All Else Equal, Which Of The Following Will Cause The Money Supply To Fall?

THERE IS AMPLE theoretical and empirical evidence that income expansion and inflation are oftentimes associated with increases in the money supply. Since, every bit a rule, monetary statistics are readily and currently available while inflationary pressure is a concept that is difficult to mensurate, it has become customary to accept monetary statistics as reliable indicators of aggrandizement and deflation, of expansion and contraction. When it is observed that the coin supply in a land is ascent, 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 dissimilar relationship betwixt aggrandizement and the money supply, with particular reference to countries with an open economy. "The grade of events during 1950 and 1951 showed conspicuously that, in the weather which be in the netherlands, a decrease in the volume of coin may be a symptom of inflationary strains; while on the other hand an increment in the volume of money may show that there is a motility in the management of disinflation."¹ More specifically, the period from the latter office of 1950 through the beginning one-half of 1951 was without doubt one of inflation in kingdom of the netherlands; but the money supply brutal in the quaternary quarter of 1950 and in the first ii quarters of 1951. The economic position was reversed around the eye of 1951, and the second half of that year, likewise as the whole of 1952, was characterized by disinflationary or mild deflationary weather; during that period the money supply consistently rose.

It appears, then, that the management of alter in the quantity of coin is by no means an unequivocal indicator of the direction in which the economic system is moving. An increase in the quantity of coin may bespeak 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 coin in gild to develop a theory of more general applicability.

The present assay consists of two parts, of which the kickoff is a theoretical study of the relation between domestic income expansion and the money supply in an open economy. The income expansion may exist due to a multifariousness of impulses, such equally an democratic increase in domestic spending past the government, past private investors, or by private consumers. Unless the supply situation in the land is fully inelastic, the income expansion will touch not only money income, simply existent income too. This study is not concerned with the upshot of impulses coming from away; in view of this limitation, the terms "increment in income" and "decrease in income" refer to changes in activeness and in income due to changes in domestic need conditions. In club to exist able to draw conclusions with respect to the net effects of these internal movements on the residuum of payments, an unchanged situation in other countries is causeless: the balance of payments volition then reflect merely the results of the changes of domestic origin in the country under consideration.²

The conclusion of this office of the analysis is that, in an open up economy, income expansion caused past a ascension in individual domestic investment, in consumption, or in government expenditure, provided it is not straight or indirectly financed largely past the central bank will, after a sure lapse of time, lead to a subtract in the quantity of money; and that the reverse causes, a fall in private investment, individual consumption, or government expenditure, provided it is not matched in large part by a contraction of central depository financial institution credit, will lead, after a certain lapse of fourth dimension, to an increase in the quantity of money. A more formal treatment is given in the Appendix.

It would follow, therefore, that caution should exist used in drawing the traditional inferences from observed changes in the quantity of coin. While very large increases could hardly occur without the presence of some inflationary primal banking concern action, more than moderate increases could well be an indication of contraction in the economic system 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 outcome exercised by the fall in the money supply itself.

The 2d part of the analysis is statistical. Its purpose is to decide 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.due east., in practice for virtually all countries except the United States, the critical time menstruation would appear to be less than one twelvemonth.

In the first one-half of the statistical inquiry, an attempt is fabricated to measure for a big number of countries three of the five relevant coefficients that make up one's mind the disquisitional time period. These are ratios which may exist causeless to be reasonably constant for each country and whose measurement presents relatively few problems.

The measurement of elasticities with respect to the charge per unit of interest of the demand and supply of money raises many more problems. The 2d part of the statistical inquiry represents a tentative endeavor in this field, applied to the The states only.

The statistical measurement of the elasticity of demand for coin with respect to the charge per unit of involvement—i.e., the gradient of the "liquidity preference function"—is believed to have importance beyond the scope of the present newspaper. Information technology indicates the extent to which the success of a monetary policy intended to achieve effects in the existent sphere by changing the cost of money may exist misjudged if attending is directed to the responses of the economy with respect to the holding of money rather than with respect to the property or acquisition of real assets.

Theoretical Analysis

Analysis Without Regard to Time

The possibility that a alter 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 every bit fractional theories, each paying attending to a particular aspect of the inflationary or deflationary process.

When income expands in an open economic system, the money supply will be subject to two unlike pressures. On the i manus, there will be a trend 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 employ in transactions. Thus there is non only an initial temporary demand on the banks in society to finance the additional investment, but also a lasting increase in the stock of money to facilitate the larger menses of payments associated with a college national income.

