximation, the short-run behavior of the authorities may be represented by a linear curve in the efficient region, such as cc' in Chart 1. Using the result that the adjustment function will pass through point d, it follows that the intercept of cc' with the vertical axis is equal to unity minus its slope. Writing y for the slope of cc', the equation for an efficient linear adjustment function will have the form:

ΔRtFtM*t=(1γ)+γ[R*tRt1FtM*t],0<γ<1.

This is equation (3) of the text.

*

Mr. Hemphill, an economist in the Current Studies Division of the Research Department, is a graduate of Monmouth College (Illinois) and Princeton University.

In addition to the comments of staff colleagues, the author is very grateful for the suggestions of William H. Branson and Sherman Robinson of Princeton University. He emphasizes that he alone is responsible for the present text.

1

The most important example involves countries that rely on multiple exchange rate systems and collect “direct dollar” data for import values, as well as national currency data. The former are prepared by aggregating directly the dollar values given on individual shipping documents; the latter result from converting each shipment to national currency at the rate designated for that commodity by the prescribed rate structure. The quotient of the two series provides a perfectly weighted aggregate exchange rate for imports. The product of this conversion factor and the unit value index thus reflects the relative price changes that occur as commodities are shifted among rates over time, as well as changes in supplier costs. For countries utilizing multiple rates, these commodity shifts typically constitute a substantial portion of the price effects of all trade and exchange restrictions.

2

For estimates of the standard import function with data from less developed countries, see Mr. Khan’s article, pp. 678–93, in this issue of Staff Papers.

3

See J. E. Meade, The Balance of Payments (London, 1951), Chapter 1.

4

See J.J. Polak, An International Economic System (London, 1954), pp. 43–44; Jacques J. Polak and Rudolf R. Rhomberg, “Economic Instability in an International Setting,” American Economic Association, Papers and Proceedings of the Seventy-Fourth Annual Meeting (American Economic Review, Vol. 52, May 1962), pp. 110–18; Rudolf R. Rhomberg and Lorette Boissonneault, “Effects of Income and Price Changes on the U. S. Balance of Payments,” Staff Papers, Vol. 11 (March 1964), pp. 59–124, especially p. 62; and Rudolf R. Rhomberg, “Transmission of Business Fluctuations from Developed to Developing countries,” Staff Papers, Vol. 15 (March 1968), pp. 1–29, especially pp. 16–17.

5

See W. Whitney Hicks, “Estimating the Foreign Exchange Costs of Untied Aid,” Southern Economic Journal, Vol. 30 (October 1963), pp. 168–74. Hicks” study was used by Walter S. Salant, and others, The United States Balance of Payments in 1968, The Brookings Institution (Washington, 1963), pp. 25–27, and a more extensive, unpublished version developed by Alan M. Strout, reported by Carmella Ullman, in “Direct and Indirect Effects of Untied Aid on U. S. Commercial Exports,” U.S. Department of State, Agency for International Development, Office of Program and Policy Coordination (mimeographed, Washington, September 7, 1967) is discussed by Jagdish N. Bhagwati, “The Tying of Aid,” United Nations Conference on Trade and Developmet, Document TD/7/Supplement 4 (mimeographed, UNCTAD, November 1, 1967). Hicks attributes the form of the model to Richard Cooper and Karl Shell. A further elaboration of the respendings approach is developed by Rolf Piekarz and Lois Ernstoff Steckler, “Induced Changes in Trade and Payments,” Review of Economics and Statistics, Vol. 49 (November 1967), pp. 517–26.

6

See Ronald I. McKinnon, “Foreign Exchange Constraints in Economic Development and Efficient Aid Allocation,” Economic Journal, Vol. 74 (June 1964), pp. 388–409; and Hollis B. Chenery and Alan M. Strout, “Foreign Assistance and Economic Development,” American Economic Review, Vol. 56 (September 1966), pp. 679–733.

7

Some writers prefer to use “adjustment” in a narrower sense, excluding both direct exchange control and cost-type policies such as tariffs. That distinction is not important for this study, however; here adjustment is used to refer equally to restrictions and to changes in relative prices such as are achieved by exchange rate changes.

