Regulation of Short-Term Interest Rates Through Monetary Action

The Increase in the scope for short-term capital movements over the last few years has led to discussion of the desirability of concerting the short-term interest rate policies of the countries of the European Economic Community or of other countries with convertible currencies.1 At the same time, there has been some discussion of the desirability of determining domestic interest rate policies so as to influence the flow of short-term capital in order to minimize the “exchange-market balance of payments.”2 Before these discussions proceed much further, it would seem to be desirable to consider the magnitude of the operations by the central authorities implicit in the discussions.

Abstract

The Increase in the scope for short-term capital movements over the last few years has led to discussion of the desirability of concerting the short-term interest rate policies of the countries of the European Economic Community or of other countries with convertible currencies.1 At the same time, there has been some discussion of the desirability of determining domestic interest rate policies so as to influence the flow of short-term capital in order to minimize the “exchange-market balance of payments.”2 Before these discussions proceed much further, it would seem to be desirable to consider the magnitude of the operations by the central authorities implicit in the discussions.

The Increase in the scope for short-term capital movements over the last few years has led to discussion of the desirability of concerting the short-term interest rate policies of the countries of the European Economic Community or of other countries with convertible currencies.1 At the same time, there has been some discussion of the desirability of determining domestic interest rate policies so as to influence the flow of short-term capital in order to minimize the “exchange-market balance of payments.”2 Before these discussions proceed much further, it would seem to be desirable to consider the magnitude of the operations by the central authorities implicit in the discussions.

In the present discussion, it will be assumed that the problem facing the monetary authorities is to determine the volume of net open market sales that would be required to raise short-term interest rates by a given amount. To determine the amount of monetary restriction required for a given rise in short-term rates, the authorities must have an idea of the extent to which the public will react to a tightening of money by reducing the amount it desires to hold, at given income levels, and of the extent to which the banks will react to a reduction in their liquidity or legal reserve holdings by reducing their desired levels of surplus cash holdings (instead of restoring their prior surplus cash position by reducing their earning assets and therefore their deposit liabilities) as the interest yield on loans increases. The more the public reduces its desired holdings, and the more the banks increase the amounts they are willing to lend on the basis of a given volume of liquidity, the greater is the reduction in that liquidity which the monetary authorities must produce in order to achieve any given rise in interest rates. The authorities would also have to offset any addition to liquidity resulting from a capital inflow that the increase in interest rates might produce; however, for purposes of discussion, it is here assumed that the rate increase is adopted merely to prevent a capital outflow and that it does not create any inflow.

For countries where the official decision to raise interest rates is immediately reflected in the market place, the kind of analysis here presented might seem irrelevant. However, that is not the case. Consider the situation in the United Kingdom. Bank lending rates there are tied to the central bank’s rediscount rate; and the central bank, by open market operations, forces the part of the money market that specializes in holding Treasury bills (the “discount houses”) to use central bank rediscounts to finance a portion of their bill holdings and to adjust the price they pay for bills in accordance with the cost of rediscounts. Even in this situation, the central bank must evaluate the extent to which the rise in interest rates will cause the public to shift from holdings of bank deposits to holdings of interest-bearing securities. Any reduction in the banks’ deposit liabilities will free a portion of their required reserves and permit more reserves to be loaned to the discount houses; that will nullify the effect of an equal amount of the central bank’s restrictive open market operations.

In some countries, the banking system may be so heavily indebted to the central bank that no plausible reduction in needed reserves attributable to a rise in interest rates could free the banking system from the influence of the price of central bank credit. The problem for the central bank is then simpler, since the amount of reserves it makes available to the banks will adjust passively, leaving the authorities free of the need (and the power) to make independent decisions. The questions raised in this paper will remain significant, however, if successive tranches of credit are supplied at higher interest rates. The reduction of the volume of bank deposits which the public wishes to hold may improve the banks’ reserve position enough to make them eligible for a lower interest charge on their borrowings from the central bank; if so, the rise in the central bank’s schedule of lending charges will have less than the intended effect on market rates of interest. Either a further rise in the schedule of lending charges or sufficient open market sales to force the banks back to the higher credit tranche previously used will then be necessary.

This paper will concentrate on the strength of the monetary measures required in the United States, in view of the importance of the U.S. money market and because the data available for the United States permit evaluation of the effects of changes in interest rates not only on the public’s demand for money but also on the supply of it by the banks.3

The reduction in liquidity appropriate to any given rise in interest rates may seem to be determined easily by the traditional central bank procedure of gradual trial-and-error adjustment according to the “feel of the market.” But efforts to estimate the reduction that will be ultimately required remain justified, if only to establish whether a large increase in short-term rates, if needed, can be attained within the limits of reasonable central bank action. Moreover, a quick approach to the right amount of restriction may be desired when prevention of movement of volatile short-term capital is sought. The gradual approach may be circuitous: the banks may at first shield their loans and investments from the restriction by tolerating abnormally low reserve positions, so that restrictions at first applied may prove excessive; this danger may make the central bank afraid to apply even the smaller amount of restraint that will ultimately be necessary. Any quantitative evidence that can be provided on the behavior of the banks and the public with respect to the level of the short-term interest rate may thus increase the workability of the present exchange system.

