THERE IS AMPLE theoretical and empirical evidence that income expansion and inflation are often associated with increases in the money supply. Since, as a rule, monetary statistics are readily and currently available while inflationary pressure is a concept that is hard to measure, it has become customary to accept monetary statistics as reliable indicators of inflation and deflation, of expansion and contraction. When it is observed that the money supply in a country is rising, it is inferred that expansionary factors must be at work and that anti-inflationary policies should be introduced. Likewise, when the money supply declines, it is inferred that contractionary forces are more powerful and that anti-inflationary policies can safely be relaxed or reversed.


THERE IS AMPLE theoretical and empirical evidence that income expansion and inflation are often associated with increases in the money supply. Since, as a rule, monetary statistics are readily and currently available while inflationary pressure is a concept that is hard to measure, it has become customary to accept monetary statistics as reliable indicators of inflation and deflation, of expansion and contraction. When it is observed that the money supply in a country is rising, it is inferred that expansionary factors must be at work and that anti-inflationary policies should be introduced. Likewise, when the money supply declines, it is inferred that contractionary forces are more powerful and that anti-inflationary policies can safely be relaxed or reversed.

THERE IS AMPLE theoretical and empirical evidence that income expansion and inflation are often associated with increases in the money supply. Since, as a rule, monetary statistics are readily and currently available while inflationary pressure is a concept that is hard to measure, it has become customary to accept monetary statistics as reliable indicators of inflation and deflation, of expansion and contraction. When it is observed that the money supply in a country is rising, it is inferred that expansionary factors must be at work and that anti-inflationary policies should be introduced. Likewise, when the money supply declines, it is inferred that contractionary forces are more powerful and that anti-inflationary policies can safely be relaxed or reversed.

In its Annual Reports for 1951 and 1952, the Netherlands Bank has drawn attention to a different relationship between inflation and the money supply, with particular reference to countries with an open economy. “The course of events during 1950 and 1951 showed clearly that, in the conditions which exist in the Netherlands, a decrease in the volume of money may be a symptom of inflationary strains; while on the other hand an increase in the volume of money may show that there is a movement in the direction of disinflation.”1 More specifically, the period from the latter part of 1950 through the first half of 1951 was without doubt one of inflation in the Netherlands; but the money supply fell in the fourth quarter of 1950 and in the first two quarters of 1951. The economic position was reversed around the middle of 1951, and the second half of that year, as well as the whole of 1952, was characterized by disinflationary or mild deflationary conditions; during that period the money supply consistently rose.

It appears, then, that the direction of change in the quantity of money is by no means an unequivocal indicator of the direction in which the economy is moving. An increase in the quantity of money may point either to inflationary strains (expansion) or to the presence of contractionist tendencies. It is necessary, therefore, to analyze the relation between changes in income and changes in the quantity of money in order to develop a theory of more general applicability.

The present analysis consists of two parts, of which the first is a theoretical study of the relation between domestic income expansion and the money supply in an open economy. The income expansion may be due to a variety of impulses, such as an autonomous increase in domestic spending by the government, by private investors, or by private consumers. Unless the supply situation in the country is fully inelastic, the income expansion will affect not only money income, but real income as well. This study is not concerned with the effect of impulses coming from abroad; in view of this limitation, the terms “increase in income” and “decrease in income” refer to changes in activity and in income due to changes in domestic demand conditions. In order to be able to draw conclusions with respect to the net effects of these internal movements on the balance of payments, an unchanged situation in other countries is assumed: the balance of payments will then reflect only the results of the changes of domestic origin in the country under consideration.2

The conclusion of this part of the analysis is that, in an open economy, income expansion caused by a rise in private domestic investment, in consumption, or in government expenditure, provided it is not directly or indirectly financed largely by the central bank will, after a certain lapse of time, lead to a decrease in the quantity of money; and that the reverse causes, a fall in private investment, private consumption, or government expenditure, provided it is not matched in large part by a contraction of central bank credit, will lead, after a certain lapse of time, to an increase in the quantity of money. A more formal treatment is given in the Appendix.

It would follow, therefore, that caution should be used in drawing the traditional inferences from observed changes in the quantity of money. While very large increases could hardly occur without the presence of some inflationary central bank action, more moderate increases could well be an indication of contraction in the economy which, if verified by other indicators, could justify expansionist policies. Conversely, declines in the money supply may be an indication of an inflationary process running its course and could signal a need for anti-inflationary policies to reinforce the contractionary effect exercised by the fall in the money supply itself.

The second part of the analysis is statistical. Its purpose is to determine quantitatively the length of the critical time period on which the theoretical analysis gives only qualitative information. The very tentative finding of this statistical investigation is that for countries in which foreign trade plays a considerable role, i.e., in practice for almost all countries except the United States, the critical time period would appear to be less than one year.

In the first half of the statistical inquiry, an attempt is made to measure for a large number of countries three of the five relevant coefficients that determine the critical time period. These are ratios which may be assumed to be reasonably constant for each country and whose measurement presents relatively few problems.

The measurement of elasticities with respect to the rate of interest of the demand and supply of money raises many more problems. The second part of the statistical inquiry represents a tentative endeavor in this field, applied to the United States only.

The statistical measurement of the elasticity of demand for money with respect to the rate of interest—i.e., the slope of the “liquidity preference function”—is believed to have importance beyond the scope of the present paper. It indicates the extent to which the success of a monetary policy intended to achieve effects in the real sphere by changing the cost of money may be misjudged if attention is directed to the responses of the economy with respect to the holding of money rather than with respect to the holding or acquisition of real assets.

Theoretical Analysis

Analysis Without Regard to Time

The possibility that a change in the quantity of money may be associated with a change in income either in the same or in the opposite direction can be explained if both relationships are seen as partial theories, each paying attention to a particular aspect of the inflationary or deflationary process.

When income expands in an open economy, the money supply will be subject to two different pressures. On the one hand, there will be a tendency for the money supply to increase. Expansion of investment activity will require additional credit from the banks. The expansion of income which goes along with expansion of investment (through the operation of the multiplier) will lead to an increased desire to hold cash for use in transactions. Thus there is not only an initial temporary demand on the banks in order to finance the additional investment, but also a lasting increase in the stock of money to facilitate the larger flow of payments associated with a higher national income.

At the same time, there will be an opposite tendency. Higher incomes will lead to higher imports. Exports will tend to decline as more resources are absorbed internally. If the balance of payments was just in equilibrium before the expansion phase started, it will now show a deficit. The public will buy more foreign exchange from the banks than it sells to the banks and, in the process, will reduce its holdings of money by an amount equal to the net reduction in the country’s foreign exchange holdings. As the reserves of the banking system decline, and the central bank takes no steps to offset this decline, the banking system will wish to have less money outstanding.

Here it is assumed that the central bank adheres to a moderate form of the “rules of the game” in that, on the one hand, it does not offset the loss of reserves by the commercial banks (e.g., by open market purchases of securities) but, on the other hand, does not act to contract further the quantity of money by attempting, for instance, to restore the previous ratio of its foreign assets to its sight liabilities. It is similarly assumed that the central bank does not itself finance the greater part of the expansionary impulses which give rise to the increase in income.

These assumptions regarding central bank behavior are important in determining the outcome of the analysis; very different assumptions would lead to quite different results. For example, if the central bank fully finances a government deficit, the reserve base of the commercial banking system will increase more from this action than it will decline from the increase in imports to which the associated income expansion will give rise.3

The desire of the public for more money and the wish of the banks to contract the money supply cannot be reconciled without bringing in another element. The two tendencies can be reconciled as soon as both the demand for money and the supply of money are considered in the schedule sense and a price, in this case the rate of interest, is brought into play as the equilibrating factor. The public wants more money at a given rate of interest, but it will squeeze its holdings of money as they become more expensive. The banks want a smaller money supply, but they are willing, within limits, to give in to the pressure for more money by squeezing their reserve ratios as the rate of interest goes up.

The end result must be an increase in the rate of interest; there may be an increase or a decrease of the money supply depending on a number of elements which can most conveniently be discussed by means of a chart.