At the same time, at that place will be an reverse tendency. Higher incomes will lead to college 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 volition now show a deficit. The public will purchase more foreign commutation from the banks than information technology sells to the banks and, in the process, will reduce its holdings of money by an corporeality equal to the net reduction in the country's foreign exchange holdings. As the reserves of the banking arrangement pass up, and the fundamental depository financial institution takes no steps to get-go this reject, the cyberbanking system will wish to take less coin outstanding.

Here it is causeless that the central bank adheres to a moderate form of the "rules of the game" in that, on the i mitt, it does not outset the loss of reserves by the commercial banks (e.thousand., by open market purchases of securities) but, on the other hand, does not act to contract further the quantity of money by attempting, for example, 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 banking concern behavior are important in determining the issue of the analysis; very different assumptions would lead to quite different results. For case, if the fundamental banking concern fully finances a regime deficit, the reserve base of the commercial banking system will increase more from this activeness than it will decline from the increase in imports to which the associated income expansion volition requite rise.ⁱⁱⁱ

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 chemical element. The two tendencies can be reconciled as shortly every bit both the need for money and the supply of money are considered in the schedule sense and a price, in this example the rate of interest, is brought into play equally the equilibrating factor. The public wants more coin at a given rate of interest, but it will squeeze its holdings of money every bit 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 every bit the rate of interest goes up.

The end result must be an increment in the charge per unit of interest; there may be an increment or a subtract of the money supply depending on a number of elements which can most conveniently be discussed past ways of a chart.

In Chart 1, the demand (D) and supply (South) of money are plotted. The curves D and S indicate the initial equilibrium state of affairs before the beginning of the expansion procedure. The initial money supply is indicated every bit MO ₀. This satisfied the public'due south demand for money at the given rate of involvement, r₀, and at the given level of income which determines the position of the demand schedule. The same money supply, MO ₀, besides satisfied the banks, given the rate r₀ and their reserve position which determines the position of the supply schedule.

A in one case and for all rise, thereafter sustained, of the national income of 10 million (of national currency units) above the previous equilibrium situation is at present assumed. To make the higher payments, the public will desire more money. If the income velocity of money is, say, 2, the desired increase in the quantity of coin would be v meg. This is indicated in the chart by a new demand bend D ⁱ, 5 units to the right of curve D.

Suppose that the 10 one thousand thousand higher level of income persists for i year, and that the marginal propensity to import⁴ is 0.2. Then the land would lose ii million in reserves. At the stop of the yr, therefore, the banking organization'due south supply curve of coin will have moved to the left (to South ⁱ ). The distance of the shift can exist 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 And so at the given rate of involvement the banking arrangement will want to contract the coin supply at the stop of i yr past 2.5 X 2 million = five million. Under these numerical assumptions, information technology so happens that the supply curve Southward ¹ in Chart 1 is moved to the left by the same altitude as the need curve is moved to the right.

The new rate of involvement r′ and the new quantity of money MO′ are found by the intersection of the D′ bend and the S′ bend (at P′). The charge per unit of interest, r′, is college than r₀, and the quantity of money, MO′, is higher than MO ₀. All the same, the increment in MO is pocket-sized, i.east., i million.

The increase in the rate of interest needs no comment. But the fact that at that place is an increment in the coin supply and not a decrease is clearly due to the numerical assumptons made. An equal horizontal shift (with contrary sign) of the demand and the supply curves has been obtained by bold a detail numerical relationship between the income velocity of money, on the i hand, and the marginal propensity to import and the banks' reserve ratio, on the other hand. Specifically it has been assumed that

$\frac{one}{income velocity of money} = \frac{marginal propensity to import}{banks' reserve ratio}$

(e.g., in the simplified case outlined above, $\frac{1}{2} = \frac{0.ii}{0.iv}$ ).

These figures are plausible for certain countries although in that location is no particular reason why the shift of the demand bend should not exist greater or smaller than the shift of the supply curve.

Equal shifts having been assumed, the result as far equally MO′ is concerned depends on the relative elasticity of the ii curves. In Chart 1, Southward and Southward′ have been drawn every bit more elastic (flatter) than D and D′. Appropriately, P′ lies to the correct of P and MO′ is greater than MO. The increase of the rate of interest from r ₀ to r would past itself induce the banks to expand the money supply past 6 million. It would induce the public to compress their demand for coin by 4 million. The combination of these movements along the curves with shifts of v 1000000 in both curves leads to a new equilibrium position in which the public holds 5 — four (= 1) one thousand thousand more money and the banks have an increase in their liabilities of 6 — 5 (= i) 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 coin would accept shown a decrease.