8

For examples, see Carlos F. Diaz Alejandro, Exchange-Rate Devaluation in a Semi-Industrialized Country: The Experience of Argentina, 1955–1961 (Cambridge, Massachusetts, 1965), pp. 53–54; Edward E. Learner and Robert M. Stern, Quantitative International Economics (Boston, 1970), pp. 13 and 15–16; and Piekarz and Steckler, op cit. The logical error is smaller the more external balance policies are carried out solely through changes in restrictions (if measurable relative-price changes exclude entirely the effects of changes in restrictions).

9

In part this treatment is taken from Rhomberg (cited in footnote 4), pp. 14–15 and 18.

10

Two tests of the exogeneity of specific flows were considered, although there is a recognized methodological inconsistency in using data both to define a hypothesis and to test it. Christopher A. Sims develops such a test in “Money, Income and Causality,” American Economic Review, Vol. 62 (September 1972), pp. 540–52, based on estimated correlation coefficients between present and future values of the variables in a model. However, Sims’ procedure requires, in the present context, that future values of F have no effect on current balance of payments policies, while in fact the authorities may well have specific information on which to base their estimates of future F (aid flows, for example, in which case commitments significantly precede the eventual flow of goods), and may adjust current imports accordingly. Sims’ test was therefore ruled out.

The second test considered is that proposed by Milton Friedman and David Meiselman, in “The Relative Stability of Monetary Velocity and the Investment Multiplier in the United States, 1897–1958,” in the Commission on Money and Credit, Stabilization Policies (Englewood Cliffs, New Jersey, 1964), pp. 105–268, especially pp. 180–85 and 246–58. The Friedman-Meiselman test is particularly attractive because of the formal theoretical equivalence between the national income context for which it was developed and the foreign exchange model of the present paper (see footnote 13). However, by examining the underlying statistical properties of the flows in question relative to the outcome of the test, it can be shown that the latter may well be dominated by correlation among flows which is irrelevant to the behavior that the model represents, and the test may therefore fail. See the author’s “Note on the Friedman-Meiselman Test of Autonomous Expenditure,” available on request.

11

International Monetary Fund, Balance of Payments Yearbook, Washington, various issues. Hereinafter referred to as Balance of Payments Yearbook.

12

The sum of these assets is equal to “international reserves” as defined in International Monetary Fund, International Financial Statistics, Washington, various issues. Hereinafter referred to as International Financial Statistics.

13

The analogy is appealing because of the similar roles of reserves and inventories. There is a second similarity in that the more types of national expenditure there are that are counted as exogenous, the more C approaches zero, so that Y = I, such as the import exchange case in which reserves cannot change and M = F, a tautology. Thirdly, just as the consumption and savings functions are not independent because of the national income identity, the import and change- in-reserves functions are linearly dependent by way of the balance of payments identity. Finally, while there are no domestic multiplier effects in the case of the import-exchange equation, the international multiplier effects are quite analogous. It is well known that the distinction between “autonomous” and “accommodating” international flows is difficult to achieve empirically. It is perhaps less well known that the same difficulty is inherent in the simple national income model.

14

The author is indebted to William H. Branson for this point. Note that in the limiting case in which all flows other than imports have been counted as exogenous, the flow of net foreign exchange receipts becomes simply the amount of foreign exchange spent on imports. There is zero variation in imports that this variable does not explain; the relationship is a tautology. Short of that point, however, addition of endogenous flows to exogenous receipts will not in general increase the computed R2. A proof of this is given in the author’s “Note on the Friedman-Meiselman Test” (cited in footnote 10).

15

In reviewing an early version of Rhomberg’s “Transmission of Business Fluctuations” (cited in footnote 4), F.J.M. Meyer-Zu-Schlochtern seems to be making this point in his “Comment” in Martin Bronfenbrenner, editor, Is the Business Cycle Obsolete? (New York, 1969), pp. 279–83.