All available evidence suggests that the interest elasticities of the private sector’s demand for money4 and of the banks’ supply of credit5 are comparatively low, and that, therefore, small reductions in the banks’ reserve position should suffice to cause significant increases in the interest rate. Control of the short-term interest rate should thus be well within the capabilities of the monetary authorities. Although the variety of institutional conditions is great, the above conclusion is so clear-cut for the United States that it ought to be safe to generalize it so as to cover most other countries that have developed money markets.

Analysis

The present exposition attempts to determine the degree of action required by the U.S. monetary authorities if they wish to adjust U.S. interest rates to the levels prevailing in other developed countries. The investigation is made under the simplifying assumptions that money income is constant (the effect of monetary policy on gross national product (GNP) being counteracted by other measures) and that bank deposits other than the public’s demand deposits are constant. Savings deposits are assumed to be a function more of time than of interest rates. Time deposits may vary with or against interest rates, depending on the comparative movements of yields on deposits and on money market securities, and are here assumed not to vary; the significance of the increase in the flexibility of deposit yields in recent years, following the relaxation of Federal Reserve restrictions and the introduction of marketable time deposit certificates, will be considered later. Further, U.S. Government demand deposits may be assumed, as a first approximation, to be associated with the (unchanging) level of GNP. Interbank deposits may vary both with the stock of private deposit holdings and with the rate of turnover of that stock; as a first approximation, it will be assumed that interbank deposits are unchanged when GNP, and hence the volume of transactions made with the private holdings of demand deposits, are unchanged. (Because changes in interbank deposits have little net effect on required reserves, under the regulations of the Federal Reserve, close conformity to this assumption is not necessary.) Currency in circulation is assumed to be unchanged; it is the purest form of “transactions” balance and, when as small a fraction of total money as it is in the United States, can be assumed to be beyond the reach of interest rates.

Given these assumptions, the interest rate will be determined by the interaction between the private sector’s interest-demand curve for demand deposits and the banks’ interest-supply curve of credit. Open market sales by the central bank will reduce the amount of credit that the banks can supply at any given interest rate and (given the constancy of currency, time deposits, etc.) reduce by an equal amount the public’s demand deposits. The consequences will be a rise in interest rates, equilibrium between demand and supply being restored by a reduction in the private sector’s desired holdings of demand deposits (i.e., a rise in the velocity of circulation of deposit money) and by some rise in the amount supplied.

The crucial policy variable for the central bank can be considered to be the reserve base underlying the banks’ private demand deposit liabilities: the required reserves, plus desired excess reserves held against these liabilities, less the portion provided by the banks’ borrowings from the central bank.6 In the United States, this is the same—with a few omissions—as Federal Reserve Bank credit (holdings of government securities, etc.), less the part created by member bank borrowings, plus gold stock, minus currency in circulation, minus required and excess reserves held against those deposits which may be assumed to be unchanging (time, U.S. Government, etc.). To create a given proportional reduction in the “supply” of demand deposits at the existing level of interest rates, the central bank must reduce this reserve base by the same proportion.7

It is easily seen that the necessary proportional reduction in demand deposits, or their reserve base, varies with the height of the desired proportional rise in interest rates and of the interest supply and interest demand (sign ignored) elasticities. That the demand for money should vary with the level of interest rates is well established.

Some interest elasticity in the banks’ supply curve is to be expected because banks, like other holders of wealth, obtain benefits in the form of convenience and safety from holdings of surplus idle cash balances (and of unused borrowing facilities at the central bank). These benefits must be balanced against the interest income and customers’ goodwill that could be obtained if the idle funds (and the funds that could be borrowed) were placed in securities or loans. When interest rates are high, the banks will hold less idle cash (excess reserves) and will tend to draw more heavily on their lines of credit at the central bank; hence, rising interest rates cause a reduction in the ratios of desired free reserves to the (unchanging) time, savings, and interbank deposit liabilities and to the (rising) demand deposits. This contributes interest elasticity to the supply curve by making more of the reserves available to serve as a base for additional supplies of demand deposits, and by increasing the amount that can be supplied for any given reserve base.