Field of study to what is to be said below—and this is an of import qualification—it has been plant that, if central bank activeness is in accordance with the assumptions fabricated above, the following five factors will determine whether changes in the quantity of coin and changes in income are in the same or in contrary directions:

The income velocity of coin
The marginal propensity to import
The reserve ratio of the banking system
The elasticity of demand for money^vi with respect to the rate of interest on the function of the public
The elasticity of supply of coin with respect to the charge per unit 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 quaternary 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 go more specific on this point.

On closer analysis it becomes clear that the shift of the demand bend and the shift of the supply bend 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 one time and for all shift. Equally soon equally income (expressed every bit an almanac rate) increases past ten one thousand thousand, and as long equally it remains at this college level, D′ beingness five one thousand thousand to the right of D, will represent the demand for coin. The shift in the supply curve is different. Information technology 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 yr period of higher income. If income stays at the aforementioned level for another twelvemonth, another 2 meg of imports above the normal level will have been wanted, and reserves will have been reduced by another 2 million. Accordingly, the supply bend volition shift some other v units to the left.

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

Changes in the quantity of money tin can exist read along the horizonta axis. At the very beginning of the year when income is x million higher than in the preceding year, the banks have not still lost any reserves. Their supply schedule is, therefore, still practically unchanged at South. The intersection of D′ with Southward gives P₀′, which indicates the rate of involvement, r₀′, and the quantity of money, MO ₀ ′, at that time. This money supply must exist larger than MO₀, whatever the numerical values of any of the five factors. After one year, nosotros volition accept MO ₀ and r₁′ which are equal to MO′ and r′ in Chart ane. The supply bend continues to move to the left, and at the end of two years the money supply (MO₂′) is at present clearly below the original money supply. Every bit fourth dimension goes on and income remains at the given level, the money supply will keep to autumn.

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 atomic number 82 to an increase in the quantity of money. (two) Every bit the same higher level of income persists for a longer time, it will lead to a reduction in the quantity of coin below the higher level initially reached. (3) If the same college level of income persists for a long enough period, it volition atomic number 82 to a quantity of money below the level that existed before the increment in income occurred.

These 3 propositions take full 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 in a higher place.

The third proposition is of little importance, however, unless it can plausibly exist 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 give-and-take.

Gradual Increase in Income

The preceding assay has been concerned with one sudden increase in income which was then assumed to be maintained for some time. A somewhat unlike aspect of the same problem may now exist considered. Let us presume 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 1 menstruum can autumn below the money supply of the preceding period (in dissimilarity to the conditions under which it falls beneath the initial, pre-inflation coin supply)?

The answer to this question can be derived from Chart 4. The acme half of this chart repeats the relationship for the erstwhile increase in income. In the bottom one-half, income is shown rise by one stride per fourth dimension unit. At every step, the quantity of coin initially rises correspondingly (the scales have been selected in such a manner that the rising in the quantity of coin at each step shown on the nautical chart equals the ascent in income). But as the time period during which income remains at a given stride passes, the quantity of coin falls, for bank reserves are continuously tuckered off by the excess of imports over exports. From fourth dimension moment 1 to moment 2, information technology falls past one fifth of a step, i.e., with the same slope as the coin curve in the height half of the chart. During the adjacent catamenia, from moment 2 to moment 3, information technology falls past ii fifths of a step—ane fifth each for the offset and second income footstep.⁷ In the next menses it declines past three fifths of a step, etc. Later on income has risen for five fourth dimension units, the refuse in the quantity of money per unit of measurement resulting from the shift to the left of the supply curve only equals the charge per unit of increase in the quantity of coin resulting from the shift of the need curve. The two forces residue; the quantity of coin reaches its maximum. Thereafter, as income continues to grow at the aforementioned charge per unit, the cumulative effect on the supply side of by growth in income exceeds the effect of current income growth on the need side, and the quantity of money volition refuse.

Instead of by steps, the same reasoning can be presented past continuous curves. If income rises as a straight line, the quantity of money volition increase at a decreasing charge per unit, so reach a maximum, and decline thereafter. It tin can easily exist 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 reject 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 coin. The maximum for the quantity of money will exist reached after a flow of time depending on exactly the same combination of v parameters as that plant in an before section (pp. 401-4). Thus the flow 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 expire before the money supply can fall below its immediately previous level in the continuous aggrandizement case.⁸

Eastffect of the Rate of Interest on Income

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

It may be useful, withal, to expand the analysis to cover the situation where, equally a effect of the rise in the rate of interest, investment actually declines (and/or savings actually increase) and, consequently, income volition decline in spite of the persistence of democratic factors of unchanged magnitude. For instance, regime spending may be maintained at 10 million in a higher place the level of the original equilibrium situation; but the consequent persistent rise in the charge per unit of interest may reduce private investment by y per year. While at outset 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 2 years, etc.

