Monetary Variables and the Balance of Payments

Victor E. Argy

doi:10.5089/9781451947298.024.A005

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Monetary Variables and the Balance of Payments

Author: Mr. Victor E. Argy¹

¹ 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Publication Date:: 01 Jan 1969

eISBN:: 9781451947298

Language:: English

Keywords:: SP; investment; income equation; deficit in the balance of payments; balance of payments to external shocks; models work; improvement in the balance of payments; Monetary base; Personal income; Central bank credit; Domestic credit; Exports

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IN THIS PAPER a very simple macromodel will be constructed as a basis for examining the role of monetary variables in the balance of payments. The model is basically Keynesian. It is expressed in real terms, the behavioral relations are simple and lagless, the interest rate is the only link between monetary and real variables, and monetary variables are treated as autonomous (under the control of the authorities). All functional relations will be assumed to be linear for simplicity.

Abstract

In the first part we discuss the model on the assumption that money is the monetary instrument; in the second part we assume that the monetary instrument is total domestic credit; in the third part we compare the results for the two alternative assumptions; in the fourth part we take central bank credit as the monetary instrument; in the fifth part we manipulate the model on the assumption that the interest rate is held constant by the authorities; in the sixth part all four alternative models are briefly brought together and compared.

I. Money as the Monetary Instrument

Symbols used

Equations:

\begin{matrix} (1) & Y = C + I + G + T \end{matrix}

\begin{matrix} (2) & C = cY \end{matrix}

\begin{matrix} (3) & I = A - bR \end{matrix}

\begin{matrix} (4) & T = F - dY \end{matrix}

\begin{matrix} (5) & K = V + gR \end{matrix}

\begin{matrix} (6) & R = eY - fM \end{matrix}

\begin{matrix} (7) & B = T + K \end{matrix}

Gross national product is represented in equation (1) as made up of consumption, investment, government expenditure, and exports less imports. Equation (2) shows consumption as a function of income. Equation (3) shows investment as a function of the rate of interest and an autonomous component. Equation (4) represents exports less imports as a function of income and an autonomous component. Exports will be treated as entirely autonomous,¹ so that the coefficient d is the marginal propensity to import. In Equation (5), K, the capital balance, is assumed to be determined by an autonomous component and the rate of interest. Assuming that long-term flows are unresponsive to the rate of interest, the autonomous component would represent the net long-term balance as well as the autonomous element in short-term flows. Equation (6) shows the rate of interest as determined by the level of income and the money supply. No distinction is made between the short and the long rate, so the implicit assumption is that all interest rates move together. Equation (7) is an identity, showing the net overseas balance as the sum of the excess of exports over imports and the net capital inflow.

Equations (1) to (7) may be combined to yield two basic equations:

\begin{matrix} (8) & Δ Y = \frac{1}{1 - c + d + be} \end{matrix} Δ (A + G + F) + \frac{bf}{1 - c + d + be} Δ M

\begin{matrix} (9) & Δ B = & Δ (F + V) - \frac{d - ge}{1 - c + d + be} Δ (A + G + F) \\ - \frac{bf (d - ge) + gf (1 - c + d + be)}{1 - c + d + be} Δ M \end{matrix}

Equation (8) explains the change in income in terms of the change in autonomous expenditures and the change in the money supply. Equation (9) explains the change in the net overseas balance by the change in the autonomous elements in the balance of payments, the change in autonomous expenditures,² and the change in the money supply.

As a basis for determining the order of magnitude of the coefficients in the two equations, an attempt was made to obtain crude estimates for the behavioral coefficients in the model. The estimates were arrived at by using the results of empirical work. The method and sources of the derivations are explained in Appendix I. Table 1 shows the combination of values of coefficients used for each of six solutions a to f. The six solutions are shown in Table 2. Equation (8a), for example, gives the coefficients for autonomous expenditures and the money supply computed on the basis of the values of the underlying coefficients shown in row (a) of Table 1. Equation (8b) is the solution based on row (b) in Table 1, and so on.

Table 1.

Assumed Values of Coefficients

^¹Elasticity coefficients (see Appendix I).

^{^*}Indicates change in row.

Table 2.

Equations Based on Assumed Coefficients

Some comments on the solutions shown in Table 2 are in order. The effects of lowering the value of g from 100 to 20 may be seen by comparing solution (b) with solution (a). The changes are only slight, suggesting that raising the response of short-term flows to interest rates will have fairly negligible effects on the balance of payments. The effect of raising b (increasing the response of investment to the interest rate) may be seen by comparing c with a. As expected, monetary variables become much more significant, with the monetary coefficient rising quite substantially. Solution (d), compared with (b), gives the effects of lowering the marginal propensity to import: the effect on income of monetary and real changes is increased; at the same time the effect of real or monetary changes on the balance of payments is reduced. Solution (e), compared with (c), shows the effect of reducing the response of the interest rate to a change in income: both monetary and real changes will now have stronger effects on income and the balance of payments. Finally, solution (/), compared with (d), shows the effects of reducing the response of interest rates to monetary changes. As expected in this case, monetary variables now become less powerful.

According to these results an increase of one unit in autonomous expenditures, given the money supply, will raise income by only 1 to 1.5 units. This multiplier is small partly because of the leakage into imports and partly because of the financial constraint.³ An increase of one unit in the money supply, given autonomous expenditures, would raise the level of income by 0.15 to 0.45 unit, depending on the values assigned to the coefficients.

A unit increase in autonomous expenditures (A or G) will affect the balance of payments adversely by 0.3 to 0.45 unit. An increase in exports (F) may be illustrated by reference to solution (9a). If the money supply and expenditure effects are offset, the balance of payments would improve by one unit. If the expenditure effect is not offset, the net improvement in the balance of payments will be approximately 0.56. If, in addition, the money supply is allowed to increase and is maintained (unrealistically) at the new level, the net improvement in the balance of payments is reduced further, to 0.43 unit. An increase of one unit in the money supply will affect the balance of payments adversely by 0.03 to 0.23 unit. Part of this adverse effect is due to the increase in imports and part is due to the reduction in capital flows owing to the drop in the interest rate.