16

For examples, see Peter Barton Clark. “Optimum International Reserves and the Speed of Adjustment,” Journal of Political Economy, Vol. 78 (March-April 1970), pp. 356–76, and Michael G. Kelly, “The Demand for International Reserves,” American Economic Review, Vol. 60 (September 1970), pp. 655–67. While it is criticized below, Clark’s assumption can also be defended on the grounds that it requires less information on the part of the authorities than the proposed treatment.

17

M* and R* are specified below in this section. For the present it may simply be noted that in a static model M* would be equal to average M; smoothing of imports means constant imports. R* would be a fixed number, proportional to average receipts and invariant with respect to current receipts. However, as will be discussed, the assumptions of a static model seem unacceptable in the present context.

18

This is an application of Thiel’s decision theory model. See Henri Theil, in association with P. J. M. Van Den Bogaard and assisted by A. P. Barten, J. C. G. Boot, C. Van De Panne, Optimal Decision Rules for Government and Industry, Vol. 1 of Studies in Mathematical and Managerial Economics (Amsterdam, 1964), Section 2.1.

19

It can be shown that a cost function of the same form as equation (5), of any order except n = 1, results in the linear allocation function (4), with γ/(1–γ) = (b/a)exp[1/(n–1)]. An exponential cost function also results in the linear allocation function. Therefore, the assumption that costs are quadratic is not a necessary condition for linearity.

20
Let T (for tranche) represent the country’s outstanding drawings (with sign reversed—the cost function is in terms of net assets), or any other particular net reserve asset, and let O represent the sum of all other net reserve assets. The cost function becomes
Ct=a(MtM*t)2+b(0t0*t)2+c(TtT*t)2.
Minimizing costs subject to the balance of payments identity, which has become Mt + Δ0t + ΔTtFt yields
Mt=(1γ)M*t+γ(Ft)γ[(0t0*t)+(TtT*t)]

where γ' = bc/(ab + bc + ac). The coefficient of (0t0*t) is the same as that of (TtT*t).

21

It is useful to distinguish between the cost of reserve fluctuations and the cost of the average stock of reserves. The latter is given by the difference between the rate of return on real capital and the average yield earned on net reserves.

22

For a description of the conditions for obtaining a Fund stand-by agreement, for example, see Emil G. Spitzer, “Stand-By Arrangements: Purposes and Form,” and “Factors in Stabilization Programs,” Chapters 20 and 21 in The International Monetary Fund, 1945–1965: Twenty Years of International Monetary Cooperation, Vol. 2, ed. by J. Keith Horsefield, International Monetary Fund (Washington, 1969).

23

The political costs are larger if only because, under current arrangements, payments surpluses require less consent from trading partners than do deficits. As for the financial costs, the interest rates on short-term loans obtained from foreign commercial banks by central banks of countries included in this paper are known to have been as high as 30–35 per cent after adjustment for the minimum deposit required by the lender. If the prices of internationally traded goods rise by something like 5 per cent a year, then the real cost of reserve shortfalls is 25–30 per cent toward the upper end of the relevant range. It seems unlikely that the real rate of return, the maximum cost of reserve excesses, is greater than 15 per cent for aggregate investment at the margin.

24

Suppose imports are primarily producer goods—machinery, maintenance items, and semifinished components. Producers will respond to an increase (decrease) in the supply of foreign inputs by some combination of two policies. They can leave their relatively fixed domestic factors of production unchanged, over- utilizing (underutilizing) them to the extent permitted by the increase (decrease) in available imported inputs, thus incurring the costs associated with a level of output different from optimal capacity utilization. Alternatively, they can increase (decrease) their stocks of fixed domestic factors to bring them into line with the supply of imports, keeping production levels optimal but incurring the costs of acquiring (depreciating) capital and other relatively fixed factors, thus adding to fixed costs. The longer the expected duration of the current change in the level of imports, the more adjustment will take the form of a change in fixed factors; the shorter this duration, the more will firms change output to nonoptimal levels, leaving the stock of fixed factors constant.