In Diagram 1 it is assumed that the private sector’s demand for deposits is represented by curve D and the banks’ supply by curves S0 and S1. To raise the interest rate from i0 to ii it is necessary that the amount of demand deposits (OD0) hitherto supplied at the rate i0 be reduced by the sum of the distances A and B (to OD’0). (This means that the reserve base must be reduced in the same proportion: A+BA+B+C.) Of the total reduction, A will be related to the supply curve and B to the demand curve. A/E is an index of the elasticity of the former, and B/E an index of the elasticity of the latter. It is clear that the larger the sum of the two elasticities, the larger must be the leftward shift (A + B) of the supply curve. It is easily demonstrated that the necessary open market sales will be the proportion of the existing reserve base for demand deposits given by multiplying the proportional rise in interest rates by the sum of the interest supply elasticity and (the absolute value of) the interest demand elasticity. This formula is an approximation which yields a slight (e.g., 10 per cent) overestimate of the amount of intervention by the central bank actually required. (See Appendix for a full discussion.)

Availability of Securities to Replace Undesired Demand Deposits

The public is willing to accept reductions in the quantity of money supplied by the banks (i.e., in the demand deposits the public can hold) because a rise in interest rates makes it willing to switch from money to interest-bearing securities. It is obvious that the increase in the demand for securities must be equal to the decrease in the demand for money, but it may not be clear that an equal rise in the supply of securities will be forthcoming without disruptive changes elsewhere in the system.

In the simplest case the central bank sells securities to the commercial banks, thereby causing an equal reduction in the banks’ reserves. The commercial banks then make the necessary reductions in their deposit liabilities simply by selling some larger quantity of government securities to the private sector; the private sector is made willing to hold these securities in place of idle balances by the rise in the interest yield obtainable.

The picture is not significantly changed if (some of) the securities sold by the central bank are bought directly by the public rather than by the commercial banks. The banks’ reserves are then reduced by the same amount but their deposit liabilities—against which reserves must be held—are also reduced. The amount of security holdings that the banks are obliged to sell to the community to bring their deposits into line with the new reserve position is smaller than in the first case, the amount of sales necessary being reduced by exactly the amount of the central bank’s open market sales that were bought by the private sector. Hence, the fact that the central bank’s open market offerings may be bought by the private sector rather than by commercial banks does not affect the equality between the reduction in commercial bank credit (the reduction in the public’s money holdings), on the one hand, and the increase in the public’s security holdings, on the other.

This conclusion continues to be valid if the reduction in commercial bank credit takes the form of a reduction in the banks’ loans to the public rather than of sales of government securities to them. Insofar as the businesses that redeem bank loans issue their own debt to the public, the changes in money and in securities remain equal. Insofar as businesses reduce their fixed or inventory investment outlays when they redeem (or are denied) bank credit, the government will be issuing an equal amount of extra securities. (This follows from the assumption of this study that the government will raise its expenditures relative to its revenues by an amount sufficient to cancel out any contractionist effects from the rise in interest rates.)

One small break in the equalities may develop. Insofar as borrowers from banks are included among those whose cash holdings are made to seem excessive by a rise in interest rates, there will not be a fully equivalent rise in the supply of securities; some cash will be used to pay off debt rather than to buy securities. However, the reduction in the interest-bearing debt of such money holders can be considered equivalent to a rise in their net holdings of interest-bearing assets.

Interest Elasticity of Private Sector’s Demand for Demand Deposits

Numerous estimates are available of the interest elasticity of the private sector’s demand for money in the United States. Problems arise in calculating elasticity, such as a coincidence of strong time trends in interest rates and in velocity, and cyclical variations in the ratio of desired money holdings to income which are independent of the interest rate (being caused, e.g., by the public’s view that peak income levels are abnormal and transitory or by cyclical variations in the share of total money transactions carried out by sectors which use money efficiently, e.g., heavy industry) .8

Brunner found for the conventional relationship (fitted to annual data, 1929-55) a statistically reliable elasticity of 0.23.9 This figure has to be inflated by approximately 70 per cent to correct for the fact that the dependent variable includes currency and time deposits (both here assumed to be unaffected by interest rates), and then to be deflated by between one third and one half to allow for the fact that the interest rate variable used is a less flexible “index of bank loan rates and bond yields.” These adjustments leave the elasticity of 0.23 unchanged or only slightly changed.

Brunner also tested two variants of the “permanent income” hypothesis of Friedman (which suggests that the ratio of desired liquid assets to current income varies over the cycle because desired holdings are linked to a normal income level, such as that given by a moving average of income, rather than to the perhaps abnormal income of the current year).10 It is interesting that one test yielded about the same interest elasticity as that found under the simple, conventional assumption, while the other yielded a slightly higher elasticity: 0.30. Again the correlations were high and the interest regression coefficient statistically quite significant. With the interest elasticity so little influenced by the introduction of “permanent income” among the independent variables, it can be assumed that neglect of the “permanent income” hypothesis does not create a serious upward bias in the estimate of interest elasticity.