The issue of the expansion of the analysis tin can, again, exist represented graphically past an extension of Nautical chart 3. This is washed in Chart 5; the mathematical deductions will be establish in the Appendix.

Income, instead of remaining at its raised level, volition now gradually decline until it approaches asymptotically the original level. The rate of interest will ascension, not in a straight line and without limit but asymptotically approaching a maximum. This maximum will exist such that the negative upshot of the rate of interest on investment (plus the negative outcome information technology has on consumption through increasing saving) will just balance the initial autonomous increase in expenditure. The quantity of coin will decline, subsequently its initial rise, and approach an asymptote below its base period level. The level of this latter asymptote volition depend on the amount of autonomous investment and the ratio between the responsiveness of the demand for coin 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 three. The point of intersection of the MO curve with the nada line may fall somewhat earlier or somewhat afterwards. Fifty-fifty those instances in which the quantity of money returns to its base-period level at a later time practise not affect significantly our before findings, since (a), within the plausible range of values for the various parameters, the lengthening of the fourth dimension period is quite minor; and (b), when the simpler assay yields a time period of less than 1 year, the present, more complicated, analysis must besides yield a flow of less than one twelvemonth, while for a time period of but ane year the results of the two methods coincide.⁹

Statistical Measurements

The management of the movement of the money supply in response to modify in income has been found in the circumstances assumed in this study to depend on five coefficients and on time. Three of these coefficients—(i) the consequence on the need for money of a change in income, (2) the effect of a change in money on commercial depository financial institution reserves, and (3) the effect of a modify in income on imports—are conveniently discussed together. They have in mutual the characteristic that marginal coefficients may be estimated on the basis of sure boilerplate ratios. The 2 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 want of the public to hold coin as income changes, (2) the marginal desire (or obligation) of the banks to concur 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 shut to the corresponding average coefficients; and (ii) that the actual effects of changes in other variables (including changes in interest rates) are non so dandy as to make the observed values of the average coefficients vary widely over time.

If these ii 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 iii cases.

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

Tabular array 1.

Ratio Coefficients for 38 Countries in 1952

^¹ d = ratio of deposits to total coin supply; f = ratio of commercial banks' reserves to deposits.

^² $\frac{Col . (1) \times Col . (4)}{Col . (5)}$

^³Australia's actual f may be fabricated extremely loftier for increases in deposits, according to primal banking concern determination. The combined ratio would then rise to a maximum of one.1.

^⁴1951.

^⁵1950.

Table 1.

Ratio Coefficients for 38 Countries in 1952

			Reserve Issueⁱ
	Land	Ratio of Coin Supply to Income (1)	d (2)	f (3)	1-d(ane-f) (4)	Ratio of Imports to Income (5)	Combined Ratio² (6)	Ratio of Short-Term Debts to Money Supply (7)
Europe
	Austria	.30	.53	.12	.53	.22	.7	.46
	Belgium	.57	.40	.07	.63	.39	.9	.23
	Denmark	.32	.73	.10	.34	.31	.four	.73
	Finland	.12	.40	.09	.64	.30	.3	1.14
	France	.41	.49	.07	.54	.15	one.5	.55
	Germany	.21	.51	.35	.67	.16	.nine	.89
	Ireland	.40	.56	.08	.49	.43	.5	.76
	Italian republic	.41	.60	.13	.48	.eighteen	1.1	.77
	Netherlands	.45	.61	.06	.43	.48	.4	.20
	Kingdom of norway	.51	.67	.07	.38	.38	.v	.89
	Sweden	.25	.56	.07	.48	.22	.v	.96
	Switzerland	.57	.56	.22	.56	.26	1.2	.58
	United Kingdom	.39	.73	.09	.34	.25	.five	.33
Republic Countries
	Commonwealth of australia	.44	.76	.08ⁱⁱⁱ	.30	.33	.4³	.54
	New Zealand	.38	.76	.39	.54	.36	.6	.56
	Matrimony of South Africa	.37	.79	.25	.41	.37	.4	.44
Canada		.29	.73	.10	.34	.22	.4	.65
Center and Far East
	Burma	.19	.35	.23	.73	.22	.6	.26
	Ceylon⁴	.20	.60	.29	.57	.39	.3	.xviii
	Egypt^v	.42	.48	.27	.65	.23	one.2	.36
	State of israel^iv	.47	.63	.32	.57	.23	1.2	.57
	Japan⁴	.22	.53	.04	.49	.41	.three	1.45
	Philippines	.15	.43	.19	.65	.12	.viii	.61
	Thailand⁵	.18	.27	.41	.84	.12	1.3	.18
	Turkey^five	.26	.57	.13	.51	.fifteen	.9	.98
United states		.44	.79	.22	.38	.04	four.two	.40
Latin America
	Argentina^four	.40	.47	.11	.58	.14	1.vii	.48⁵
	Brazil⁴	.39	.69	.26	.49	.16	1.two	.73^v
	Chile^five	.17	.66	.12	.42	.xi	.6	.78
	Republic of colombia⁵	.17	.52	.nineteen	.56	.13	.7	.04
	Cuba⁴	.73	.36	.46	.81	.32	i.8	.22⁵
	Dominican Republic	.15	.55	.31	.62	.19	.five	.40⁵
	Guatemala	.12	.33	.54	.85	.xiv	.vii	.28⁵
	Honduras^iv	.13	.46	.70	.86	.26	.4	.49^five
	Mexico⁵	.16	.51	.58	.79	.13	1.0	.33
	Paraguay⁴	.22	.46	.65	.84	.09	2.0	.33⁵
	Republic of peru^four	.nineteen	.sixty	.17	.l	.27	.4	.78^five
	Venezuela⁴	.23	.50	.48	.74	.30	.half dozen	.45⁵