25

In any system of production or consumption in which random shortages may occur, there will be a tendency to stockpile any item in uncertain supply. In this way producers themselves smooth fluctuations, at the cost of foregone interest, warehousing, and deterioration.

26

This follows from the assumption that the foreign-capital/output ratio is greater than the foreign-input/output ratio.

27
For example, consider the vertical sum of a hyperbola and a straight line. While not fully general, this curve has the desired property that the costs of negative discrepancies increase faster than those of positive discrepancies. The cost function becomes
Ct=a1(MtM*t)+1b1+c1(MtM*t)+a2(RtR*t)+1b2+c2(RtR*t).
Minimizing the costs with respect to Mt and Rt, subject to the balance of payments constraint, yields
Mt=d0+M*t±{d1+d2/[d3+FtMtR*t+Rt1]2}1/2,
where the di are functions of the ai bi, and ci. By inspection, it is not possible to solve for Mt. Apart from this problem, ideally one would like to have a curve which is symmetric or asymmetric depending on the magnitudes taken on by the parameters in empirical estimates.
28

See Clark and Kelly (cited in footnote 16).

29

The “desired” or “long-run” values are not consistent from a balance of payments point of view. Not only does M*t=F*t, but it will be seen that, in general, ΔR*t0,, so that M*t+ΔR*tF*t, This is done because it seems quite useful to define M* as sustainable, long-run imports, without regard to the necessity of using current receipts to finance any increases in the desired stock of reserves. Such increases are implicitly treated in the model in the same way as the response to below-normal, actual reserves is treated, since the consequence for current imports of either deficiency is the same.

30

Changes in M* are not without cost in reality, even in the case in which those changes amount to a steady, positive trend. However, this element of adjustment cost is ignored because it cannot be known, even probabilistically. The cost is smaller when the flow of receipts is more regular—because the total adjustment cost is smaller—and when the authorities’ estimate of long-run receipts is more accurate, but it is never zero, except under static assumptions.

31

This is the “extrapolative expectations” construct. See, for example, Stephen J. Turnovsky, “Empirical Evidence on the Formation of Price Expectations,” Journal of the American Statistical Association, Vol. 65 (December 1970), pp. 1441–54.

32

The theoretical and empirical literature on these points has been surveyed by John Williamson, “Surveys in Applied Economics: International Liquidity,” Economic Journal, Vol. 83 (September 1973), pp. 685–746, especially pp. 688–97.

33

See Clark and Kelly (cited in footnote 16).

34

For example, if one is willing to assume that (FtF*t) is distributed randomly and normally with zero mean and finite variance, the Clark-Kelly result can be shown to hold.

35

See, for example, Fritz Machlup, “The Need for Monetary Reserves,” Banca Nazionale del Lavoro, No. 78 (September 1966), pp. 175–222, especially p. 199.

36

Ibid., passim. Note that the rate of change of actual reserves does not enter the desired reserve function as specified above, but it is likely to influence the authorities’ estimate of long-run receipts (F*) and thus affect adjustment.

37

A full discussion of this problem, together with an argument for the course followed here, is given by Franklin M. Fisher in “Selective Estimation and the Dilemma of Objectivity,” Part I of his A Priori Information and Time Series Analysis: Essays in Economic Theory and Measurement (Amsterdam, 1962).

38

Estimates of the nonlinear structural coefficients derived algebraically from estimates of the reduced form coefficients are asymptotically unbiased and efficient, but their small sample properties are unknown. Their standard errors may be approximated by the formula, var(s)[∂s/∂c]”.[Σ].[∂s/∂c], where s is the vector of structural coefficients, c is the vector of reduced form coefficients, and ∑ is the variance-covariance matrix of the reduced form coefficients.

Alternatively, estimates may be produced directly by nonlinear methods. It can be proved that the asymptotic distributions of the estimates of the two methods are identical. (The author is indebted to Phoebus J. Dhrymes, Columbia University, for assistance with this proof, which is available from the author on request.)

Since the standard errors of the structural coefficients to be reported in Section III are large sample standard errors, the t test of statistical significance does not apply, strictly speaking.