The first of the two “permanent income” relationships tested also contained a statistically significant variable representing the phase of the cycle—the ratio of real income in the current year to the average over the last few years. It might be argued that the introduction of such a variable would remove any upward bias in the interest elasticity caused by cyclical variations in velocity of circulation that are due to systematic cyclical changes in the distribution of transactions between high-velocity and low-velocity segments of the economy.11 However, that view can be no more than tentatively held until the experience in years more recent than 1955 is tested.

Bronfenbrenner and Mayer have presented a melange of estimates of money elasticity, some using previous-year income as an independent variable, some including the stock of wealth, etc. The results most directly relevant to the present study are comparisons of year-to-year changes in the money/income ratio with changes in the Treasury bill rate. These comparisons were made only where a scatter diagram showed that at least three successive annual observations lay in something close to a straight line that had a negative slope (the rationale being that the movements between adjacent observations which did not form such a line reflected shifts in the liquidity preference function). The median elasticity found for such “runs” was 0.34, with the quartiles lying at 0.19 and 0.64.12 Whatever value is accepted, it should be inflated by one fifth to one fourth to allow for the fact that in the present study the interest-insensitive segment (currency) is excluded from the dependent variable. Presumably the median elasticity found by Bronfenbrenner and Mayer, 0.34, will be the most acceptable figure; the resulting elasticity for our purposes is thus about 0.4.

The Banks’ Elasticity of Supply of Credit

Total “primary” or “reserve” money, R, provided at the initiative of the central bank (i.e., excluding any reserves that the commercial banks have borrowed from the central bank) is absorbed by the reserves legally required against banks’ deposits, by the banks’ desired excess reserves (net of borrowings from the central bank), and by currency in circulation.13

RC0(rrOD+frODTotalprimarymoneyCurrencyoutsidebanks(constant)Allotherdeposits(constant)Desiredfreeratioforotherdeposits=Desiredfreeratioforotherdeposits=DDs×(rrDD+frDD)PublicsdemanddepositssuppliedbybanksRequiredanddesiredfreereserveratiosfordemanddeposits(1)

Let

frDD=(a+bi)DDs(2)
frOD=(a+bi)ODo14(3)

Substituting (2) and (3) in (1), solving for DDs, and differentiating with respect to the interest rate (i), leads to the interest elasticity of the banks’ supply of demand deposits:

ηs=brrDD+ai+b.{1+ODoDDs}15(4)

The average required ratio of reserves to the public’s demand

deposits was 14.8 per cent for all member banks during the eight

weeks ended mid-May 1962.16 For the free reserve/deposits ratio, a recent study has quantified the relationship, a + bi, as .005 — .23 i.17

The average interest (Treasury bill) rate was 2.7 per cent during March, April, and May 1962, while the daily average ratio of other deposits to demand deposits held by the public in member banks was 1.0 during the eight-week period ended in mid-May.18 Then, given the actual level of reserve money and the existing interest rate in the spring of 1962, the interest elasticity of the supply of bank credit going into the public’s demand deposits was just under 0.10.19

Induced Changes in Long-Term Rates

So far, this discussion has been limited to a consideration of the effects of reserve policy on the level of short-term rates. It should be recognized that any movements of short-term rates may be accompanied by some movement in long-term rates. If the preceding analysis is based on the assumption that only the short-term rate rises when the banks’ reserve base is reduced, it might seem that a further reduction of reserves would become necessary (an extra leftward shift in the supply curve) as the effects of the initial reductions in supply are partly diverted into the long-term market. The rise in the short-term rate will cause some short-term borrowers to shift to the long-term market (and some lenders to shift the opposite way), so that the long-term rate will be pulled up, and a counteracting, downward pressure on short-term rates will be created that holds the short-term rate below i1. Restoration of the assumed rise in short-term rates (by a further reduction of the reserve base and money supply) will cause the long-term rate to be pulled up still further. In consequence, reductions in the stock of money must be made not only to counter the shift from cash to short-term securities which the public would make if the short-term market were isolated, but also to counter the additional shifts from cash to long-term securities that will be evoked because the two markets are interconnected.

It would be difficult to determine the exact contraction of money required, for the various substitution elasticities involved are not known. This obstacle can be side-stepped, however. The maximum possible rise in long-term rates that could be induced by borrower and lender shifts is one which would equal (after adjustment for the differing characteristics of the two kinds of security)20 the ultimate rise in short-term rates. Shifts of lenders out of, and of borrowers into, the long-term market would stop once long-term rates had risen by as much as short-term rates. It follows that the maximum rise in the public’s demand for securities is set by the condition of equal (adjusted) change in long-term and short-term rates, for the public obviously makes its largest shift from money to securities (of all terms) when the given rise in short-term rates is accompanied by the largest possible rise in yields on long-term issues.