These equations also illustrate how two targets may be satisfied by manipulating two policy instruments. In this simple model the two targets would be a real income level and a balance of payments position. The two instruments would be government expenditures and the money supply. If A, F, and V are given, and Y and B are predetermined (at their target levels), the two equations could be solved for G and M (the required levels of the policy instruments). Suppose, for example, that export receipts fell, and suppose that both real income and the balance of payments were to be maintained at their original levels. Government expenditures could rise to offset the drop in export receipts and in this way real income would be maintained, but the balance of payments would still be off target by the fall in export receipts. The two targets could be achieved simultaneously if government expenditures rose sufficiently and the money supply contracted sufficiently so that real income was maintained and if the rise in the rate of interest restored the original balance of payments position.⁴ Of course, if the required rise in the rate of interest was “unacceptable,” the two targets could not be attained under these conditions. In effect, we would be imposing constraints on the monetary instrument.

The two most serious limitations of the model used are the following. First, only the simplest functions were used. Clearly we would expect the consumption, investment, and interest rate functions to be considerably more complicated. Second, the model assumes that no lags operate. The main effect of allowing for lags would be to reduce somewhat the size of the coefficients given in Table 2. In other words, within the relevant period the effect of changes in monetary or real variables would be less than indicated by the coefficients in the table.⁵

II. Domestic Credit as the Monetary Instrument

It is interesting to examine what modifications are required to our results when the monetary variable is total domestic credit. Several new equations now need to be introduced:

\begin{matrix} (10) & Δ M = Δ CP + Δ DB \end{matrix}

\begin{matrix} (10 a) & Δ DB + Δ LB = Δ CB + Δ RB + Δ AB \end{matrix}

\begin{matrix} (10 b) & Δ M = Δ CP + Δ CB + Δ AB + (Δ RB - Δ LB) \end{matrix}

\begin{matrix} (10 c) & Δ M = Δ H + Δ AB + (Δ RB - Δ LB) \end{matrix}

\begin{matrix} (10 d) & Δ H = Δ D_{1} + B \end{matrix}

\begin{matrix} (10 e) & Δ M = [Δ AB + Δ D_{1}] + [Δ RB - Δ LB + B] \end{matrix}

{\begin{matrix} (10 f) & Δ M = Δ D + B \end{matrix}}^{6}

Equation (10) shows that the change in the money supply is made up of the change in cash held by the nonbank public and the change in bank deposits. Equation (10a) sets out the bank’s consolidated balance sheet in first difference form with total liabilities (domestic and foreign) shown on the left and total assets (including cash, domestic and foreign) shown on the right. Equation (10b) is obtained by substituting (10a) (for ΔDB) in (10). Equation (10c) simply substitutes the change in base money (ΔH) for the sum of the change in cash held by the nonbank public and the banks. Equation (10d) sets out the two sources of changes in base money: the change in the domestic assets of the central bank and the change in net overseas assets of the central bank. Equation (10e) shows that the change in the money supply is equal to the change in total domestic credit plus the change in net foreign assets of the monetary system. In this paper we will assume that the banks do not alter their net foreign assets, so that ΔRB — ΔLB = 0; this item is then dropped from equation (10f).

We now assume that the change in domestic credit is fixed by the monetary authorities and that the money supply is allowed to change by the amount of the overseas imbalance. Suppose, for example, that base money and deposits of the banking system fall by one unit as a result of an external deficit; the banking system under these conditions would not be in equilibrium, as their cash/deposit ratio would now have fallen. The assumption of an equivalent change in money and net overseas assets can be retained in one of two ways: First, we could suppose that the authorities adjust the legal reserve ratio in such a way that multiple deposit contraction is avoided. Second, we could suppose that government securities liquidated by the banks are absorbed by the monetary authorities. In this instance a fall in bank credit (— ΔAB) is exactly offset by an increase in the claims held by the central bank (+ ΔD₁). In other words, the authorities provide just enough base money to accommodate the level of deposits immediately following the external imbalance.

Before manipulating this model we must note a distinction to be made now between “short-term” and “long-term” equilibrium. Short-term equilibrium is achieved when the behavioral relations in the model are satisfied; however, this need not entail equilibrium in the balance of payments in the sense that the change in net overseas assets is zero. Long-term equilibrium obtains when equilibrium holds in the balance of payments; in the conditions of the model this means that there is no further tendency for the money supply to change as a result of a change in net overseas assets.

To simplify the transformations, we now write

\begin{matrix} p = & \frac{1}{1 - c + d + be} \\ s = & \frac{d - ge}{1 - c + d + be} \\ Z = & (A + G + F) \\ r = & \frac{bf}{1 - c + d + be} \\ h = & \frac{bf (d - ge) + gf (1 - c + d + be)}{1 - c + d + be} \\ W = & (F + V) . \end{matrix}

Then

\begin{matrix} (11) & Δ Y = pΔ Z + r Δ M \end{matrix}

\begin{matrix} (12) & Δ B = Δ W - s Δ Z - h Δ M \end{matrix} .

We begin by substituting (10f) into (12). This yields

\begin{matrix} (13) & B_{t} = \frac{1}{1 + h} Δ W - \frac{s}{1 + h} Δ Z - \frac{h}{1 + h} Δ D + \frac{1}{1 + h} B_{t - 1} . \end{matrix}

Since the lagged value of the dependent variable appears in the equation, changes in the autonomous variables operate with a distributed lag; i.e., a change in domestic credit will affect the net overseas balance not only in the current period but in future periods as well. As an illustration of this, we may rewrite (13) as

\begin{matrix} B_{t} = & \frac{1}{1 + h} Δ W + \frac{1}{{(1 + h)}^{2}} Δ W_{t - 1} - \frac{s}{1 + h} Δ Z - \frac{s}{{(1 + h)}^{2}} Δ Z_{t - 1} \\ - \frac{h}{1 + h} Δ D - \frac{h}{{(1 + h)}^{2}} Δ D_{t - 1} + \frac{1}{1 + h} B_{t - 2} . \end{matrix}

This clearly shows that the effect of a change in domestic credit will have the strongest effect in the same period, and thereafter a progressively declining effect.