39
In the empirical work the base year was arbitrarily chosen to be 1968, so that t – 1 may come before b. More precisely, therefore,
Rt1=Σ0t1ΔRiΣ0bΔRi
where the sample runs from year 1 through year t.
40
The algorithm used (provided by Data Resources, Inc.) treats an overdetermined equation as a nonlinear equation, and it approximates the structural parameters directly by an iterative procedure. The algorithm failed to converge in a trial attempt to estimate equation (8) as specified but was successful when the following simplifying substitutions were used:
c0γα0;Δc0(Δα0γ+Δγα0+ΔγΔα0);c4γα1;Δc4Δα1γ+Δγα1+ΔγΔα1.
It follows that the algorithm approximates λ and γ directly, but estimates of α1, Δα1, and Δα0 must be obtained by solving for them in terms of these simplifying equations. (In the tables below these left-hand terms are called “reduced form coefficients,” which goes somewhat beyond the usual definition.) It follows that
α1=c4γ;Δα1=Δc4γΔγc4γ(γ+Δγ)(10)
While α0 continues to be unidentified after substituting Rb+Rt1 forRt1, Δα0is identified. It is given by
Δα0=Δγc0Δc0γγ(γ+Δγ)
41

This writer groups El Salvador and Thailand in the category of countries placing little reliance on restrictions; China is in an intermediate category, having ended its use of controls in the early 1960s; the remaining countries have relied on restrictions to a relatively large extent. Details are given in the Statistical Annex (available from the author on request).

42

There is a distinction between the “permanent income” and “expectations formation” interpretations of an equation such as (6), above. In the latter case the economic agent wants to forecast the value of, say, Xt+1 during period t. If the agent lacks specific information on autonomous factors affecting X in period t + 1, he may resort to basing his prediction on past values. While, as a result, the time series of predicted values of X may be smoothed out relative to that of observed X, this is merely incidental. The permanent income interpretation is the one intended here, however. The authorities do not want to predict the next period’s receipts per se, but average or long-run receipts.

43

Throughout Section III reference is made to the ratio of an estimate to its standard error, not to its t value. Since the structural coefficient estimates are nonlinear, the t test is not applicable, strictly speaking. See footnote 38.

44
Let St represent the standard deviation, and let Dt=FtF*t.Then
St=[[(Dt+1D¯)2+(DtD¯)2+(Dt1D¯)2]/2]1/2
where D¯=(Dt+1+Dt+Dt1)/3. Consequently, the series for St has two fewer figures than the sample used for estimation of the model.
45

In fact, the F test is not well defined in the present case either, since the equation including shifts has four more variables but only three more parameters than the equation with no shifts. The reported value of F was computed in the straightforward way except for using the number of parameters (4 + 3, including the constant term) in place of the number of independent variables (4 + 4, including the constant term) in the standard formula.

In the three cases in which the shift hypothesis was “arbitrarily” rejected, the F value would not have been statistically significant at the 50 per cent level if that test were applicable; in the two cases in which it was accepted, the value of F would have been significant at the 97.5 per cent level—that is, the differences in the change in R¯2 between the accepted and rejected cases is fortuitously quite large and the lack of a systematic test is therefore less troubling. For each of these five countries, the alternative specification is given in the Statistical Annex (available from the author on request).

46

See Section II, the allocation function.

47

M*tandR*t are defined in Section II, under nontransitory disturbances and desired net reserves.

48

These ratios allow the relevant interrelationships to be shown in two dimensions instead of three.

49
That is, for any point lying above aa’ it follows that
ΔRt/(FtM*t)>1.
Therefore ΔRt>FtM*t;

therefore FtMt>FtM*t,by(1);

therefore Mt<M*t;

since FtM*t>0. The assertions to be made subsequently may be verified in a similar manner.

IMF Staff papers: Volume 21 No. 3
Author: International Monetary Fund. Research Dept.
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    Ratios of Desired and Actual Changes in Reserves to the Excess or Shortfall in Foreign Exchange Receipts