Observation of movements in interest rates over the business cycle suggests that there are sympathetic movements of long-term and short-term rates. As increasing demands of business for short-term financing raise the supply of short-term securities during a cyclical expansion, increasing demands for long-term financing simultaneously raise the supply of long-term securities; both short-term and long-term rates therefore tend to rise together (and substitution elasticities should be sufficiently strong to cancel out much of the effect on relative interest rate levels of any tendency for unbalanced changes in the two supplies). Since the observed relationships between short-term interest rates and money holdings that are used to derive interest elasticities of demand for money are dominated by such cyclical variations, it follows that the estimates of the amount of open market operations necessary for given increases in the short-term rate obtained by use of these elasticities are maximum values. Hence, fairly full allowance has already been made for all possible diversion of pressure on the short-term interest rate into the long-term market.

In the situation under discussion, there must of course be some diversion of pressure to the long-term market. Even if borrowers could not shift their public issues of securities from short-term to long-term form, and even if savers could not shift funds from the long-term to the short-term market, some rise in long-term rates would be certain to occur (provided the maturity of the pre-existing government debt was not shortened), because a part of the addition to the supply of securities would consist of issues of more than short term: the government securities sold off by commercial banks may include two-year to five-year issues, and businesses that are refused bank loans will, to some extent, issue medium-term and long-term debt instead. (This must happen because of the limitations of the nonbank market for short-term private debt and because some of the refused bank loans would themselves have been almost medium-term.) In sum, the long-term rate should show some sympathetic response to the rise in the short-term rate but less than its normal response where the change in the short-term rate was a cyclical one. Thus, the elasticity of demand for demand deposits with respect to the short-term rate is most probably lower than the observable interest elasticity; the status of the figure derived in this study for needed open market operations as an upper-limit estimate is therefore unshaken and probably strengthened.21

Relaxation of Assumption of Constant Time Deposits

The preceding discussion has assumed for simplicity of exposition that the rise in market rates of interest would exceed the accompanying rise in rates on time deposits by just enough to keep the total of time deposits unchanged. It is necessary to see whether this assumption has biased the findings on the scale of open market operations.

The observable interest demand curve for demand deposits has probably satisfied the conditions of the simplifying assumption in the past. Time deposit rates have tended to move sluggishly and to be restrained by comparatively low legal ceilings. Until 1957 the maximum rate payable was 2½ per cent for all savings deposits and for time deposits held over 6 months; for time deposits for 3-6 months and for less than 3 months the maxima were, respectively, 2 per cent and 1 per cent. Beginning with 1962, however, the maximum rates have been set at 4 per cent for 1-year time or savings deposits, 3½ per cent for 6-12 month time (and all other savings) deposits, etc.22 It is likely, therefore, that today a large part of the interest elasticity in the demand for demand deposits is accounted for by shifts from demand deposits to time deposits rather than to other securities.

Insofar as the new availability of time deposits as a profitable alternative investment means that some of the funds shifted out of demand deposits now go into time deposits instead of into government securities, etc., the reduction in the banks’ total deposit liabilities required (for any given rise in Treasury bill yields) is smaller than the reduction (in demand deposits alone) assumed above. The necessary reduction in the banks’ reserve base through open market operations is correspondingly smaller.

The effects on the reserve base are not entirely in one direction. A part of the additions to time deposit holdings will represent extra reductions in the holdings of demand deposits: the development of time deposits as an alternative to demand deposits which is profitable as well as convenient may enlarge the size of the transfer from demand deposits that occurs in response to any given increase in the yield on Treasury bills. To this extent, larger open market operations would be required, for the reserve requirement on time deposits is lower than that on demand deposits, so that conversion of demand deposits into an equal amount of time deposits means a reduction in the required reserves of the banking system. Expressed in other terms, the likelihood of higher flexibility in time deposit interest rates means a higher interest elasticity of demand for demand deposits and therefore connotes a need for more reduction in the banks’ reserve base than would be necessary if time deposits were not so attractive. It should be kept in mind that this conclusion holds only for countries where, as in the United States, the reserve requirements for time deposits are lower than those for demand deposits; where the two reserve requirements are equal, the part of the interest elasticity of demand for demand deposits that represents shifts between demand and time deposits should be entirely disregarded because such shifts do not affect the amount of banks’ required reserves.23

Given the probability that the reaction of the yield on time deposits to the yield on Treasury bills is still sluggish in the United States, it is safe—in the absence of contrary information—to assume that there would be no important difference between the reserve-using effect of those increases in time deposits which occur in place of the acquisition of other interest-bearing assets and the reserve-saving effect of those shifts which occur in place of the retention of demand deposits.24

The two opposing biases created by disregarding the variation in time deposits may not be of equal size, but the difference between them can be expected to be quantitatively unimportant. Constancy of time deposits can be retained as a working assumption, unless conditions change to make the difference between the two opposite biases important.