If we use the combination of values in solution (a) in Table 1, equation (13) becomes ⁷

\begin{matrix} (14) & B_{t} = 0.88 Δ W - 0.38 Δ Z - 0.12 Δ D + 0.88 Δ B_{t - 1} . \end{matrix}

Suppose that ΔW and ΔZ are both zero; then a 100-unit increase in domestic credit will result in an adverse movement of 12 units in the balance of payments in the initial period. The effect on the balance of payments over time will be

a series which sums to —100. This result means that a once-over 100-unit increase in domestic credit will ultimately affect the balance of payments adversely by 100 units. The rationale is simple: As a result of the domestic credit creation, there will be a tendency for both income and imports to rise above their initial levels. The rise in imports will reduce the excess money supply and hence also the domestic excess demand; but as long as the money supply is higher than the initial level and there is any tendency for income to be higher, imports will continue to be at a higher level, and as long as imports are at a higher level, some of the original addition to the money supply is drained away. In the end, total imports will have risen by the full increase in domestic credit; in terms of equation (10f) the ΔM will be zero and the ΔD will be fully offset by the movement in B.⁸ In other words, the increase in the money supply will have been fully drained away, and imports and the level of income will revert back to their initial levels.⁹

The “stationary” solution for the balance of payments may be obtained from equation (13) by putting B_t = B_t–1. Then

\begin{matrix} (13 a) & B_{t} = \frac{1}{h} Δ W - \frac{S}{h} Δ Z - Δ D . \end{matrix}

This again clearly demonstrates that a unit change in credit will affect the balance of payments adversely by one unit.¹⁰ The stationary solution also shows that “in equilibrium,” when all autonomous changes are zero, the balance of payments must be zero; this follows from the fact that any surplus or deficit in the balance of payments opens up an excess or deficiency in the money supply and hence cannot represent an equilibrium situation.

The stationary solution for (14) now becomes

\begin{matrix} (14 a) & B_{t} = 7.3 Δ W - 3.1 Δ Z - Δ D . \end{matrix}

According to this result, an increase of one unit in autonomous expenditures (A + G), with all other changes equal to zero, will cumulatively worsen the balance of payments by something like 3.1 units. The long-term effect of a permanent increase of one unit in exports will be an improvement in the balance of payments of something like 4.2 units (7.3 — 3.1). This result may appear puzzling, but in fact the explanation is fairly simple. The balance of payments is improved cumulatively over time; as long as the surplus exists period after period, the excess money supply represents a disequilibrium situation; the equilibrium will be restored only when the balance of payments becomes zero again. The behavior of the balance of payments over time resulting from a unit increase in exports would be as follows:

The effect of a unit increase in autonomous capital can also be seen from equation (14). Suppose that the money supply effect is initially neutralized so that ΔW and ΔD move in opposite directions. Then, in the initial period, the effect on the balance of payments is an improvement of one unit (0.88 + 0.12). But this is not the end of the matter; the term B_t-1 in the equation ensures that there will be longer run repercussions; this is because the increase in capital will continue to raise the money supply in subsequent periods. In fact, equilibrium will be restored in our example only after the balance of payments will have improved by 8.3 units (7.3+1). The reason why an increase in autonomous capital improves the cumulative reserve position by more than an equivalent increase in exports is that, for exports, the adjustment mechanism works more quickly (with direct expenditure effects, which are absent from capital inflows).

The long-term solutions for income are worth noting, although they will not be discussed in detail. The stationary solution for equation (11) is

\begin{matrix} (15) & Y = \frac{r}{h} Δ W + (p - \frac{rs}{h}) \end{matrix} Δ Z .

The coefficient for ΔD is now zero, implying that, consistently with the results noted earlier, the long-term effect on income of a once-over change in credit will be nil. To repeat, this is because the whole of the excess credit goes ultimately into imports.

On the basis of solution (a), equation (15) becomes

\begin{matrix} (16) & Δ Y = 1.7 Δ W + 0.54 Δ Z . \end{matrix}

An increase of one unit in autonomous expenditures will ultimately raise income in this model by only about 0.5 unit. A permanent unit increase in exports in the model will raise income by something like 2.24 units.

III. The Money and Credit Models Compared

In this section the models are compared for three autonomous changes: first, an increase of 100 units in autonomous investment (Table 3); second, a fall of 100 units in exports (Table 4); and third, an increase of 100 units in autonomous capital outflows (Table 5). In each case the effects are examined over three periods only; effects beyond three periods are uninteresting and will be largely disregarded in what follows. Only solution (a) will be used.

Table 3.

An Increase of 100 Units in Autonomous Investment

Table 4.

A Fall in Exports of 100 Units

Table 5.

An Autonomous Capital Outflow of 100 Units

In the money model in Table 3, income increases by 110 units in the first period and then remains at the new level in the next two periods. The balance of payments deteriorates by 44 units, and, since there is no adjustment mechanism in this model, the deficit is in effect maintained in subsequent periods. In the credit model, income increases by 104 units in the first period and the balance of payments deteriorates by 38 units. In the next period, income is still higher, and this continues to produce a deficit in the balance of payments. This deficit reduces the money supply and depresses somewhat the level of income below that operative at the end of the first period. In the next period, a smaller deficit depresses further the level of income.¹¹

In the money model in Table 4, income falls by 110 units and the balance of payments deteriorates by 56 units. With a fall in income and no change in the money supply, the interest rate will be lower, thus inducing some net capital outflow, which represents a partial offset to the lower imports. The deficit persists in subsequent periods. In the credit model, the drop in income is larger in the first period because of the fall in the money supply. The deficit progressively declines, but as long as there is a deficit, the money supply and therefore income continue to fall. The behavior of income in periods 2 and 3 is due to the drop in the money supply.