In Chart 1, the demand (D) and supply (S) of money are plotted. The curves D and S indicate the initial equilibrium situation before the beginning of the expansion process. The initial money supply is indicated as MO0. This satisfied the public’s demand for money at the given rate of interest, r0, and at the given level of income which determines the position of the demand schedule. The same money supply, MO0, also satisfied the banks, given the rate r0 and their reserve position which determines the position of the supply schedule.

A once and for all rise, thereafter sustained, of the national income of 10 million (of national currency units) above the previous equilibrium situation is now assumed. To make the higher payments, the public will want more money. If the income velocity of money is, say, 2, the desired increase in the quantity of money would be 5 million. This is indicated in the chart by a new demand curve D1, 5 units to the right of curve D.

Suppose that the 10 million higher level of income persists for one year, and that the marginal propensity to import4 is 0.2. Then the country would lose 2 million in reserves. At the end of the year, therefore, the banking system’s supply curve of money will have moved to the left (to S1). The distance of the shift can be expressed in units comparable to the shift of the demand curve. It will depend on the loss of international reserves and on the reserve ratio (the ratio of reserves to deposit liabilities plus currency in circulation) of the commercial banks. Suppose the latter ratio is 40 per cent.5 Then at the given rate of interest the banking system will want to contract the money supply at the end of one year by 2.5 X 2 million = 5 million. Under these numerical assumptions, it so happens that the supply curve S1 in Chart 1 is moved to the left by the same distance as the demand curve is moved to the right.

The new rate of interest r′ and the new quantity of money MO′ are found by the intersection of the D′ curve and the S′ curve (at P′). The rate of interest, r′, is higher than r0, and the quantity of money, MO′, is higher than MO0. However, the increase in MO is small, i.e., 1 million.

The increase in the rate of interest needs no comment. But the fact that there is an increase in the money supply and not a decrease is clearly due to the numerical assumptons made. An equal horizontal shift (with opposite sign) of the demand and the supply curves has been obtained by assuming a particular numerical relationship between the income velocity of money, on the one hand, and the marginal propensity to import and the banks’ reserve ratio, on the other hand. Specifically it has been assumed that


(e.g., in the simplified case outlined above, 12=0.20.4).

These figures are plausible for certain countries although there is no particular reason why the shift of the demand curve should not be greater or smaller than the shift of the supply curve.

Equal shifts having been assumed, the result as far as MO′ is concerned depends on the relative elasticity of the two curves. In Chart 1, S and S′ have been drawn as more elastic (flatter) than D and D′. Accordingly, P′ lies to the right of P and MO′ is greater than MO. The increase of the rate of interest from r0 to r would by itself induce the banks to expand the money supply by 6 million. It would induce the public to compress their demand for money by 4 million. The combination of these movements along the curves with shifts of 5 million in both curves leads to a new equilibrium position in which the public holds 5 — 4 (= 1) million more money and the banks have an increase in their liabilities of 6 — 5 (= 1) million.

It is clear that if elasticity had been assumed to be greater for the public than for the banks, instead of smaller, the quantity of money would have shown a decrease.

Subject to what is to be said below—and this is an important qualification—it has been found that, if central bank action is in accordance with the assumptions made above, the following five factors will determine whether changes in the quantity of money and changes in income are in the same or in opposite directions:

  1. The income velocity of money

  2. The marginal propensity to import

  3. The reserve ratio of the banking system

  4. The elasticity of demand for money6 with respect to the rate of interest on the part of the public

  5. The elasticity of supply of money with respect to the rate of interest on the part of the banks.

If the first three factors happen to be such that the shifts of the demand and supply curves are of equal magnitude, the money supply increases when the fourth factor is less than the fifth, and decreases when it is greater.

Dynamic Analysis

In the preceding section the time dimension has deliberately been glossed over. It is necessary now to become more specific on this point.

On closer analysis it becomes clear that the shift of the demand curve and the shift of the supply curve are not of the same character. On the assumption made, i.e., a single but sustained rise in the level of income, the shift of the demand curve may be considered as a once and for all shift. As soon as income (expressed as an annual rate) increases by 10 million, and as long as it remains at this higher level, D′ being 5 million to the right of D, will represent the demand for money. The shift in the supply curve is different. It is a movement over time, caused by the loss of reserves over time. S′ has been drawn quite arbitrarily at the point corresponding to a one year period of higher income. If income stays at the same level for another year, another 2 million of imports above the normal level will have been wanted, and reserves will have been reduced by another 2 million. Accordingly, the supply curve will shift another 5 units to the left.

In Chart 2 the dynamic development of the money supply is presented in a general form. Curves D, D′, and S are the same as in Chart 1. Curve S1 is the same as S′ in Chart 1; the suffix 1 is attached to denote the particular timing of the curve, i.e., after one year.

Changes in the quantity of money can be read along the horizonta axis. At the very beginning of the year when income is 10 million higher than in the preceding year, the banks have not yet lost any reserves. Their supply schedule is, therefore, still practically unchanged at S. The intersection of D′ with S gives P0, which indicates the rate of interest, r0, and the quantity of money, MO0, at that time. This money supply must be larger than MO0, whatever the numerical values of any of the five factors. After one year, we will have MO0 and r1 which are equal to MO′ and r′ in Chart 1. The supply curve continues to move to the left, and at the end of two years the money supply (MO2′) is now clearly below the original money supply. As time goes on and income remains at the given level, the money supply will continue to fall.

Chart 3 shows the movement over time of income, the rate of interest, and the quantity of money on the basis of the findings in Chart 2.

The conclusions derived from the dynamic analysis are as follows: (1) Initially, an increase in income will lead to an increase in the quantity of money. (2) As the same higher level of income persists for a longer time, it will lead to a reduction in the quantity of money below the higher level initially reached. (3) If the same higher level of income persists for a long enough period, it will lead to a quantity of money below the level that existed before the increase in income occurred.

These three propositions have general validity for an increase in income for which the associated import surplus is not entirely compensated by central bank financing. They do not therefore depend on any particular numerical magnitudes of the five coefficients mentioned above.

The third proposition is of little importance, however, unless it can plausibly be expected that an increased level of income will actually produce a decline in the money supply below the level previously existing within a small number of years. To answer this question, we have to turn to evidence regarding the numerical magnitude of the factors involved; this will be examined below. Before the statistical aspect of the problem is considered, however, two further theoretical aspects require discussion.

Gradual Increase in Income

The preceding analysis has been concerned with one sudden increase in income which was then assumed to be maintained for some time. A somewhat different aspect of the same problem may now be considered. Let us assume a continuous rise in income. How, under the assumptions made, will the quantity of money vary? Specifically, what are the conditions under which, given expanding income, the money supply of one period can fall below the money supply of the preceding period (in contrast to the conditions under which it falls below the initial, pre-inflation money supply)?

The answer to this question can be derived from Chart 4. The top half of this chart repeats the relationship for the one-time increase in income. In the bottom half, income is shown rising by one step per time unit. At every step, the quantity of money initially rises correspondingly (the scales have been selected in such a manner that the rise in the quantity of money at each step shown on the chart equals the rise in income). But as the time period during which income remains at a given step passes, the quantity of money falls, for bank reserves are continuously drained off by the excess of imports over exports. From time moment 1 to moment 2, it falls by one fifth of a step, i.e., with the same slope as the money curve in the top half of the chart. During the next period, from moment 2 to moment 3, it falls by two fifths of a step—one fifth each for the first and second income step.7 In the next period it declines by three fifths of a step, etc. After income has risen for five time units, the decline in the quantity of money per unit resulting from the shift to the left of the supply curve just equals the rate of increase in the quantity of money resulting from the shift of the demand curve. The two forces balance; the quantity of money reaches its maximum. Thereafter, as income continues to grow at the same rate, the cumulative effect on the supply side of past growth in income exceeds the effect of current income growth on the demand side, and the quantity of money will decline.

Instead of by steps, the same reasoning can be presented by continuous curves. If income rises as a straight line, the quantity of money will increase at a decreasing rate, then reach a maximum, and decline thereafter. It can easily be understood on the basis of Chart 4 that the money curve in this case will reach its maximum after the same number of time periods that it takes the curve in the top half of the chart to decline to the initial level.