^¹ d = ratio of deposits to total coin supply; f = ratio of commercial banks' reserves to deposits.

^ⁱⁱ $\frac{Col . (1) \times Col . (4)}{Col . (5)}$

^³Commonwealth of australia's actual f may be made extremely high for increases in deposits, according to central banking company decision. The combined ratio would then rise to a maximum of 1.i.

^⁴1951.

^⁵1950.

The 2d coefficient involves two steps: the ratio of deposits to the full coin supply and the ratio of commercial bank reserves^ten to deposits. If the former ratio is chosen 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 = [one - d(one - f)]K (Table 1, Columns ii, 3, 4).¹¹

Assumption (i) above may exist open to some incertitude with respect to the propensity to import (Column 5). Existing statistical studies almost generally testify that the marginal propensity to import appears to exist 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 mostly 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 split up measurements were made for the twenties and the thirties) with the respective average propensities yielded seven cases of elasticities in excess of 2.0, 10 betwixt 1.0 and 2.0, and only 4 below unity.¹²

These loftier import elasticities, all the same, are based on comparisons of real income and real imports. Much lower elasticities would be indicated insofar as changes in coin income are due to price changes. With respect to the latter, the residue of trade expressed as a per centum of imports would probably worsen by less than the increment in the price level; i.eastward., the ascension in coin value of imports (plus whatsoever fall in value of exports) would exist less than in proportion to the rise in coin income.¹³ On the whole, therefore, the assumption of unitary elasticity of the need for imports with respect to income, both expressed in terms of money value, would non seem to be likewise unreasonable. The figures in Column 5 of Table i have therefore been obtained merely past dividing imports by national income.

In Column 6 of Table one, the three coefficients are combined in the manner in which they are relevant for our calculations. In terms of Charts one and two, the figures in this column represent the ratio of the displacement of the need curve for money to the deportation of the supply bend for money after i year. If this ratio is less than unity it means that, at equal involvement elasticities of demand and supply for money, the quantity of money would fall below the initial position within one yr after the beginning of a higher level of income. Conversely, these ratios provide a disquisitional value for the ratios of the interest elasticities. Thus, for the commencement land in the table, Republic of austria, the combined ratio is establish to be .7. This can exist interpreted every bit significant 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 inside 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 but if plausible assumptions can be made regarding the ratio of the two interest elasticities and if, furthermore, the fourth dimension is stipulated during which changes in income may be assumed to persist. Information technology volition be shown beneath that there seems to be evidence that in the United States, at to the lowest degree, the demand elasticity for money exceeds considerably the supply elasticity, their ratio being about iv to i in the postwar flow. There is no particular reason to believe that similar results might not exist found for other countries. In Table 2, the results are summarized, assuming three alternative, more conservative, values for the ratio of the 2 elasticities, viz., 2, one, and ½ For each value of the "combined ratio," Table 2 enables us to estimate the menstruum of time during which an increase in income would have to persist to lead to a subtract in the money supply. The table shows that on the first supposition, viz., the demand for money twice as elastic as the supply of coin, 37 of the 38 countries (all except the United states) would show an opposite movement betwixt 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 farthermost), where the ratio of the elasticities is the reverse, xv of the countries would all the same show an opposite movement subsequently a year, and 27 would evidence it afterward two years, had elapsed.

Table 2.