The effects of an autonomous capital outflow in the money model in Table 5 are simple. There is no income effect nor any money supply effect, and the deficit in the balance of payments persists indefinitely. In the credit model, the deficit in the balance of payments remains large because the adjustment mechanism depends only on changes in the money supply. The changes in income are worth comparing with the corresponding changes in income where autonomous exports fall. The initial fall in income is much larger for the exports because exports also affect income directly. However, in subsequent periods, the fall in income is larger for the capital flow because the drop in the money supply is larger.

IV. Central Bank Credit as the Monetary Instrument

We now consider briefly the implications of a third model where the control variable is the change in claims held by the central bank. Suppose now that these claims are predetermined in a given period, and suppose that net overseas assets fall by one unit. From equation (10d) we can see that base money in the system will now fall by the change in net overseas assets. Bank assets cannot now be purchased by the central bank, since this will now result in increased holdings of central bank claims. The only way now to retain the assumption that the fall in the money supply is equal to the fall in net overseas assets is to suppose that the legal cash/deposit ratio is automatically varied to bring about this result. If we disregard this possibility, then the model in this case works differently. Since part of the fall in base money cannot be offset by assumption (given the claims held by the central bank), a process of multiple deposit contraction cannot be avoided.¹² Suppose that x represents the ratio of the change in money (ΔM) divided by the change in base money (ΔH) and that ΔD₁ represents the change in claims held by the central bank. Then, from equation (10d) and remembering that ΔM = xΔH equation (12) becomes

\begin{matrix} (12 a) & Δ B = Δ W - sΔZ - hx (Δ D_{1} + B) \end{matrix}

and the alternative to (13) is

\begin{matrix} (13 b) & B_{t} = \frac{1}{1 + hx} Δ W - \frac{s}{1 + hx} Δ Z - \frac{hx}{1 + hx} \end{matrix} Δ D_{1} + \frac{1}{1 + hx} B_{t - 1} .

Using the United Kingdom as an illustration, x is of the order of 3.5. Hence, the coefficients for ΔW, ΔZ, and B_t-1 all fall. Since h is normally less than 1 and the coefficient for ΔD₁ was also less than 1, the coefficient for ΔD₁ now rises. For example, for autonomous investment, an increase in autonomous expenditures will have a smaller adverse effect on the balance of payments simply because the contraction in the money supply is now larger. On the other hand, an increase in claims on government will increase the external deficit, because this will create a larger increase in the money supply.

The stationary solution for (13b) is

\begin{matrix} (13 c) & B_{t} = \frac{1}{hx} Δ W - \frac{s}{hx} Δ Z - Δ D_{1} . \end{matrix}

These results are not surprising. Again, a change in claims on government will ultimately create an equivalent adverse effect on the balance of payments, but now changes in other autonomous elements will reduce the long-term reserve loss. This is because the external adjustment mechanism is more efficient in this instance.

To obtain some idea of the extent of the difference, suppose that x = 3.5; then, from solution (a), (13c) would now become

\begin{matrix} (13 d) & B_{t} = 2.2 Δ \end{matrix} W - Δ Z - Δ D_{1} .

Comparing this result with (14a) in the text, we can see that the coefficients fall sharply. A unit increase in autonomous expenditures will ultimately worsen the balance of payments by only one unit (against 3.1 previously), and a unit increase in exports will improve the balance of payments by only 1.2 units, against 4.2 units previously.

V. A Passive Monetary Policy Model (Constant Interest Rate)

In this section we suppose that the monetary authorities maintain a constant interest rate by accommodating the money supply to changes in monetary demand. The same three autonomous changes may now be considered. The solutions in these cases are simple and may be derived by examining equations (8) and (9). Suppose that autonomous expenditures increase and the increased demand for money is met by the authorities; then the interest rate will be unchanged, and coefficients be and ge will drop out of the equations in the expressions for autonomous expenditures. If c = 0.6 and d = 0.4, then the coefficient in the income equation is 1.25 and the coefficient in the balance of payments equation is 0.5. Here the 0.5 represents simply the increased imports owing to the increased level of income: with a marginal propensity to import of 0.4, an increase in income of 125 units owing to an autonomous increase in expenditure of 100 units will raise imports and affect the balance of payments adversely by 50 units.¹³

If exports drop by 100 units, income would fall by about 125 units. This reduces imports by something like 50 units, so that the net adverse effect on the balance of payments would be about 50 units.

An increase of 100 units in autonomous capital outflow is also very simple. There is no income effect, and the balance of payments will deteriorate by 100 units.

VI. A One-Period Comparison of the Four Models

Table 6 compares, for one period, the results for the four alternative models of three autonomous changes. When autonomous investment increases, the increase in income is largest in the fixed interest rate model and smallest in the central bank credit model. Again, the deterioration in the balance of payments is largest in the fixed interest rate model and least in the central bank credit model. The reason for these results is simple: in the fixed interest rate model, money supply increases to accommodate the increased monetary needs; in the central bank credit model, the accompanying deficit will reduce the money supply by a multiple of the deficit, and this dampens both the increase in income and the deficit.

Table 6.

Comparison of Four Models, Showing Results of Three Autonomous Changes

For a drop in exports, the largest drop in income and the smallest deterioration in the balance of payments occurs in the central bank credit model. The reason is that the multiple contraction in the money supply produces the largest fall in income and therefore the largest drop in imports. The money model shows the smallest drop in income and the smallest deterioration in the balance of payments.

The solutions for an increase in autonomous capital outflows are simple. The money and fixed interest rate models work in an identical way. The difference between the domestic and central bank credit models is that in the central bank credit model there is a magnified effect on the money supply.