In summary, therefore, in the circumstances here postulated, a continuously increasing rate of income will lead first to an increasing, then to a decreasing, quantity of money. The maximum for the quantity of money will be reached after a period of time depending on exactly the same combination of five parameters as that found in an earlier section (pp. 401-4). Thus the period of time which must elapse before the money supply falls below its initial level in the single income increase case is exactly the period which must elapse before the money supply can fall below its immediately previous level in the continuous inflation case.8

Effect of the Rate of Interest on Income

In describing the process of changes in income and money over time, any possible effect of the rising rate of interest on investment or saving, and thereby on income, has been left out of account. This manner of treatment is not necessarily unrealistic. While the increase in the rate of interest will necessarily have some restraining effect on investment, it is quite likely that the accompanying increase in income will tend to stimulate investment.

It may be useful, nevertheless, to expand the analysis to cover the situation where, as a result of the rise in the rate of interest, investment actually declines (and/or savings actually increase) and, consequently, income will decline in spite of the persistence of autonomous factors of unchanged magnitude. For instance, government spending may be maintained at x million above the level of the original equilibrium situation; but the consequent persistent rise in the rate of interest may reduce private investment by y per year. While at first the annual rate of income will exceed the original level by x times the multiplier, it will decline to (x — y) times the multiplier after one year, (x — 2y) times the multiplier after two years, etc.

The effect of the expansion of the analysis can, again, be represented graphically by an extension of Chart 3. This is done in Chart 5; the mathematical deductions will be found in the Appendix.

Income, instead of remaining at its raised level, will now gradually decline until it approaches asymptotically the original level. The rate of interest will rise, not in a straight line and without limit but asymptotically approaching a maximum. This maximum will be such that the negative effect of the rate of interest on investment (plus the negative effect it has on consumption through increasing saving) will just balance the initial autonomous increase in expenditure. The quantity of money will decline, after its initial rise, and approach an asymptote below its base period level. The level of this latter asymptote will depend on the amount of autonomous investment and the ratio between the responsiveness of the demand for money and of investment, respectively, to the rate of interest.

As Chart 5 indicates, the general nature of the process for reasonably short periods of time is not greatly different from that shown in Chart 3. The point of intersection of the MO curve with the zero line may fall somewhat earlier or somewhat later. Even those instances in which the quantity of money returns to its base-period level at a later time do not affect significantly our earlier findings, since (a), within the plausible range of values for the various parameters, the lengthening of the time period is quite small; and (b), when the simpler analysis yields a time period of less than one year, the present, more complicated, analysis must also yield a period of less than one year, while for a time period of just one year the results of the two methods coincide.9

Statistical Measurements

The direction of the movement of the money supply in response to change in income has been found in the circumstances assumed in this study to depend on five coefficients and on time. Three of these coefficients—(1) the effect on the demand for money of a change in income, (2) the effect of a change in money on commercial bank reserves, and (3) the effect of a change in income on imports—are conveniently discussed together. They have in common the characteristic that marginal coefficients may be estimated on the basis of certain average ratios. The two elasticities are examined separately in later sections of this paper.

Coefficients Derived from Average Ratios

The analysis calls for coefficients reflecting certain marginal coefficients: (1) the marginal desire of the public to hold money as income changes, (2) the marginal desire (or obligation) of the banks to hold reserves as deposits change and the marginal need to provide currency as the supply of money changes; and (3) the marginal desire to import as income changes. These coefficients should be interpreted in the “partial” sense: they are to reflect the change in the dependent variable on the assumption that only the specified independent variable changes.

It is believed that estimates of sufficient accuracy for the present analysis can be derived on the basis of the two following assumptions:

(1) that the marginal coefficients concerned are reasonably close to the corresponding average coefficients; and (2) that the actual effects of changes in other variables (including changes in interest rates) are not so great as to make the observed values of the average coefficients vary widely over time.

If these two assumptions are accepted, it follows that the coefficients sought can be approximated by taking the observed average ratios of the variables concerned in each of the three cases.

For the first coefficient the empirical ratio of the money supply to national income (for a few countries, GNP) is taken (see Table 1, Column 1).

Table 1.

Ratio Coefficients for 38 Countries in 1952

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d = ratio of deposits to total money supply; f = ratio of commercial banks’ reserves to deposits.


Australia’s actual f may be made extremely high for increases in deposits, according to central bank decision. The combined ratio would then rise to a maximum of 1.1.



The second coefficient involves two steps: the ratio of deposits to the total money supply and the ratio of commercial bank reserves10 to deposits. If the former ratio is called d and the latter f, an increase in the money supply of M will involve a drain on the reserves of the commercial banks of (1 — d)M for the currency part of the increase, dfM for the deposit part of the increase, or a total of (1 — d + df)M = [1 - d(1 - f)]M (Table 1, Columns 2, 3, 4).11

Assumption (1) above may be open to some doubt with respect to the propensity to import (Column 5). Existing statistical studies almost generally show that the marginal propensity to import appears to be in excess of the average propensity to import. In other words, the income elasticity of imports—which is the ratio of the marginal to the average propensity to import—is generally found to be above 1. A comparison of 21 marginal propensities to import for 16 countries in the interwar period (for some of the countries separate measurements were made for the twenties and the thirties) with the corresponding average propensities yielded 7 cases of elasticities in excess of 2.0, 10 between 1.0 and 2.0, and only 4 below unity.12

These high import elasticities, however, are based on comparisons of real income and real imports. Much lower elasticities would be indicated insofar as changes in money income are due to price changes. With respect to the latter, the balance of trade expressed as a percentage of imports would probably worsen by less than the increase in the price level; i.e., the rise in money value of imports (plus any fall in value of exports) would be less than in proportion to the rise in money income.13 On the whole, therefore, the assumption of unitary elasticity of the demand for imports with respect to income, both expressed in terms of money value, would not seem to be too unreasonable. The figures in Column 5 of Table 1 have therefore been obtained simply by dividing imports by national income.

In Column 6 of Table 1, the three coefficients are combined in the manner in which they are relevant for our calculations. In terms of Charts 1 and 2, the figures in this column represent the ratio of the displacement of the demand curve for money to the displacement of the supply curve for money after one year. If this ratio is less than unity it means that, at equal interest elasticities of demand and supply for money, the quantity of money would fall below the initial position within one year after the beginning of a higher level of income. Conversely, these ratios provide a critical value for the ratios of the interest elasticities. Thus, for the first country in the table, Austria, the combined ratio is found to be .7. This can be interpreted as meaning that, if the interest elasticity of the demand for money is anywhere above .7 times the interest elasticity of the supply of money, the quantity of money (given the assumptions listed above about central bank neutrality, etc.) will fall below the initial position within a year after an increase in income.

Table 1 therefore gives information on the crucial question of the parallel or opposite movement of money supply and income only if plausible assumptions can be made regarding the ratio of the two interest elasticities and if, furthermore, the time is stipulated during which changes in income may be assumed to persist. It will be shown below that there seems to be evidence that in the United States, at least, the demand elasticity for money exceeds considerably the supply elasticity, their ratio being about 4 to 1 in the postwar period. There is no particular reason to believe that similar results might not be found for other countries. In Table 2, the results are summarized, assuming three alternative, more conservative, values for the ratio of the two elasticities, viz., 2, 1, and ½ For each value of the “combined ratio,” Table 2 enables us to estimate the period of time during which an increase in income would have to persist to lead to a decrease in the money supply. The table shows that on the first assumption, viz., the demand for money twice as elastic as the supply of money, 37 of the 38 countries (all except the United States) would show an opposite movement between the quantity of money and national income within a year, and 27 would show it within half a year. At the other extreme shown (which, of course, is not in any sense either a logical or an empirical extreme), where the ratio of the elasticities is the reverse, 15 of the countries would still show an opposite movement after a year, and 27 would show it after two years, had elapsed.

Table 2.

Estimates of Length of Time (in Years) Before Increase or Decrease in Income Would Lead to an Opposite Movement in Money Supply

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Based on data in Table 1, Column 6.

Ratio of “Interest Elasticity of Demand for Money” to “Interest Elasticity of Supply of Money.”