Estimates of Length of Time (in Years) Before Increase or Decrease in Income Would 50ead to an Opposite Govement in Money Due southupply

^{^one}Based on data in Table 1, Column half dozen.

^ⁱⁱRatio of "Interest Elasticity of Demand for Money" to "Interest Elasticity of Supply of Coin."

Tabular array 2.

Eaststimates of Length of Time (in Years) Before Increase or Decrease in Income Due westould Fiftyead to an Opposite Movement in Chiliadoney Due southupply

Combined Ratio^ane
Interest-Elasticity Ratio²	0- $\frac{1}{2}$	$\frac{1}{2}$ -1	1-2	two and Over
two	0- $\frac{i}{4}$	$\frac{1}{4}$ - $\frac{1}{2}$	$\frac{1}{2}$ -1	>1
1	0- $\frac{1}{2}$	$\frac{1}{2}$ -ane	one-2	>2
$\frac{1}{2}$	0-1	1-2	2-four	>4
	Countries in Each Combined Ratio Class
	Kingdom of denmark	Austria	French republic
	Finland	Belgium	Switzerland
	Ireland	Germany	Italy
	Netherlands
	Kingdom of norway
	Sweden
	United Kingdom
	Commonwealth of australia	New Zealand
	Canada
	Spousal relationship of South Africa
	Ceylon	Burma	Egypt
	Japan	Philippines	Israel
		Turkey	Thailand
				United States
	Dominican	Chile	Argentine republic
	Republic	Colombia	Brazil
	Honduras	Guatemala	Cuba
	Peru	United mexican states Venezuela	Paraguay

^{^ane}Based on data in Tabular array 1, Column 6.

^²Ratio of "Interest Elasticity of Need for Money" to "Involvement Elasticity of Supply of Coin."

One qualification of these findings needs word. The elasticity of need on the side of the public has been discussed in terms of a comparison of the relative advantages of liquidity (the property of coin) with its cost in the form of the involvement foregone by not holding an involvement-yielding asset. This comparison may not be the predominant cistron 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 involvement elasticity of demand for money is particularly interesting considering 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 involvement elasticity of demand for coin will be higher (all other things being equal) than in countries where the ratio is low. For almost countries this ratio in 1952 was well above that for the Usa (Tabular array one, Column seven). On this score, at least, at that place appears to exist no reason to fear that the transposition of an elasticity institute for the United States would pb us to underestimate the critical period.

Eastlasticity of the Public's Demand for Grandoney

In order to find the responsiveness of the public'southward demand for money with respect to the rate of interest, we must endeavor to isolate i of the factors determining the total need for money. The principal gene determining this demand is usually believed to be the total value of business organisation turnover, measured by some indicator such every bit the value of GNP. Here we desire to abstract from this "income" factor in guild to isolate the "cost" gene. One possible procedure would exist to attempt a multiple correlation calculation explaining movements in the quantity of money in terms of both an income and a cost gene. This is the process 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 refuse 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 (east.g., from 3 to four per cent) in the short-term charge per unit of involvement. This effigy seems extremely low on a priori grounds; and like and then many price elasticities where the income elasticity is dominant, it is probably subject to a wide margin of mistake.

An alternative method of measurement therefore seems more advisable. The essence of this method is to determine the income coefficient from other sources. Information technology 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 organisation turnover of $ten million per twelvemonth requires for a particular firm an average cash remainder of $i million, it seems reasonable that if the business concern grows to $xxx meg, distributed over three firms, the desired cash residual should increase to $3 1000000. If it is reasonable to assume this proportionality more than 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 make up one's mind the rate of turnover of the money supply, and a comparison of the covariations of these two variables would indicate the effect of the charge per unit of interest on the money supply at a given level of GNP.

As volition be seen beneath, a comparison of this sort turns out to be quite satisfactory equally an gauge indicator of the sensitivity of the quantity of money to changes in interest rates in the United states in the concluding thirty years.¹⁶

Observed interest-velocity relationships in the Usa, 1920-53

In Nautical chart 6 the income velocity of apportionment in the Us (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 iii-9 month Treasury bills, the charge per unit on prime number commercial paper, and the long-term government bail yield.

The use of several interest rate series rather than a single "representative" series is necessary considering of the separation of the various financial markets. For case, business borrowers will build upward or reduce their working balances of money in response to changes in the price and availability of brusque-term commercial credit. Investors volition build up or reduce their idle balances according to the charge per unit of involvement 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 exist considered. Thus it is necessary to accept available several involvement 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 twelvemonth-to-year movements of the velocity of circulation and interest charge per unit series: a rise in interest rates tends to be accompanied by a ascension in velocity, i.eastward., past an economic system in the holding of money.