It is difficult to draw any general conclusions from these results. Some of these difficulties may be illustrated by reference to the central bank credit model. For all three autonomous changes, the adverse effect on the balance of payments is least in this model. The balance of payments, in other words, is most immune to external shocks. In an increase in autonomous investment the effect on income is also minimized, but in the other two instances the change in income is largest in the central bank credit model. A drop in exports in this model generates the smallest adverse effect on the balance of payments because it is allowed to produce the largest drop in income. In the same way, an increase in autonomous capital outflows will have the least impact on the balance of payments because it will allow the largest drop in income. In the second and third models, therefore, the greater immunity in the balance of payments to external shocks is achieved only at the expense of greater instability in the level of income and employment.

APPENDICES: I. Estimation of Coefficients

In estimating the coefficients, the United Kingdom was used as an illustration. The methodology used will be illustrated by taking the coefficient for ΔM in equation (9)

\frac{bf (d - ge) + gf (1 - c + d + be)}{1 - c + d + be} .

To begin with, it is easy to assign plausible values for some coefficients: c, the marginal propensity to consume, was given a single value of 0.6, and d, the marginal propensity to import, was given two values—a lower limit of 0.2 and an upper limit of 0.4. The figure for the upper limit was derived from Ball and Drake,¹⁴ who estimated the following import equation:

M_{t} = 1, 500 + 0.392 {GDP}_{t} - 0.068 K_{t - 1}^{8}

where M represents imports of goods and services; GDP, gross domestic product; and K⁸, the stock of inventories. The coefficient for GDP is the marginal propensity to import. This coefficient is almost certainly too high; however, it is used in the text for illustrative purposes.

Suppose now that the coefficients b, f, e, and g were available in “elasticity” form (b_e, f_e, e_e, g_e), where b_e for example, represented the percentage change in investment divided by the percentage change in the interest rate, f_e represented the percentage change in interest rate divided by the percentage change in the money supply, and so on. Then

\begin{matrix} b & = b_{e} I / R \\ f & = f_{e} R / M \\ e & = e_{e} R / Y \\ g & = g_{e} K / R \end{matrix}

where I, R, M, K, and Y represent “mean” values of these variables. Our coefficient for ΔM would then be

\frac{b_{e} f_{e} I / M (d - e_{e} g_{e} K / Y) + g_{e} f_{e} K / M (1 - c + d + b_{e} e_{e} I / Y)}{1 - c + d + b_{e} e_{e} I / Y} .

We would need to know not only the size of the relevant elasticities but also the relative mean values of I, M, Y, and K (with R eliminated by substitution). The only problem with this procedure is in the estimation of the g. First, it is difficult to get a meaningful figure for K (net short-term capital flows); second, g_e would appear to have little meaning in an equation where the dependent variable was net short-term capital imports, whose value could approach zero. As a result, arbitrary figures of 100 and 20 were used for g. A figure of 100, for example, implies that a 1 per cent change in the interest will normally result in a change of £100 million in short-term capital flows. Elasticities were used for b_e, f_e, and e_e, but a slope value was used for g. On the basis of U.K. data, the ratio I/Y was assumed to be 0.2 and the ratio I/M was assumed to be 0.5. The mean interest rate was assumed to be 6, the mean gross national product was assumed to be £37,000 million, and the mean money supply was assumed to be £13,000 million. Two values were used for b_e: 0.4 and 0.8. There is no empirical work on this for the United Kingdom, but these values are consistent with econometric studies in the United States.¹⁵ In the estimation of f_e and e_e, the U.K. study that is most useful is one by Kavanagh and Walters.¹⁶ They estimated the following interest rate equation (for the period 1926–60):

\begin{matrix} \log R_{t} = - 0.99 {logM}_{t} + 1.01 \log Y_{t} & R^{2} = 0.57 \end{matrix}

where R is the long rate, M is the money supply, and Y is aggregate income. Both coefficients were significant, and both approximated 1. Elasticities for both variables of 0.5 and 1 were used in the computations.

II. Keynes and the Quantity Theory in an Open Economy

In Section II of the text we examined the implications of a Keynesian-type model in an open economy where the money supply was allowed to respond to changes in the overseas balance. It is instructive to contrast this model with a simple Quantity Theory-type model under similar conditions.¹⁷ The Quantity Theory model in an open economy may be represented by a new set of equations:

\begin{matrix} (17) & B_{t} = F_{t} - {dY}_{t} + K_{t} \end{matrix}

\begin{matrix} (18) & Y_{t} = {vM}_{t} (where v is income velocity of money) \end{matrix}

\begin{matrix} (10 f) & Δ M = Δ D + B \end{matrix}

These equations may now be combined to yield short-term and long-term solutions for the overseas balance.

\begin{matrix} (19) & B_{t} = \frac{1}{1 + dv} Δ (F + K) - \frac{dv}{1 + dv} Δ D + \frac{1}{1 + dv} B_{t - 1} [Short - term solution] \end{matrix}

\begin{matrix} (20) & B_{t} = \frac{1}{dv} Δ (F + K) - Δ D [Long - term solution] \end{matrix}

These two solutions may now be compared with the short-term and long-term solutions obtained for the Keynesian model. They are reproduced here:

\begin{matrix} (13) & B_{t} = \frac{1}{1 + h} Δ (F + V) - \frac{s}{1 + h} Δ (A + G + F) - \frac{h}{1 + h} Δ D + \frac{1}{1 + h} B_{t - 1} \end{matrix}

\begin{matrix} (13 a) & B_{t} = \frac{1}{h} Δ (F + V) - \frac{s}{h} Δ (A + G + F) - Δ D \end{matrix}

It is clear that the two solutions become identical when s = 0 and h = dv. Under Quantity Theory assumptions, s = 0 represents the case where changes in autonomous expenditures have no independent effect on the balance of payments either in the short run or in the long run. In the Keynesian model, h is the coefficient for money against the change in the overseas balance (see equation 9); in the Quantity Theory model, dv is the coefficient for money against the change in the overseas balance (substituting vM_t for Y_t in equation 17). In the Keynesian model, h is a composite of a number of structural coefficients; h ranges, for plausible values of these coefficients, from 0.03 to about 0.23. In contrast, dv, for plausible values of velocity and the marginal propensity to import, would normally range from 0.4 to over 2.0. Hence, a major difference between the two models is in the likely size of the money coefficient. Since h < dv in the Keynesian model, this means that a given change in exports or capital flows will generate a larger cumulative change in overseas assets in the Keynesian case than in the Quantity Theory case. This may be seen by contrasting the long-term solution for Keynes, $\frac{1}{h}$ , with the long-term solution for the Quantity Theory, $\frac{1}{dv}$ ; the total loss in reserves from a unit fall in exports is $\frac{1}{h}$ in the Keynesian case and $\frac{1}{dv}$ in the Quantity Theory case. The reason for this difference is that because money is more powerful in the Quantity Theory case, the adjustment mechanism restores long-term equilibrium with a smaller loss of reserves.