One qualification of these findings needs discussion. The elasticity of demand on the side of the public has been discussed in terms of a comparison of the relative advantages of liquidity (the holding of money) with its cost in the form of the interest foregone by not holding an interest-yielding asset. This comparison may not be the predominant factor in determining the elasticity of demand. For many business firms the cost of liquidity may rather be the interest to be paid on short-term borrowing from the banks; and for them the choice may present itself primarily in the form of a comparison of the advantages of short-term bank credit with its cost. This aspect of the interest elasticity of demand for money is particularly interesting because data are available which permit intercountry comparison of elasticities.

In general, it would seem reasonable to assume that in countries where the ratio is high the interest elasticity of demand for money will be higher (all other things being equal) than in countries where the ratio is low. For most countries this ratio in 1952 was well above that for the United States (Table 1, Column 7). On this score, at least, there appears to be no reason to fear that the transposition of an elasticity found for the United States would lead us to underestimate the critical period.

Elasticity of the Publics Demand for Money

In order to find the responsiveness of the public’s demand for money with respect to the rate of interest, we must attempt to isolate one of the factors determining the total demand for money. The primary factor determining this demand is usually believed to be the total value of business turnover, measured by some indicator such as the value of GNP. Here we want to abstract from this “income” factor in order to isolate the “price” factor. One possible procedure would be to attempt a multiple correlation calculation explaining movements in the quantity of money in terms of both an income and a price factor. This is the procedure followed by Tinbergen for the interwar period.14 By this procedure he found for the United States a very low elasticity with respect to the interest rate: a decline of $420 million (or about 1 per cent of the average amount outstanding during the period) in deposit money (demand plus time deposits) held by the public for every 1 per cent increase (e.g., from 3 to 4 per cent) in the short-term rate of interest. This figure seems extremely low on a priori grounds; and like so many price elasticities where the income elasticity is dominant, it is probably subject to a wide margin of error.

An alternative method of measurement therefore seems more appropriate. The essence of this method is to determine the income coefficient from other sources. It seems plausible that, at a given rate of interest, businesses and consumers would vary the cash balances they want to hold proportionally with their transactions. If a business turnover of $10 million per year requires for a particular firm an average cash balance of $1 million, it seems reasonable that if the business grows to $30 million, distributed over three firms, the desired cash balance should increase to $3 million. If it is reasonable to assume this proportionality more generally,15 then it would follow that the velocity of turnover of money at given rates of interest would be independent of the total turnover. The rate of interest would then determine the rate of turnover of the money supply, and a comparison of the covariations of these two variables would indicate the effect of the rate of interest on the money supply at a given level of GNP.

As will be seen below, a comparison of this sort turns out to be quite satisfactory as an approximate indicator of the sensitivity of the quantity of money to changes in interest rates in the United States in the last 30 years.16

Observed interest-velocity relationships in the United States, 1920-53

In Chart 6 the income velocity of circulation in the United States (defined as the ratio of GNP to money supply) is plotted for the years 1920-53, together with several interest rates. The interest rates used are the yield of 3-9 month Treasury bills, the rate on prime commercial paper, and the long-term government bond yield.

Chart 6.
Chart 6.

Income Velocity of Money Supply and Interest Rates in the United States, 1920-53

Citation: IMF Staff Papers 1955, 002; 10.5089/9781451930832.024.A002

1 Yield on long-term government bonds: 1920-42, partly tax exempt; 1942-53, taxable.2 Rate on prime commercial paper, 4-6 months.3 Average yield: 1920-30, 3-6 month Treasury notes and certificates, plus 0.25 for “linking”; 1931, Treasury bills, average rate on new issues.4 Average yield: Treasury bills, average rate on new issues, plus 2⅙ per cent.5 Money supply data: June 30, 1920-23; average end June (June double weighted), end December, and end December of previous year, 1924-42; average of monthly data, 1943-53. Series linked.

The use of several interest rate series rather than a single “representative” series is necessary because of the separation of the various financial markets. For example, business borrowers will build up or reduce their working balances of money in response to changes in the cost and availability of short-term commercial credit. Investors will build up or reduce their idle balances according to the rate of interest on securities. Within the security market, both the long-term and the short-term sectors have to some extent distinct clienteles; the movements of both classes of interest rates ought therefore to be considered. Thus it is necessary to have available several interest series for judging the responsiveness of velocity to the cost of borrowing or the income from lending.

Chart 6 reveals a good correspondence in the year-to-year movements of the velocity of circulation and interest rate series: a rise in interest rates tends to be accompanied by a rise in velocity, i.e., by an economy in the holding of money.

There are a number of instances of poor correspondence between the interest and the velocity series. Several of these, however, are attributable to special factors which are irrelevant in the present context. In 1920 and 1921, the postwar speculative boom and collapse presumably distorted the interest rate-money supply relationship. The lack of response between 1927 and 1928 and the very small response between 1928 and 1929 of the velocity index to the sharp rises in interest rates are due to the somewhat limited definition of the base taken to measure this velocity. In 1928, and especially in 1929, as a result of the rise in stock market speculation, there was a great increase in the volume of those transactions which were unrelated to the size of GNP; and speculative transactions require some quantity of money for their execution. If the measure used for the total volume of transactions had contained an allowance for the abnormal rise in purely financial transactions, the rise in interest rates would have been reflected in increased velocity figures.17 The correlation between interest rates and money supply broke down during the period between 1931 and 1934, but this failure of the relationship is again explainable by the severely disturbed conditions of the period. Special conditions also provide the basis for the breakdown of the relationship during the period 1942 to 1946: omnipresent controls modified the relationship between the use of money and the interest rate.18

The data on interest rates and the ratio of money supply to GNP shown in Chart 6 are reproduced in scatter diagram form in Chart 7.

Chart 7.
Chart 7.

Relation Between Money Demand and Supply and Interest Rates in the United States, 1922-53

(Logarithmic verticle scale)

Citation: IMF Staff Papers 1955, 002; 10.5089/9781451930832.024.A002

Choice of representative rate of interest

To make possible measurement of the interest elasticity of demand for money by the scatter diagram technique, a single rate of interest had to be selected from Chart 6 to be plotted against desired cash holdings. The problem thus arises of finding the one rate most nearly representative of all interest rates. A rate on government securities is probably more appropriate than any rate on private loans or securities, for fear of the debtor’s insolvency must have caused a varying risk-charge factor to have influenced the rate during the depression of the thirties even with respect to prime quality loans.19 In addition, some forms of private lending are carried out to a large extent on the basis of variations in the degree of “credit rationing” rather than of allocation via the price mechanism. On the commercial loan market the banks are in the position of monopolistic competitors. Each bank recognizes the danger that raising interest charges will drive some of its clients to other banks while lowering charges will be matched by competitive reductions of charges in other banks. This consideration, plus the customs of loyalty to longstanding clients, etc., makes too frequent interest adjustment an undesirable method of changing the volume of bank loans. But the same conditions which force banks to alter the amount of business loans outstanding will also, ceteris paribus, cause them to alter the amount of government securities, etc., held. And the market for government securities is not monopolized by the banks; other investors participate in it, and the interest rates determined in it are highly sensitive to shifts of demand. Banks therefore adjust their holding of government securities (a large fraction of their total assets) without regard to the effects of their purchases or sales on the prices of these securities; thus government security yields are likely to be as good an indicator of the price-cum-availability of bank credit for business as the rate actually charged on these credits. And since business cash balance holdings must vary in response to the availability of credit just as they vary in response to the cost of credit, government security yields should be pertinent not only for investors who shift funds between securities and cash balances but also for borrowers who can shift between cash holdings and debts. For these two reasons, yields of government securities appear in general to be the better indexes of interest rates.