Conclusion

The available evidence regarding the interest elasticities of the demand for money and the supply of bank credit indicates that central bank intervention on a relatively small scale will lead to substantial changes in the short-term interest rate. In the United States, it seems that the upper limit for the sum of the interest demand and interest supply elasticities is about ½. From the formula developed above, it follows that to effect a one-third rise in the yield on U.S. Treasury bills—from 2.7 per cent to 3.6 per cent—would require, as a first approximation, a reduction of one sixth in the reserve base underlying the demand deposit portion of member banks’ liabilities. That base being about $13 billion, the Federal Reserve would have to sell about $2.1 billion, or 7 per cent, of its $30 billion portfolio of government securities. Given the upward bias in the formula, and the likelihood of an upward bias in the demand elasticity, the necessary volume of open market sales required to raise short-term U.S. interest rates by one third can safely be assumed to be below $2 billion.

The quantitative importance of the associated money and credit changes may be of interest. If the private sector’s elasticity of demand for demand deposits is 1/3, a one-third rise in the Treasury bill rate would imply that the private sector’s demand deposits were reduced by (less than) 11 per cent. This represents less than a 9 per cent reduction in the money supply of $145 billion or a reduction of less than 6 per cent in the $220 billion total of commercial bank credit (loans and security holdings). Although these percentages are not large, the required reduction of commercial bank credit would be sufficient to create the risk of depressing the economy if antideflationary budget policies were not implemented skillfully. Nevertheless, the finding of this study remains: the monetary authorities probably are well equipped to bring about substantial increases in short-term interest rates in the United States. The facility with which the change can be achieved is so marked as to suggest that substantial changes in short-term rates are well within the capabilities of the central banks of other financially developed countries even though institutional conditions may be less favorable.

APPENDIX I: Formula Relating Increase in Interest Rates to Amount of Reduction of Bank Reserves

Let ηS = interest elasticity of supply of demand deposits

ODs = demand deposits supplied

ηD= interest elasticity of demand for demand deposits

ODD = demand deposits demanded

i0 = initial level of short-term interest rate

di = desired change in short-term interest rate

A,B,E are defined in connection with Diagram 1 above.

Bydefinition:ηS=dODsdii0ODs(1)
FromDiagram1:dODsdiAE(2)
Substituting:ηs=AE.i0ODsAE.i0OD0(3)
Bydefinition:|ηD|=|dODD|di.i0ODD(1)
FromDiagram1:|dODD|di.BE(2)
Substituting:|ηD|=BE.i0ODDBE.i0OD0(3)

Combining (3) and (3)’, we have

ηS+|ηD|(AOD0+BOD0).i0E=A+BOD0.idi(4)
A+BOD0dii.(ηS+|ηD|)(5)

where A+BOD0 is the proportional shift in the supply curve for demand deposits. (interest rate held constant) or the proportional reduction in the reserve base underlying the demand deposits.

Given the crudity of the available estimates of elasticity, this formula can be accepted as a sufficiently close approximation where small proportional changes in the interest rate are involved. However, because as much as a one-third rise in the interest rate is at issue, the formula can yield appreciable biases. For S1 in Diagram 1 to have the same elasticity as S0, it would have to have a steeper slope than S0. The steeper slope would mean a higher intersection with the unchanged demand curve, D—i.e., a larger rise in the interest rate as the supply curve was shifted from S0 to S1. It follows that the formula exaggerates the amount of shift (and the amount of open market operations) necessary to produce any substantial rise in interest rates. The exaggeration can be shown to be minor, however. A rise in the slope of S1. sufficient to hold its elasticity equal to that of S0. would reduce the necessary percentage reduction in supply of demand deposits (A + B)/OD0 by only the very small fraction,ηS.dii1+ηS.dii (by about 3 per cent if a one-third rise in interest rates is sought). Moreover, the formula employed for the elasticity of the supply curve (fn. 15, equation 3c) shows that shifting the supply curve to the left by reducing the reserve base would cause some increase in the curve’s elasticity; it follows that the overestimate is still smaller than this.

A more serious bias in the formula is found if the supply and demand curves are concave upward (instead of being the straight lines shown in the diagram). Concavity is justified both under the “normal” assumption of constant elasticity and by statistical observation. But if the higher ranges of the curves are steeper than the lower ranges, S1 and D must intersect at an interest rate higher than i1, and once more a shift smaller than (A + B) in the supply curve will be sufficient to raise the interest rate to i1 In the absence of data on the actual shapes of the curves, it is possible to say only that an appreciable overestimation of the necessary shift in the supply curve, e.g., a one-tenth overestimate, should exist.