On the other hand, it may be seen that the long-term solution for the change in credit is the same in the two models. A once-over increase in credit will in both models generate an equivalent cumulative loss in reserves. (The coefficient for credit in both long-term solutions is 1.)

It is also interesting to compare the long-term income solutions for the two models. The long-term solution for income for the Quantity Theory is

\begin{matrix} (21) & Δ Y = \frac{1}{d} Δ (F + K) . \end{matrix}

The Keynesian solution was

\begin{matrix} (15) & Δ Y = \frac{r}{h} Δ (F + V) + (p - \frac{rs}{h}) Δ (A + G + F) . \end{matrix}

The coefficient for the change in credit is zero in both instances, as expected, but there are differences between the models for disturbances stemming from changes in exports-capital flows and autonomous expenditures. The contrast between the two models becomes more interesting in the special case, for the Keynesian model, where g = 0, that is to say, where capital flows are not sensitive to interest rate changes.

Equation 15 now becomes

\begin{matrix} (15 a) & Δ Y = \frac{1}{d} Δ (F + V) . \end{matrix}

In this special case, the long-term income solutions are identical. The coefficient for autonomous expenditures becomes zero; income, in other words, cannot be permanently raised by an increase in autonomous expenditure because this would imply a higher level of imports and hence some disequilibrium in the balance of payments. Where capital flows do respond to interest rate changes, a permanently higher level of income is sustained by higher imports matched by capital flows induced by a higher interest rate. Again the coefficient for exports and capital flows is the same for the two models; under both models a permanent increase in income is possible only when there is a permanent increase in exports or net capital flows.

The most interesting conclusions emerging from these comparisons are the following. A change in domestic credit will have the same effect on reserves in the two models; this is true for the expanded (g > 0) as well as the simplified (g = 0) Keynesian model. The long-term income solutions will be identical when g = 0 but different when g > 0; even here the differences are only slight, since (as we saw in the text) the increase in income when g > 0 is only a fraction of the increase in autonomous expenditures. The cumulative reserve change for disturbances other than changes in credit is quite different in the two models. The reason for this difference lies in the fact that the adjustment mechanism, i.e., the impact of money changes, is more powerful in the Quantity Theory model.

Variables monétaires et balance des paiements

Résumé

Dans cette étude, l’auteur développe un modèle keynésien simple applicable à une économie ouverte et étudie les effets de certaines perturbations dans diverses hypothèses de politique monétaire. Les perturbations dont il est tenu compte sont: les variations des dépenses autonomes, des exportations, des flux de capitaux autonomes et du crédit intérieur total. Les quatre politiques monétaires envisagées font intervenir des variables de contrôle différentes: la première variable est la monnaie; la deuxième, le crédit intérieur total; la troisième, les créances de la Banque centrale et la quatrième, une politique de taux d’intérêt constant appliquée par la Banque centrale. Lorsque le crédit intérieur total ou le crédit de la Banque centrale est la variable de contrôle, on laisse la masse monétaire réagir aux variations de la balance des paiements; dès lors, l’équilibre absolu à long terme du modèle n’est pas atteint tant que l’équilibre de la balance des paiements n’est pas réalisé. Ce processus d’ajustement prend un certain temps et l’auteur examine le comportement de la balance des paiements et des revenus au cours des années. On a attribué des valeurs plausibles aux coefficients du modèle afin de se faire une idée de l’ordre de grandeur des variations enregistrées dans les réserves extérieures et les revenus à la suite de certaines perturbations. Lorsque la monnaie est la variable de contrôle, on suppose que la masse monétaire ne réagit pas aux variations de la balance des paiements; dès lors, aucun mécanisme d’ajustement n’entre en jeu et, s’agissant du modèle, les déficits ou excédents peuvent se perpétuer.

Dans l’Annexe II, le modèle keynésien est opposé à un modèle de la Théorie quantitative dans lequel on laisse la masse monétaire réagir aux variations de la balance des paiements. Il est démontré que, lorsque les flux de capitaux ne réagissent pas aux variations du taux d’intérêt, les solutions à long terme données par ces deux modèles, pour les revenus, sont identiques. La principale différence entre les deux modèles réside dans les variations cumulatives des réserves extérieures découlant des perturbations enregistrées par les exportations et les flux de capitaux. La variation totale est plus grande dans le modèle keynésien parce que le mécanisme d’ajustement y est plus faible.

Las variables monetarias y la balanza de pagos

Resumen

En este trabajo se elabora un modelo keynesiano sencillo para una economía abierta y se examinan los efectos de las perturbaciones bajo supuestos alternativos de política. Las perturbaciones a las que se da cabida son las variaciones en el gasto autónomo, en la exportación, en los flujos autónomos de capital, y en el crédito interno total. Se examinan cuatro supuestos alternativos de política con diferentes variables de control: la primera variable es el dinero; la segunda, el crédito interno total; la tercera, el crédito concedido por el banco central; y la cuarta, una política del banco central de mantenimiento de una tasa de interés constante. Cuando la variable de control es el crédito interno total o el crédito del banco central, se deja que la oferta monetaria responda ante las variaciones en la balanza de pagos; por tanto, no se consigue el pleno equilibrio a largo plazo en el modelo hasta que se obtenga el equilibrio de balanza de pagos. Este proceso de ajuste lleva tiempo, y se ha hecho un examen del comportamiento de la balanza de pagos y del ingreso a lo largo del tiempo. Se suponen valores verosímiles para los coeficientes del modelo, dándose así una indicación sobre el orden de magnitud de las variaciones en las reservas exteriores y en el ingreso, tras determinadas perturbaciones. Cuando la variable de control es el dinero, se supone que la oferta monetaria es insensible a las variaciones en la balanza de pagos; por tanto, no hay mecanismo de ajuste y, en términos del modelo, puede ocurrir que se perpetúen los déficit o superávit.