Among them a selection has to be made between long-term and short-term rates to find the more desirable single representative measure of the yield of capital. The short-term rate appears to be the better measure of the role of capital costs as a factor in desired cash holdings: in contrast to idle cash or short-term securities, the yield of long-term securities is significantly affected by the possibility of changes in the capital value of the security, associated with future changes of the interest rate. Thus, insofar as funds can move between the two security markets, the interest yield on short-term securities will tend to move parallel to the total yield (interest plus capital gain factor) anticipated on long-term securities. Hence movements in the short-term rate of interest are in this respect more representative of movements in the true yield on long-term securities than the latter’s own interest yield.20 And they will clearly be more representative of yields in general than will the long-term interest yield. For these reasons the interest rate on short-term securities has been selected.21

In Chart 7 the rate on short-term government securities has therefore been plotted in scatter diagram form against the desired money supply. The desired money supply figures are derived by multiplication of the actual ratios of money supply to GNP (the reciprocals of the series in Chart 6) by the 1953 GNP, so that the whole presentation of money supply against the interest rate is made in terms of an income level equal to that of 1953.22

The scatter of points in Chart 7 reveals two separate interest-demand curves for money: a curvilinear relationship for the interwar period having relatively low elasticity for very low interest rates, and a linear postwar relationship showing both a higher elasticity of demand and a higher level of demand for money.23

The postwar relationship is very convincing, its only weakness being the absence of a reversal in the direction of both series over time. This deficiency is partly compensated, however, by the presence of two pairs of successive observations (1948-49 and 1951-52) of almost no change in the interest rate, both of which were accompanied by stability of the money supply-GNP ratio.

The curve fitted to the prewar dates is somewhat less satisfactory, for it has been fitted to two widely separated clusters of observations: 1922-30, all of which show interest rates over 2.4 per cent, and 1933-42, for all of which the rate was 0.5 per cent or less. In actuality, therefore, there may have been two separate interest-demand relationships in the interwar period: one for the twenties (which is rather like the postwar relationship) and a much less elastic one for the thirties. Of course, the fact that the demand curve for money may shift over time is no limitation of the validity of the theoretical relationships between the direction of money supply and income changes found in this paper. All that is necessary for the purposes of this study is the existence of some relationship between the interest rate and the desired money supply.24

Elasticity of Banks’ Supply of Money

The analysis of the banks’ supply elasticity of money runs along the same general lines as that of the public’s demand for money. It has been shown that the public changes its cash reserve ratio (which is the inverse of the velocity of circulation of money) in the light of the rate of interest. It is plausible to assume that banks operate in a similar manner. Like the public they will want to balance the convenience of a high reserve ratio against a low rate of interest, the inconvenience and risk of a lower ratio against a higher rate of interest.

The larger part of the reserves of the banking system is fixed by the prescribed reserve ratios of the Federal Reserve System. The “free” part of reserves that would be relevant in a comparison with interest rates would, therefore, be reserves held in excess of legal requirements.

But these excess reserves will have been created to some degree out of funds borrowed from the Federal Reserve System by particular banks which would otherwise have inadequate reserves. Since indebtedness to the Federal Reserve System is considered undesirable, reserve balances secured through the medium of such debt ought not to be included when excess reserves are being measured. Therefore, “free” reserves which are relevant in a comparison with interest rates should be interpreted as meaning excess reserves minus net borrowings from the Federal Reserve System.

Deflation of excess reserves by deposit liabilities

The definition of these net excess reserves is made more closely relevant to the interest rate problem by one further modification of the data. Clearly, net excess reserves of, say, $1 billion for all member banks provided a higher degree of liquidity when deposit liabilities were $30 billion (in the thirties) than they did with total deposit liabilities at $144 billion (in 1953). This change in conditions can be allowed for if the need for net excess reserves is taken as proportional to the total of deposit liabilities—a procedure justified logically by the fact that reserves are desired as a cushion between variations in actual reserves relative to required reserves. Other things equal, these variations are proportional to the volume of deposit liabilities; larger deposits imply larger volumes of transactions by depositors and therefore greater (absolute) changes in the banks’ reserve positions, with the consequence of larger lines of credit from the Federal Reserve System and larger needs for excess reserves. In the following analysis of the banks’ supply of money, therefore, the relationship between the rate of interest and banks’ excess reserves has been derived from the observed data, with actual net excess reserves (total excess reserves of member banks less borrowings from the Federal Reserve System) expressed as a ratio to the existing total deposit liabilities.25

Observed interest-reserves relationship

In Chart 8 the data for the ratios of member banks’ net excess reserves to deposit liabilities are plotted in scatter diagram form against the short-term government security rate (yield of Treasury bills). By use of a logarithmic scale for interest rates, the chart makes possible observation of the effect on excess reserves during the thirties when the rate varied between the very low levels of 0.01 per cent and 0.5 per cent, and it is found that a good linear relationship can be fitted to the entire range of points over the period 1920-53.26 (As in the case of demand for money discussed above, the years 1920, 1921, 1931-33, and 1942-46 were disregarded in the fitting of this relationship.)

Chart 8.
Chart 8.

Relation Between Banks’ Net Excess Reserves as Percentage of Deposit Liabilities and Interest Rates in the United States, 1922-531

(Logarithmic verticle scale)

Citation: IMF Staff Papers 1955, 002; 10.5089/9781451930832.024.A002

1 Reserves data are averages of daily figures; annual deposits are June 30 data; 1947 reserves include some Treasury bill holdings which were freely convertible into reserves without cost.

Reliability of observed interest-reserves relationship

The reliability of the relationship fitted might be questioned because the data used cover more than 30 years—a period during which financial institutions and financial practices would be expected to change. The fit of the curve may be poor, it is true, at its lower end, e.g., for interest rates below 0.12 per cent, but such extremely low rates are not likely to recur, and the unreliability of the relationship in this region is therefore not a serious matter. In the higher ranges of the curve, the experience of the late forties and early fifties tends to corroborate that of the twenties; although interest rates had remained well below the levels of the twenties for a period of 20 to 30 years, when they returned to nearly these levels the movement traced out almost exactly the preexisting reserve-interest relationship.27

The corroboration of the relationship of the twenties by recent annual data is reinforced by a study of quarterly data for the two years showing the highest interest rates in the period following World War II. Chart 9 shows quarterly movements in net excess reserves, the Treasury bill rate, banks’ customers’ loan rate, the commercial paper rate, and the 3-5 year government bond yield. Net excess reserves, which were approximately constant during 1951, declined continuously during 1952, then rose continuously through the first quarter of 1954. The interest rates moved as expected, rising in 1952 and falling in 1953. The peak in interest rates was, however, lagged behind the minimum excess reserves, for the highest rates were reached only in the second quarter of 1953. Thus in relating interest rates of this period to net excess reserves on a quarterly basis it is necessary to lag the rate two quarters behind the net reserve position.28

Chart 9.
Chart 9.

Banks’ Net Excess Reserves and Interest Rates in the United States, Fourth Quarter, 1949-Fourth Quarter, 1954

Citation: IMF Staff Papers 1955, 002; 10.5089/9781451930832.024.A002

* Federal Reserve discount rate raised one fourth of 1 per cent† Federal Reserve discount rate reduced one fourth of 1 per cent.

When the reserves for the fourth quarter of 1952 (deflated by deposit liabilities) are thus plotted against the interest rate for the second quarter of 1953 (1952-iv in Chart 8), the interest-reserves relationship at the time when the postwar interest rate was highest is found to be very close to the relationship in prewar years, and even closer than the relationship indicated by postwar annual data. This point is perhaps particularly significant because it carries the postwar series of interest rate observations closer to the series of the twenties than any other recent observation, strengthening the case for the continuing validity of the prewar relationship.29

Supply curve of money derived from banks’ interest-reserves relationship

The regression line based on this scatter of interest-reserve points indicates that a given proportional change in the short-term interest rate tends to affect the desired net excess reserves/deposit liabilities ratio by the same absolute amount, whatever the value of the initial interest rate.

From this relationship it is easy to derive the effect of any change in the interest rate on the banks’ supply of deposits and—assuming that currency in circulation varies proportionally with deposits—on the total money supply.30

The banking supply curve for the money supply derived in this manner and defined (with respect to banks’ legal reserve requirements, total and component deposit liabilities, currency in circulation, etc.) in terms of the situation of 1953 has already been shown above (Chart 7) super-imposed on the demand curves derived in the previous section. This supply curve is found to have a fairly constant elasticity (between .07 and .08) with respect to the interest rate.