Régulation des taux d’intérêt à court terme par l’action monétaire

Résumé

La libéralisation croissante des mouvements de capitaux internationaux et la progression de l’intégration économique ont mis en lumière le problème de la prévention des trop grandes différences de taux d’intérêtà court terme entre pays à marchés monétaires développes. L’avantage d’un tel contrôle est déterminé, en partie, par l’aptitude des autorités monétaires à intervenir facilement et à bref délai en vue de modifier sensiblement les taux d’intérêt sur le marché monétaire.

Si les désirs d’encaisse des particuliers sont, à niveau constant du produit national brut, influencés par le niveau des taux d’intérêt, on peut considérer qu’une variation de la masse monétaire entraíne une variation déterminée du taux d’intérêt à court terme, et vice versa. Un tel rapport subsiste, quelles que soient les institutions monétaires et de banque centrale d’un pays. Ce rapport fait apparaítre que le volume de l’augmentation du taux à court terme est déterminé par (1) le montant de la réduction décidée par la banque centrale quant aux crédits et par conséquent à la monnaie qui sont mis par les banques commerciales à la disposition des particuliers, (2) le volume de l’accroissement compensateur de l’octroi de credit par les banques commerciales, provoqué par la hausse du taux d’intérêt pratiqué sur les prêts et les valeurs mobilières, et (3) l’importance de la réduction con-comitante des désirs d’encaisse des particuliers, provoquée par l’augmentation des taux d’intérêt. II ressort des renseignements disponibles sur les Etats-Unis que l’élasticité de l’offre ainsi que de la demande de crédit bancaire en ce qui concerne le taux d’intérêt est si faible que des relèvements substantiels de l’intèrêt à court terme peuvent être réalisés au moyen de faibles réductions proportionnelles de la réserve de base pour l’ensemble des dépôts bancaires. La vente sur le marché libre d’une légère fraction des titres publics à court terme détenus par le Système de Réserve Fédérale serait probablement suffisante pour faire monter d’un point le rendement des Bons du Trésor.

Cette conclusion repose sur deux hypothèses: l’une d’après laquelle la politique de déficit budgétaire systématique de l’Etat est menée de telle sorte que le relèvement des taux d’intérêt ne puisse provoquer de pressions déflationnistes, et l’autre d’après laquelle l’augmentation induite des taux d’intérêt à long terme atteindra le montant maximum prévisible. La première hypothèse évoque certains des grands problèmes que peut soulever toute variation des taux d’intèrêt; la seconde convertit l’estimation en ce qui est probablement une valeur maximum de l’intervention de la banque centrale.

En dépit des différences de structure entre les institutions et les comportements, la preuve même que des changements substantiels dans les taux d’intérêt à court terme peuvent être facilement provoqués est si évidente dans le cas des Etats-Unis que I’on est en droit d’attendre une souplesse analogue en ce domaine dans les autres pays où existe un marché monetaire organisé.

Regulación de las tasas de interés a corto plazo mediante la intervención en el campo monetario

Resumen

La mayor libertad existente en los movimientos internacionales de capital y la integración económica más extendida, han llamado la atención sobre la cuestión de cómo impedir que ocurran amplias divergencias entre las tasas de interés a corto plazo en los países que tienen mercados monetarios desarrollados. El que deba o no ejercerse control sobre esas divergencias depende en parte del grado de la facilidad y rapidez con que las autoridades monetarias pueden actuar para provocar cambios substanciales de las tasas de interés del mercado monetario.

Si el nivel de las tasas de interés influye sobre las tenencias monetarias que el público desea mantener, a niveles fijos del producto nacional bruto, puede considerarse que cualquier cambio verificado en el medio circulante causa un cambio definitivo en la tasa de interés a corto plazo, y viceversa. Esta relatión es válida, cualesquiera sean las instituciones monetarias y de banca central de un país. Por esta razón se demuestra que el monto del aumento de la tasa de interés a corto plazo se determina por (1) el volumen de la disminución que el banco central efectúa en la oferta de crédito de los bancos comerciales y, en consecuencia, en los medios de pago, (2) el monto del aumento compensador que se registra en la oferta de crédito de los bancos comerciales como resultado del aumento de la tasa de interés que es posible obtener sobre los préstamos y valores, (3) el alcance de la reductión concomitante en las tenencias de medios de pago que el público desea mantener, debido al alza de la tasa de interés. Los datos disponibles sobre los Estados Unidos indican que la elasticidad-interés tanto de la oferta de crédito bancario como de la demanda de dinero es tan baja que permite obtener aumentos substanciales en las tasas de interés a corto plazo mediante pequeñas reducciones pro-porcionales en la base de la reserva para el total de depósitos bancarios existentes. Las ventas en mercado abierto de una pequeña proportión de las tenencias en valores a corto plazo del Sistema de Reserva Federal bastaràan probablemente para ocasionar un alza de un punto porcentual en el rendimiento de los bonos del Tesoro.