At that place are a number of instances of poor correspondence betwixt the interest and the velocity series. Several of these, still, 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-coin 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 abrupt rises in involvement rates are due to the somewhat limited definition of the base taken to measure this velocity. In 1928, and specially in 1929, equally a consequence of the ascent in stock market speculation, there was a nifty 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 full volume of transactions had contained an assart for the aberrant rise in purely financial transactions, the rising in involvement rates would have been reflected in increased velocity figures.¹⁷ The correlation between interest rates and money supply broke downwardly during the period between 1931 and 1934, but this failure of the human relationship is over again explainable by the severely disturbed conditions of the period. Special conditions also provide the footing for the breakdown of the human 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 involvement rates and the ratio of money supply to GNP shown in Chart 6 are reproduced in scatter diagram form in Chart 7.

Choice of representative rate of involvement

To brand possible measurement of the interest elasticity of demand for money by the scatter diagram technique, a single rate of involvement had to be selected from Nautical chart 6 to be plotted against desired cash holdings. The problem thus arises of finding the one rate most virtually representative of all interest rates. A rate on government securities is probably more than appropriate than any rate on private loans or securities, for fearfulness of the debtor'southward insolvency must have caused a varying adventure-charge factor to take influenced the rate during the depression of the thirties even with respect to prime number quality loans.^nineteen In add-on, 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 toll mechanism. On the commercial loan market place 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 exist matched past competitive reductions of charges in other banks. This consideration, plus the customs of loyalty to longstanding clients, etc., makes as well frequent interest aligning an undesirable method of changing the book of bank loans. Only the same conditions which forcefulness banks to alter the amount of business loans outstanding will also, ceteris paribus, crusade them to modify the amount of regime securities, etc., held. And the market place for government securities is not monopolized by the banks; other investors participate in information technology, and the involvement rates determined in it are highly sensitive to shifts of demand. Banks therefore arrange their holding of government securities (a large fraction of their full assets) without regard to the effects of their purchases or sales on the prices of these securities; thus regime security yields are likely to be equally skillful an indicator of the toll-cum-availability of banking company credit for business as the rate actually charged on these credits. And since business cash remainder holdings must vary in response to the availability of credit merely as they vary in response to the toll of credit, government security yields should exist pertinent not only for investors who shift funds between securities and cash balances but too 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 than desirable unmarried representative measure of the yield of uppercase. The short-term rate appears to exist the amend measure of the role of capital costs every bit 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 hereafter changes of the interest charge per unit. Thus, insofar every bit funds can move betwixt the ii security markets, the interest yield on brusk-term securities will tend to move parallel to the total yield (involvement plus uppercase proceeds factor) predictable 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'southward own interest yield.²⁰ And they will conspicuously be more representative of yields in general than will the long-term interest yield. For these reasons the involvement rate on short-term securities has been selected.²¹

In Chart 7 the rate on brusque-term government securities has therefore been plotted in scatter diagram course 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) past the 1953 GNP, then that the whole presentation of money supply against the involvement charge per unit is made in terms of an income level equal to that of 1953.²²

The scatter of points in Nautical chart 7 reveals two carve up 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 need and a college level of demand for coin.²³

The postwar relationship is very disarming, its only weakness beingness 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 about no alter 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 information technology has been fitted to 2 widely separated clusters of observations: 1922-xxx, all of which show interest rates over ii.4 per cent, and 1933-42, for all of which the charge per unit was 0.v per cent or less. In actuality, therefore, there may have been two split up involvement-demand relationships in the interwar menstruation: one for the twenties (which is rather similar the postwar human relationship) and a much less elastic one for the thirties. Of form, the fact that the need curve for coin 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 human relationship betwixt the interest rate and the desired coin supply.²⁴

Elasticity of Banks' Due southupply of Money

The analysis of the banks' supply elasticity of money runs along the same general lines every bit that of the public's demand for coin. 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 charge per unit of involvement. Information technology is plausible to presume that banks operate in a similar way. Similar the public they volition want to residue the convenience of a high reserve ratio confronting a depression rate of involvement, the inconvenience and chance of a lower ratio against a higher rate of interest.

The larger function of the reserves of the banking system is fixed by the prescribed reserve ratios of the Federal Reserve Organisation. The "gratuitous" function of reserves that would be relevant in a comparing with interest rates would, therefore, exist reserves held in excess of legal requirements.