Ratio of public’s interest elasticity of demand for money to banks’ interest elasticity of supply of money

With the evidence of the demand and supply elasticities for money derived for the United States in the two preceding sections, it is now possible to confront the critical value for the ratio of the two elasticities derived in Table 1 above with an empirically determined figure.

The ratios of the demand to the supply elasticities of the curves plotted in Chart 7 above vary between 2½ and 5 when the postwar demand relationship is used and between 1 and 2 when the prewar demand relationship is used, with higher interest rates in the latter case and lower rates in the former case showing higher values for the ratio.31

If the postwar relationship is accepted as valid for the future, it is found that even in the United States changes in income might be expected to result after one year in changes in the money supply of opposite sign: the actual ratios of the elasticities fall between 2½ and 5 and include the critical value of 4.2 found for the United States in Table 1. This would not, however, be true on the basis of the prewar demand elasticity.

It is, of course, not possible to apply to other countries the ratios of elasticities found for the United States. Both demand and supply elasticities must vary from country to country and their ratio may vary even more. If it is possible at least to assume that the minimum value for the ratio in most countries will be no less than one fourth of the postwar U.S. ratio (i.e., approximately over unity), then it can be concluded that more than half of the countries recorded in Table 1 should experience opposite changes in money supply and income in a year or less, for 27 of the 38 countries covered have critical values for the elasticities ratio of unity or less. Fifteen countries—including the Netherlands, all Scandinavia, the United Kingdom, and three of the four developed Commonwealth countries—could, in circumstances where the original assumptions about central bank neutrality, etc., are appropriate, show opposite changes in money supply and income in a year or less at a ratio of the elasticities as low as one eighth of that of the United States.

Whether the U.S. ratios can be extrapolated to other countries in even so conservative a way as has just been done remains an open question. However, the data for the United States provide at least a demonstration of the fact that the ratio of the elasticities can be quite high and that it is therefore plausible to suppose that opposite changes in money supply and in income may occur in many countries.


I. The General System—No Central Bank Financing

The analysis postulates an initial situation in which there is balance between the money supply and national income at given rates of interest, and foreign trade is in balance, exports equaling imports and reserves remaining unchanged. All variables are measured as deviations from this equilibrium situation.

We then use the simplest assumptions possible. The demand for money (MO) depends on national income (Y) and the rate of interest (r):


The supply of money by the banking system depends on its reserves (R) and the rate of interest:


Consumption (CO)32 and imports (M) are related to changes in national income (Y) by the marginal propensities to consume (c) and to import (m):


Exports are assumed constant, so that


Any autonomous I will then lead to a change in income of


and this will lead to a change in commercial banks’ reserves equal to the annual increase in imports multiplied by the period t (in years) during which the changed level of Y persists:


Hence (1.2) becomes:


Equations (1.1) and (1.5) suffice to express both r and MO in terms of Y:


All coefficients are defined as positive. Hence a change in Y will lead to a change of r in the same direction. But the sign of the effect on MO is not clear. The denominator (δ + β) is positive. But the numerator is of uncertain sign. For t = 0, it is positive; for sufficiently large values of t, it must become negative.

The number of time units that it will take for MO to return to zero is found from the numerator of (1.7):


For smaller time periods, MO will deviate from its original position in the same direction as Y; for longer time periods, the deviations of MO and Y will be in opposite directions.

II. Central Bank Financing of Autonomous Investment

Let gI (0 < g <1) be the amount by which central bank credit is expanded (directly or indirectly) to finance the additional autonomous expenditure, I. As a result, commercial banks’ reserves will on this account increase by gI per unit of time. Accordingly, (1.7) becomes


or, using (1.6):


This leads to corresponding changes in (1.9) and (1.10):


In the special case where the investment is fully financed by the central bank (g = 1), (2.3) simplifies to:


This shows that under these assumptions the rate of interest must (provided c < 1), with time, fall below the initial rate—an experience not unusual with inflationary government deficit financing.

Under the same assumption (g = 1), the quantity of money must go up for all values of t (provided c < 1):


It follows from (2.4) that the condition for a turning point in the quantity of money, i.e., for MO to become negative for large enough values for t is:


This inequality means that the loss in bank reserves (the import surplus) is not fully covered by the central bank.

III. Different Interest Elasticities of Demand for Currency and Deposits

The system becomes somewhat more involved if different interest elasticities of demand are allowed for currency and deposits. It seems most reasonable to develop this case on the extreme, but perhaps not unreasonable, assumption that elasticity of demand for currency equals 0.

We can then write the demand equations for deposits (D) and currency (C):33


The supply equation for deposits would be:


R, the level of reserves of the commercial banks, will be affected in two ways: (1) initially, by the increase in C due to the autonomous rise in Y; and (2) gradually over time by the imports occasioned by the higher level of Y. The process set off by the latter cause is in no way different from that described by the equations in the previous section. Therefore, we can concentrate here on the starting point of the downward process, at time t = 0, which will have a lower MO than the starting point in Section I of this Appendix. Thus not only will MO = 0 be reached in a shorter time than derived above, but it also does not seem impossible that MO will fall below its previous equilibrium level even at t = 0. At that time:


Hence the supply equation for deposits becomes:


Combining this with (2.1), we find:


When (2.6) is combined with (2.2), the total quantity of money at time 0 is found as:


The sign of this is uncertain. Clearly (αD + αCγD) > (αD + αC). But also βDδD+βD< 1. We therefore find that whether the initial money supply (after income has increased but before imports have significantly reduced foreign exchange holdings) is greater or smaller than the money supply in the equilibrium situation just preceding will depend on:

  • (1) The (marginal) ratio of currency to deposits, αC ÷ αD

  • (2) The banks’ reserve ratio against deposits, of which γD is the reciprocal; and

  • (3) The ratio of the demand and supply elasticities.

To take an example: For αCD = 1:3 and γD = 4, the money supply corresponding to an increased income at time zero would be >0 for βDδD+βD<47, i.e., for βDδD<1.

There seems no a priori reason why this condition need be fulfilled; and the paradox may thus be true that an increase in the demand for money would, if the central bank did not compensate at least part of the currency drain, lead at once to a reduction in the quantity of money.

In that case, an increase in income would at once34 lead to a reduction in the money supply; and it would do this in an open as well as in a closed economy.

IV. The Effect of the Rate of Interest on Income

The dynamic system discussed on pages 408-10 above is constructed from equations (1.1) through (1.5) (with the modification that all variables are “dated” with the subscript t) plus two additional equations:


where Ia is the autonomous change in investment and p reflects the responsiveness of investment in general to the interest rate;


is the dynamic factor in the system, the only equation in which a lagged variable appears.

From these equations, first degree difference equations can be derived, showing the movement of the quantity of money, income, and the rate of interest over time.35 The equation for the quantity of money can be solved to find the value for t at which MO will have returned to its base-period level (zero); see Charts 3 and 5:


There is an important similarity between (4.3) and (1.11). If αδ < βmγ, it takes less than one year for MO to go to zero according to both sets of equations; if αδ = βmγ, it takes exactly one year; and if αδ > βmγ, it takes more than one year. In other words, if the simpler system which did not take account of the effect of the rate of interest on investment showed a period of less than a year for MO to cut the zero line, then the more elaborate system cannot possibly show a period in excess of one year. It would appear, moreover, that the numerical difference between the more elaborate curvilinear solution and the simpler linear situation is quite small for all plausible values of the coefficients. For instance, assuming α = 0.4, γ = 2, m = 0.25, c = 0.85 (the first three values reflecting intermediate values found in Table 1, the latter a plausible guess for the marginal propensity to consume), we find the alternative values for β, δ, and ρ given in Table 3.36

Table 3.

Time (in Years) Required for Opposite Movements in Money and Income

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It may be added that the figures in this tabulation (as well as many other alternative calculations) consistently show that the curvilinear result for t of (4.3) is always higher than the straight line result for t of (1.11) when t < 1, and lower when t > 1; but no mathematical deductive proof has been found to show that this must necessarily be so.