En el Apéndice II, este modelo keynesiano se contrasta con un modelo de la Teoría Cuantitativa en el que se deja que el dinero responda ante la balanza de pagos. Se demuestra que cuando los flujos de capital no responden a las variaciones en la tasa de interés, los dos modelos dan soluciones idénticas de largo plazo para el ingreso. La principal diferencia entre los dos modelos se halla en la variación acumulativa en las reservas exteriores como resultado de perturbaciones en la exportación y en los flujos de capital. La variación acumulativa es mayor en el modelo keynesiano porque el mecanismo de ajuste es más débil.

Mr. Argy, Assistant Chief of the Special Studies Division of the Research Department, is a graduate of the University of Sydney, Australia. He has been a lecturer at the University of Auckland, New Zealand, and a lecturer and senior lecturer at the University of Sydney. He has contributed several articles to economic journals.

There is some question as to whether the level of activity has a significant effect on export performance. For a U.K. study, see R. J. Ball, J. R. Eaton, and M. D. Steuer, “The Relationship Between United Kingdom Export Performance in Manufactures and the Internal Pressure of Demand,” The Economic Journal, Vol. LXXVI (1966), pp. 501–18.

In equation (9) if g is sufficiently large (i.e., short-term capital flows are strongly influenced by the interest rate) d — ge may be negative. In this case, an increase in autonomous expenditures will improve the balance of payments. This is true where, with fixed money supply, the rise in the interest rate will improve capital flows by more than the increment in imports owing to the rise in income. This example is excluded from the “plausible” range of solutions used in the text.

The effect of allowing for these financial and import constraints on income expansion is to lower the multiplier from $2.5 (\frac{1}{1 - c})$ to 1 to 1.5.

This disregards complications arising from the fact that different components of expenditure may have different import contents.

The model, of course, also assumes that the current and capital accounts are independent. There is also some question as to whether the interest rate in the capital account determines “stocks” or “flows.” The model uses a flow variable. A stock relationship complicates the mechanism of adjustment suggested above. If short-term flows are a function of the change in the interest rate (the stock version), then in order to maintain an improved given flow the interest rate would need to be raised continuously.

⁶

There are difficulties arising from the fact that the money in the model should strictly refer to “mean” money in the period. When money is defined in this way, the terms for domestic credit and net overseas assets should also correspond to this definition in order to satisfy the identity. This was disregarded in the interest of simplicity; also, the results would be changed only mildly by effecting this transformation.

The coefficient for ΔD for the other solutions is (b) 0.09; (c) 0.16; (d) 0.05; (e) 0.19; (f) 0.03.

This conclusion need not follow if we allow for foreign repercussions. Where the foreign impact is allowed for, the domestic expansion will generate some increase in exports; hence, some increase in the money supply in long-run equilibrium will be sustainable. This point was suggested to the author by an unpublished paper by D. Roper, “Some Dynamic Implications of a Keynesian Model of the Open Economy Under Fixed Exchange Rates.”

In our model, this must also mean that the rate of interest reverts to its original level, since the rate of interest is determined by income and the money supply, both of which are ultimately unchanged. Of course, in the progression to equilibrium, the rate of interest will change, and this will result in a temporary movement in short-term capital flows. Movements in capital flows were disregarded in the text.

If the increase in credit is constant in each period, the solution will be different. As equilibrium is approached, the money supply increases at a declining rate. In equilibrium the level of income will be higher, and the periodic increase in credit will leak overseas. This is one case dealt with by J. J. Polak in “Monetary Analysis of Income Formation and Payments Problems,” Staff Papers, Vol. VI (1957), pp. 1–50.

The total drop over time in the money supply will be the cumulative deficits. In this example they sum to roughly 310 units. In equilibrium the level of income will be some 54 units above the original level, the rate of interest will be higher (since income is higher and the money supply is lower), and the balance of payments will be zero with additional imports exactly offset by increased capital flows. Note that in this model if g = 0 (i.e., capital flows do not respond to the interest rate), the long-term coefficient for ΔZ is zero, implying in this instance that an increase in autonomous investment cannot ultimately produce a rise in income.

There are two differences worth noting between this model and the total domestic credit one. The first is the feasibility of controlling total credit instead of central bank claims; the discussion in the text suggests that the latter is easier to control. The second is the fact that where central bank claims are controlled an unanticipated change in net overseas assets will have a multiple effect on money. For total domestic credit, the multiplier was unity.

If the marginal propensity to import were 0.2, the net income multiplier would be 1.7 and the balance of payments coefficient would drop from 0.5 to 0.33.

R.J. Ball and Pamela S. Drake, “Export Growth and the Balance of Payments,” The Manchester School of Economic and Social Studies. Vol, XXX (1962), pp. 105–19.

See Thomas Mayer, “Multiplier and Velocity Analysis—An Evaluation,” The Journal of Political Economy, Vol. LXXII (December 1964), pp. 563–74.

N.J. Kavanagh and A.A. Walters, “Demand for Money in the UK, 1877–1961: Some Preliminary Findings,” Oxford University Institute of Economics and Statistics, Bulletin, Vol. 28 (1966), pp. 93–116.

This model is very similar to the model developed by Polak, op. cit. The major difference is that Polak defines his time period in such a way that an increase in money will generate an equal increase in income. This means defining the time period for any country as the fraction of the year represented by the inverse of velocity.