But these excess reserves will take been created to some degree out of funds borrowed from the Federal Reserve Organisation by detail banks which would otherwise accept inadequate reserves. Since indebtedness to the Federal Reserve Organisation is considered undesirable, reserve balances secured through the medium of such debt ought non to exist 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 past deposit liabilities

The definition of these net excess reserves is made more closely relevant to the interest rate problem by i further modification of the information. Conspicuously, 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 eolith liabilities at $144 billion (in 1953). This change in conditions can be allowed for if the need for net backlog reserves is taken as proportional to the full of deposit liabilities—a process justified logically by the fact that reserves are desired every bit a cushion between variations in bodily reserves relative to required reserves. Other things equal, these variations are proportional to the book of deposit liabilities; larger deposits imply larger volumes of transactions by depositors and therefore greater (absolute) changes in the banks' reserve positions, with the event 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 coin, therefore, the relationship betwixt the rate of interest and banks' excess reserves has been derived from the observed information, 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 eolith liabilities are plotted in scatter diagram form against the curt-term regime security charge per unit (yield of Treasury bills). Past apply of a logarithmic scale for involvement rates, the chart makes possible observation of the event 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 plant that a good linear relationship tin be fitted to the entire range of points over the period 1920-53.²⁶ (As in the case of demand for coin discussed higher up, the years 1920, 1921, 1931-33, and 1942-46 were disregarded in the fitting of this relationship.)

Reliability of observed interest-reserves relationship

The reliability of the relationship fitted might be questioned because the information used cover more than than 30 years—a period during which financial institutions and financial practices would exist expected to change. The fit of the curve may be poor, information technology is truthful, at its lower finish, eastward.g., for interest rates below 0.12 per cent, simply 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 belatedly 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 twenty to 30 years, when they returned to almost these levels the movement traced out most exactly the preexisting reserve-involvement 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 catamenia following World War Ii. Chart ix shows quarterly movements in net excess reserves, the Treasury nib rate, banks' customers' loan rate, the commercial paper rate, and the 3-5 year government bail yield. Net excess reserves, which were approximately constant during 1951, declined continuously during 1952, and so rose continuously through the outset quarter of 1954. The interest rates moved equally expected, ascension 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 just in the 2nd quarter of 1953. Thus in relating interest rates of this period to net backlog reserves on a quarterly basis information technology is necessary to lag the charge per unit two quarters behind the internet reserve position.²⁸

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 Nautical chart 8), the interest-reserves relationship at the fourth dimension when the postwar interest charge per unit was highest is found to be very close to the relationship in prewar years, and fifty-fifty closer than the human relationship indicated by postwar almanac information. This signal is peradventure particularly significant because information technology 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 standing validity of the prewar human relationship.²⁹

Supply curve of coin derived from banks' interest-reserves relationship

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

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

The cyberbanking supply curve for the money supply derived in this fashion and defined (with respect to banks' legal reserve requirements, full and component deposit liabilities, currency in circulation, etc.) in terms of the situation of 1953 has already been shown higher up (Chart 7) super-imposed on the need curves derived in the previous section. This supply bend is establish to take a adequately abiding elasticity (between .07 and .08) with respect to the interest charge per unit.

Ratio of public'due south interest elasticity of demand for coin to banks' interest elasticity of supply of money

With the evidence of the demand and supply elasticities for money derived for the The states in the two preceding sections, it is at present 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 in a higher place vary betwixt 2½ and v when the postwar need relationship is used and between 1 and ii when the prewar demand relationship is used, with higher interest rates in the latter case and lower rates in the former instance showing college values for the ratio.³¹

If the postwar relationship is accepted as valid for the future, it is constitute that even in the The states changes in income might be expected to result subsequently ane yr in changes in the money supply of reverse sign: the bodily ratios of the elasticities autumn betwixt ii½ and 5 and include the critical value of four.2 found for the United states of america in Table i. This would not, all the same, be true on the basis of the prewar demand elasticity.

It is, of course, non possible to use to other countries the ratios of elasticities found for the United States. Both demand and supply elasticities must vary from country to state and their ratio may vary even more. If it is possible at least to assume that the minimum value for the ratio in almost countries will exist no less than 1 fourth of the postwar U.Southward. ratio (i.eastward., approximately over unity), then it can be concluded that more than than half of the countries recorded in Table 1 should experience contrary 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 3 of the four adult Democracy countries—could, in circumstances where the original assumptions about key bank neutrality, etc., are appropriate, show contrary changes in money supply and income in a yr or less at a ratio of the elasticities equally depression as one eighth of that of the United States.

Whether the U.South. ratios can be extrapolated to other countries in even so conservative a way as has just been done remains an open question. Withal, the data for the Us provide at to the lowest degree 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.

Source: https://www.elibrary.imf.org/view/journals/024/1955/002/article-A002-en.xml

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