Mr. Polak, Deputy Director of the Research Department, is a graduate of the University of Amsterdam. He was formerly a member of the League of Nations Secretariat, Economist at the Netherlands Embassy in Washington, and Economic Adviser at UNRRA. He is the author of An International Economic System, and of several other books and numerous articles in economic journals.

Mr. White, economist in the Finance Division, received his undergraduate and graduate training at Harvard University. He has contributed papers to several economic journals.


The Netherlands Bank, Report for the Year 1951, p. 52. Certain qualifications are spelled out in more detail in the Report for the Year 1952, pp. 49-50.


Short-term capital movements of a “balancing” character are also assumed to be absent—a simplification that is justified either by the prevalence of controls over capital or by the fact that the influence of a worsened balance of payments will reduce confidence in the currency and thereby counter the influence of concomitant increases in interest rates.


See Appendix, Section II.


Defined as the ratio of the change in the trade balance to the change in income by which it is caused (see page 411).


For example, assume that an expansion of the money supply of 5 units consists of 4 in deposits and 1 in currency; if the legal plus conventional cash reserves against deposits are 25 per cent, there will be a rise in required reserves of 1. At the same time, the associated withdrawal of 1 unit of currency from the banks will use up 1 unit of bank reserves; allowance for this loss of reserves is made most conveniently by treating it as being simply a 100 per cent “reserve” requirement against currency “liabilities.” On this basis, the total reserve requirement for 5 units of money is 2. Therefore, if gold and foreign exchange reserves decline by 2, the banks’ supply schedule is moved to the left by 5.


The same elasticity of demand is assumed for currency as for deposits. While in fact the desire to hold currency is probably less responsive to changes in interest rates than the desire to hold deposits, it is usually considered the legitimate function of central banks to reimburse commercial banks for any loss of reserves resulting from an “internal currency drain” associated with an abnormal rise in the ratio of currency to deposit money; the central bank here is assumed to operate according to this practice. If a lower interest elasticity of demand for currency were not so offset, the decline in the money supply in response to an increase in income would tend to be much more rapid. This case is treated in Section III of the Appendix.


In comparison with the situation of the first step, the income level of the second step is twice as much above the initial equilibrium level, so that the import surplus is twice as great and hence the loss of reserves and the consequent leftward shift of the supply curve are twice as great.


The appearance of a maximum for the quantity of money is accelerated if income increases at a decreasing rate, and delayed if income increases at an increasing rate.


Numerical examples of (a) and a mathematical proof of (b) are given in the Appendix.


The present study considers only “cash” reserves (currency, central bank deposits, etc.). While a number of countries have very high commercial bank reserve requirements, with most of the reserves allowed (or required) to be placed in government securities, it is assumed that the government securities to be held as reserves are acquired or sold by the banks in dealings with the public, with other banks, or sometimes, with the government. Only where the central bank or government provides the securities as needed and holds the monetary proceeds of the transaction idle would the government security component of reserves have to be included.


It will be noted that the ratios for f in Column 3 of Table 1 vary widely, from as low as .04 for Japan to as high as .70 for Honduras. There may well be reason to doubt the significance of either the very low or very high ratios. Very low ratios are probably an indication that the definition of reserves used for the particular country does not adequately reflect all the assets that are kept—whether legally or conventionally—as reserve requirements. A very high ratio may reflect the inclusion in reserves of certain assets which do not in fact represent first line liquidities.

In order to evaluate the effect of the use of possibly unrealistic values for f in the calculations, alternative calculations were made for all countries, based on f = .10. It was found that this alternative value for f did not affect the value for the combined ratio (Column 6) for most countries, and in almost all other cases changed it only very slightly. The most important change found was for New Zealand, where the combined ratio would fall from .6 to .3 if a value for f of .10 were substituted for the value of .39 in the table.


For this comparison, see J. J. Polak, An International Economic System (London and Chicago, 1954), Synoptic Table. Figures are not given in the source.

Similar high elasticities were also found by T. C. Chang, “International Comparison of Demand for Imports,” Review of Economic Studies, Vol. XIII, No. 2 (1945-56), table, p. 64. Some of Chang’s findings, however, may not be fully comparable since they represent employment rather than income elasticities.


Unit price elasticity of the balance of payments would require that at least either the country’s import demand or the foreign demand for its exports be elastic; but in the fairly short run considered in this study both elasticities may well be below unity.


J. Tinbergen, Business Cycles in the U.S.A., 1919-1932 (League of Nations, Geneva, 1939), pp. 100-101.


Professor W. J. Baumol (in “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics, November 1952, pp. 545-56) has shown that on certain simplifying assumptons an individual business minimizing its cost would vary its transactions cash holdings in proportion to the square root of the value of its transactions, rather than in proportion to the value of its transactions. This derivation is not, however, directly applicable to a comparison of total cash holdings to total transactions, for two reasons:

(1) The large short-run fluctuations in GNP with which we have to deal are primarily price fluctuations. When prices generally change, it seems reasonable to assume that Baumol’s “broker’s fee”—the administrative and psychic cost involved in changing one asset for another—would change proportionally. If this assumption is made, Baumol’s formula shows that the cash holdings of an individual would vary proportionately to the general price level, and not to its square root.

(2) A considerable part of the change in real GNP, especially over the somewhat longer run, must be due to an increase in the number of businesses to which Baumol’s formula does not apply.


The relationships found were checked afterward by multiple correlation calculations in order to make sure that they were not spurious in character.


The “rate of turnover of demand deposits,” which moves closely in proportion to the figures used here for the velocity of circulation in other years, rose markedly above it in 1928 and 1929.


The rise in Treasury bill rates from 1940 to 1941 was caused at least partly by the discontinuance of their tax exemption privilege; if that was the sole cause of the rise, then 1940-41 was also a case of nonconformity.


These extra risk charges are, it is true, on the same footing with the “pure” interest charge as factors in the borrower’s decision to borrow. However, disregard of this relationship is partly justified on the ground that long-term borrowing is not generally carried out to enlarge cash balances relative to the level of transactions and long-term borrowings are not so easily repaid when the interest rate rises and cash holding is (apparently) made relatively costly. As for short-term borrowing, another consideration presented below justifies neglect of the actual cost from the borrower’s viewpoint


An obvious instance of this relationship is provided by the movements of the long-term rate of interest during the thirties. The short-term rate fell precipitately during the early years of the decade, but the long-term rate’s decline was slowed by the current opinion that it would not fall any further (and might instead rise) because of the “lowness” of its existing level. Only as the drop of the short-term rate continued and the long-term rate failed to show any signs of rising did investors accept the likelihood that the “equilibrium” value of the long-term rate was moving downward; and only as this readjustment of outlook occurred could the long rate follow after the short rate. Hence, as discussed above, this gradual downward shift probably did not reflect a decline in the (anticipated) total rate of return on long-term capital toward the level of the return on short-term capital. Since the anticipated capital loss component of the return was declining, simultaneous reduction of the interest rate component was necessary.

It is interesting to note that if a declining trend is eliminated from the long-term interest rate series for the period 1934-40, the adjusted series conforms very well with the short-term interest rate series and the velocity series. (The correspondence found is even more striking when a 3-5 year government security interest rate is adjusted for trend.)


A money demand relationship has been derived with the use of the long-term business bond yield (H. A. Lantane, “Cash Balances and the Interest Rate—A Pragmatic Approach,” Review of Economics and Statistics, November 1954, pp. 456-61). A high correlation is found, although in terms of year-to-year movements the relationship is inferior to the one here developed.


A slightly different method of determining desired cash balances has been proposed (J. Tobin, “Liquidity Preference and Monetary Policy,” Review of Economics and Statistics, February 1947, pp. 124-32, and November 1948, p. 316). This method distinguished two components of the demand for money: transactions (active) balances (needed for turning over the GNP) which are proportional to GNP and independent of the interest rate, and speculative (idle) balances which are independent of the level of income and are a function of the interest rate (and possibly of the value of total wealth).

This method differs from the one used above, which assumes that transactions and speculative balances are each functions of both the interest rate and the level of income. The alternative method has merit, but it is probably extreme in assuming that the volume of idle money desired is determined only by the interest rate and is not affected by the level of current income; the willingness to hold idle balances, thereby surrendering current income (in the hope of future capital gains or avoidance of future capital losses or merely to avoid the inconvenience of making investments), is closely related to the willingness to make savings; idle balance holdings should therefore vary with the current income level.