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IMF Staff papers: Volume 16 No. 2

Author: International Monetary Fund. Research Dept.

Volume/Issue:: Volume 1969: Issue 002

Publisher:: International Monetary Fund

ISBN:: 9781451947298

ISSN:: 1020-7635

Pages:: 218

DOI:: https://doi.org/10.5089/9781451947298.024

Keywords

T	= Exports less imports
K	= Net capital inflow
B	= Change in net overseas assets of the central bank
C	= Consumption
I	= Investment
G	= Government expenditure
M	= Money supply
R	= Rate of interest
Y	= Gross national product
V	= Autonomous capital inflows
F	= Exports
CP	= Cash held by the nonbank public
CB	= Cash held by the banks
RB	= Foreign assets held by the banks
AB	= Assets, other than cash and foreign, held by the banks
D₁	= Domestic assets of the central bank (claims on the government or private sector)
H	= Base money (“high-powered” money)
D	= Total domestic credit of the monetary sector
DB	= Domestic deposit liabilities of the banks
LB	= Foreign deposit liabilities of the banks
x	$= \frac{Δ M}{Δ H}$

T	= Exports less imports
K	= Net capital inflow
B	= Change in net overseas assets of the central bank
C	= Consumption
I	= Investment
G	= Government expenditure
M	= Money supply
R	= Rate of interest
Y	= Gross national product
V	= Autonomous capital inflows
F	= Exports
CP	= Cash held by the nonbank public
CB	= Cash held by the banks
RB	= Foreign assets held by the banks
AB	= Assets, other than cash and foreign, held by the banks
D₁	= Domestic assets of the central bank (claims on the government or private sector)
H	= Base money (“high-powered” money)
D	= Total domestic credit of the monetary sector
DB	= Domestic deposit liabilities of the banks
LB	= Foreign deposit liabilities of the banks
x	$= \frac{Δ M}{Δ H}$

(8a)	ΔY	= 1.1Δ (A + G + F) + 0.23ΔM
(9a)	ΔB	= Δ (F + V) ‒ 0.44Δ (A + G + F) – 0.13ΔM
(8b)	ΔY	= 1.1Δ (A + G + F) + 0.23ΔM
(9b)	ΔB	= Δ (F + V) – 0.45Δ (A + G + F) - 0.1ΔM
(8c)	ΔY	= 1Δ (A + G + F) + 0.4ΔM
(9c)	ΔB	= Δ (F + V) – 0.4Δ (A + G + F) – 0.2ΔM
(8d)	ΔY	= 1.5Δ (A + G + F) + 0.3ΔM
(9d)	ΔB	= Δ (F + V) – 0.3Δ (A + G + F) – 0.06ΔM
(8e)	ΔY	= 1.1Δ (A + G + F) + 0.45ΔM
(9e)	ΔB	= Δ(F + V) – 0.45Δ (A + G + F) – 0.23ΔM
(8f)	ΔY	= 1.5Δ (A + G + F) + 0.15ΔM
(9f)	ΔB	= Δ (F + V) – 0.3Δ (A + G + F) – 0.03ΔM

(8a)	ΔY	= 1.1Δ (A + G + F) + 0.23ΔM
(9a)	ΔB	= Δ (F + V) ‒ 0.44Δ (A + G + F) – 0.13ΔM
(8b)	ΔY	= 1.1Δ (A + G + F) + 0.23ΔM
(9b)	ΔB	= Δ (F + V) – 0.45Δ (A + G + F) - 0.1ΔM
(8c)	ΔY	= 1Δ (A + G + F) + 0.4ΔM
(9c)	ΔB	= Δ (F + V) – 0.4Δ (A + G + F) – 0.2ΔM
(8d)	ΔY	= 1.5Δ (A + G + F) + 0.3ΔM
(9d)	ΔB	= Δ (F + V) – 0.3Δ (A + G + F) – 0.06ΔM
(8e)	ΔY	= 1.1Δ (A + G + F) + 0.45ΔM
(9e)	ΔB	= Δ(F + V) – 0.45Δ (A + G + F) – 0.23ΔM
(8f)	ΔY	= 1.5Δ (A + G + F) + 0.15ΔM
(9f)	ΔB	= Δ (F + V) – 0.3Δ (A + G + F) – 0.03ΔM

Period 1	–12
Period 2	–12	(0.88)
Period 3	–12	(0.88)²
Period 4	–12	(0.88)³

An Increase of 100 Units in Autonomous Investment
	B	ΔY
Money model	— 44	+ 110
Domestic credit model	— 38	+ 104
Central bank credit model	— 30	+ 86
Fixed interest rate model	— 50	+ 125
A Drop of 100 Units in Exports
	B	ΔY
Money model	— 56	—110
Domestic credit model	— 50	— 124
Central bank credit model	— 40	— 141
Fixed interest rate model	— 50	— 125
An Increase of 100 Units in Autonomous Capital Outflows
	B	ΔY
Money model	—100	0
Domestic credit model	— 88	— 20
Central bank credit model	— 70	— 55
Fixed interest rate model	— 100	0

Period	B
1	+0.5
2	+0.44 (0.5·0.88)
3	+0.38 (0.5(0.88)²)
4	+0.33 (0.5(0.88)^a)
Equilibrium	0

Period	B
1	+0.5
2	+0.44 (0.5·0.88)
3	+0.38 (0.5(0.88)²)
4	+0.33 (0.5(0.88)^a)
Equilibrium	0

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Abstract

I. Money as the Monetary Instrument

II. Domestic Credit as the Monetary Instrument

III. The Money and Credit Models Compared

IV. Central Bank Credit as the Monetary Instrument

V. A Passive Monetary Policy Model (Constant Interest Rate)

VI. A One-Period Comparison of the Four Models

APPENDICES: I. Estimation of Coefficients

II. Keynes and the Quantity Theory in an Open Economy

Variables monétaires et balance des paiements

Résumé

Las variables monetarias y la balanza de pagos

Resumen

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