Because of the extreme lowness of interest rates in the thirties, the magnitude of the actual percentage variations would have been concealed by an arithmetic scale. Therefore the interest rate is shown in Chart 7 on a logarithmic scale.

For reasons presented above, the data for years of abnormal conditions—the years immediately following World War I, the years of U.S. participation in World War II, and the early thirties—have been disregarded in the fitting of these curves.


It might be argued that the observed relationship represents only the coincidence of two factors: improving economic conditions cause (1) use of entrepreneurs’ idle balances, thus causing velocity to rise, and (2) rising demand for credit producing rising interest rates. But even if such covariation (rather than correlation) is the actual relationship, it is sufficient for the purposes of this study, which requires only that given rises in interest rates accompany known amounts of economization of cash balances, etc. In any case, the fact that in 1927 (and even in 1924) velocity behaved in the expected manner when interest rates were changed independently of internal economic developments is evidence that the observed relationship is more than mere covariation. (Interest rates were reduced despite stable economic conditions because of an inflow of foreign capital and because of the authorities’ desire to assist European countries in their efforts to restore and maintain the gold standard in the face of capital movements to the United States; the inflow was itself responsible for some reduction in rates since it increased bank reserves, and Federal Reserve policy was altered so as to depress rates still further.)


It seems unnecessary to make a further adjustment for the height of the legal reserve ratio on the ground that excess reserves are held, in large part, to meet potential needs for legally required reserves. The higher the reserve ratio, the smaller is the reduction in a bank’s assets made necessary by any withdrawal of deposits: reserves drop by 100 per cent of the deposit withdrawal, but legally required reserves drop by larger fractions of that amount, the larger is the legal reserve requirement, so that the drop in reserves relative to required amounts is smaller as the reserve requirement is larger. More important, the amount of reduction in a bank’s earning assets which would be made necessary by a net drop in reserves is obviously smaller as the reserve ratio is higher. Hence, insofar as excess reserves are maintained as a cushion against sudden enforced liquidations of earning assets, the need for them is smaller, the higher is the legal (or conventional) reserve ratio. On the other hand, insofar as excess reserves are maintained by banks in anticipation of advantageous possibilities for expansion of earning assets, the higher reserve requirement makes necessary larger excess reserve holdings. The net effect from these counteracting factors probably favors smaller excess reserves for higher reserve requirements (since enforced curtailment of loans, etc., is probably more feared than loss of opportunities for particularly advantageous loan expansions), but the net balance between the two effects is unknown and probably small.


This chart is similar to one in Tinbergen, op. cit., p. 85, which compared the interest rate and absolute amounts of net excess reserves in the twenties and part of the thirties. That study indicated practically infinite elasticity of demand for excess reserves at the low interest rate levels of the middle thirties. This finding would not have been made, however, if the interest rate had been plotted on a logarithmic scale, as in Chart 8.


No appreciable noncomparability results from the fact that Treasury bill interest was taxable in the period following World War II but nontaxable in the twenties; tax rates were very low in the latter period so that the tax exemption feature had little influence on the level of bill yields.

The taxable bill rate for 1941, however, does require lowering if it is to be compared with the nontaxable bill rate of the thirties, for taxes were fairly high in 1941.

Note, however, that the (near) homogeneity of the Treasury bill rate series does not prevent variation in the cost (in terms of foregone interest) of holding idle money which results, even under constant interest rates, from variations in the level of income taxes.


Introduction of this lag does not imply a breakdown in the interest-reserves relationship. Borrowings from the Federal Reserve System are customarily used as a temporary means of postponing liquidation of earning assets when excess reserves have fallen. The borrowings are intended to make possible a temporary reconstitution of (gross) excess reserves to permit the pre-existing volume of assets to be reduced gradually so that capital losses may be avoided and commercial customer relations need not be disturbed.

This is what happened in 1952 and 1953; excess reserves gross of borrowings were held fairly stable during 1952, borrowing being relied on to make possible retention (and even expansion) of earning assets. But beginning with the end of 1952, government securities were gradually liquidated so that total assets fell (with part of the resulting additions to excess reserves being used for retiring Federal Reserve loans). And since rises in interest rates accompanied the asset liquidation of this period, rising rates coincided, temporarily, with rising net excess reserves.

The existence of as long a lag as six months in the appearance of the excess reserves-deposits relationship would make findings like those of Table 2 unreliable when the critical time periods discovered were under one year. However, the existence of such a lag need not be the rule. Monthly data presented by Tinbergen (op. cit., p. 85) show that during all of the twenties the lag was very short.


The rising rate-falling reserves observation of 1951-53 may be part of a complete cycle, since reserves rose and interest rates fell in 1953. The end of the cycle may be represented either by 1953-iii reserves with interest rates lagged to 1954-ii, or by the unlagged data of 1954-i or 1954-ii. In either case, the interest rate is much lower than what the actual level of reserves and the assumed interest-reserves relationship would justify. Special factors—in particular a strong expectation that banks’ excess reserves would be shortly increased via a reduction in legally required reserves (an antideflationary measure)—have been offered in banking circles as responsible for this situation.


Several additional simplifying assumptions are made: any changes in deposits associated with the fairly short-run changes in income or balance of payments under investigation in this paper affect demand deposits only; within the banking system, they affect only deposits of member banks of the Federal Reserve System. The latter assumption is necessary because of the variability of the reserve requirements of nonmember banks. (It should not be a very damaging assumption, however, because only 13 per cent of demand deposits are found outside of member banks.) A similar problem arises over the distribution of changes in deposits among the three classes of member banks which have differing legal reserve requirements and somewhat different interest-desired excess reserve relationships (Chart 8 being only the observed composite relationship). It is necessary to assume that the distribution of such changes conforms to a reasonably stable pattern. Banks’ holdings of currency (“vault cash”) were taken to be a constant ratio to deposit liabilities—as was demonstrated by the data. Finally, those liquid “reserve” holdings in the form of deposits with other banks were ignored. This is justified for the reasons (1) that the adjustments of this form of liquidity to the interest rate have been more or less in step with the adjustments of net excess reserves, and (2) interbank deposits have, in effect, zero legal reserve requirements and hence do not absorb much loan-making capacity.


The prewar elasticity ratio falls below unity for interest rates below 0.3 per cent, dropping to a minimum of 0.5 at an interest rate of about 0.02 per cent. These interest rates are abnormally low, however, and the low ratios associated with them can probably be ignored.


The symbol, C, used in Section III of the Appendix, stands for currency.


The subscripts C or D indicate whether the coefficient applies to currency or deposits. The coefficients in this section are related to those in the previous section as follows:

αD + αC = α

βD = β

γD and δD are larger than γ and δ because the former coefficients are determined only by the expansion in deposits on the basis of reserves, while the latter also make allowance for the corresponding currency drain.


Leaving out of account various institutional time lags; e.g., the need for currency may be somewhat lagged behind the need for deposits, as described by R. G. Hawtrey in The Art of Central Banking (London and New York, 1933).


These operations were carried out by T. C. Liu with the assistance of H. S. Cheng, both members of the staff of the International Monetary Fund.


Since (4.3) is of zero degree in the three interest coefficients β, δ, ρ the absolute value of these coefficients does not affect the results. The use of the numbers 1, 0.5, and 5 (in the last entry) on the first line reflects therefore only an assumption on the relative magnitudes of the coefficients, viz., that the demand for money responds twice as much (in billions of dollars) to a given change in the interest rate as the supply of money, and that the annual rate of investment responds five times as much, again in billions of dollars, to changes in the interest rate, as the demand for money. Since β and δ both relate the quantity of money and the rate of interest, the ratio of the values assumed for these two coefficients represents also the relative elasticity of the demand and the supply of money. But since the annual rate of investment is in the order of half the value of the money supply, the assumption β = 1, ρ = 5 implies roughly that the demand for investment is ten times as interest-elastic as the demand for money.

IMF Staff papers: Volume 4 No. 3
Author: International Monetary Fund. Research Dept.