Se llega a esta conclusión suponiendo que se ajustan los gastos deficitarios del gobierno de modo de evitar que el alza de las tasas de interés conduzca a presiones deflacionarias, y que tendrá lugar la máxima alza inducida que se pueda prever en las tasas de interés a largo plazo. La primera de estas hipótesis hace pensar en algunos de los mayores problemas que puede traer consigo cualquier cambio en las tasas de interés; la segunda convierte la estimatión en lo que probablemente constituye el valor máximo de la interventión del banco central.

Pese a que las instituciones y normas de conducta varían de uno a otro país, la evidencia de que pueden provocarse fácilmente cambios substanciales en las tasas de interés a corto plazo es tan concluyente en el caso de los Estados Unidos, que obliga a pensar que existe una flexibilidad parecida en otros países que cuentan con un mercado monetario desarrollado.

*

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

1

See J. J. Polak, “International Coordination of Economic Policy,” Staff Papers, Vol. IX (1962), pp. 169–72, for a brief discussion of the problems involved in this type of coordination.

2

See W. R. Gardner, “An Exchange-Market Analysis of the U.S. Balance of Payments,” Staff Papers, Vol. VIII (1960-61), pp. 195-211, for a discussion of the significance of the “exchange-market balance of payments” for economic analysis.

3

Data from Germany indicating a close statistical relationship between the short-term interest rate and the free reserves of the banks are provided by F. A. Lutz, “Die Liquiditat des Banksystems und die Zinssatze,” Weltwirt-schaftliches Archiv, Vol. 87, No. 2, 1961, pp. 273-305; see especially the series for free reserves (the excess of the banks’ surplus legal reserves over their borrowings from the central bank) and the day-to-day money rate in 1951-60 charted on page 295. As will be described below, such a relationship suggests the existence of a valid interest-supply curve for bank credit. It is not clear, however, that the series do in fact reflect such a supply relationship. Lutz himself is equivocal. At one point he accepts the data as indicating a valid causal relationship (pp. 294, 296) although he had previously observed that borrowing from the central bank was only an emergency measure adopted when other factors were reducing the bank’s reserves and loan-making power (pp. 275-79)— which may imply a weak or nonexistent interest/credit supply relationship. These views need not be inconsistent, however. On many occasions the observed coexistence of declining reserves and rising debt to the central bank may be simply an adjustment to temporary losses of reserves that are not associated with changes in the levels of the interest rate. When interest rates do rise, the banks may be made willing both to lend out excess reserves and to borrow more reserves in order to expand credit further; since expanding credit means losing some reserves through currency drains, borrowing from the central bank may coincide with reserve losses but still be caused by a different factor, i.e., rising interest rates.

4

For a fairly extensive bibliography on this subject, see Martin J. Bron-fenbrenner and Thomas Mayer, “Liquidity Functions in the American Economy,” Econometrica, Vol. 28 (1960), pp. 810-34.

5

J. J. Polak and W. H. White, “The Effect of Income Expansion on the Quantity of Money,” Staff Papers, Vol. IV (1954-55), pp. 422-28; A. J. Meigs, Free Reserves and the Money Supply (University of Chicago, 1962).

6

This exclusion would not be made for countries where these borrowings are large and their amount is in effect determined by the central bank (through varying rediscount quotas, changing the application of penalty rediscount rates, etc.).

7

The assumption that central bank open market operations must cause a proportional reduction of only the part of reserves that banks did not acquire by borrowing from the central bank is itself dependent on an implicit assumption that the banks will not raise their ratios of central bank borrowing to deposits when deposits fall. Insofar as the central bank does not reduce a bank’s (formal or informal) rediscount quota fully in proportion to reductions in the bank’s deposit liabilities, the bank may in fact show a rising ratio of borrowings to deposits—a falling ratio of free reserves to deposits—when deposits fall, even though interest rates are held constant. This would mean that the reduction in the bank’s non-borrowed reserve holdings brought about by open market operations would have to be somewhat more than in proportion to the reduction (at constant interest rates) in the bank’s deposits. However, the assumption that open market sales are no more than proportional can be retained because the reserves obtained by borrowing from the central bank are always a negligible proportion of total reserves held.

8

Another reason for expecting cyclical variations in velocity is that the average cost of investing temporarily idle funds declines as the volume of transactions—and hence the amount of funds temporarily idle—increases. (W. J. Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” Quarterly Journal of Economics, Vol. LXVI [1952], pp. 545-56.) This means that velocity should be high when business activity is high, even if the interest rate has no influence. It has been pointed out (Polak and White, op. cit., p. 416, fn. 15) that this factor should not operate insofar as the cyclical rise in the volume of transactions reflects increases in the price level or in the number of businesses carrying out the transactions. Statistical evidence on the operation of this factor within the individual firm is said to be in favor of stability in the ratio of cash holdings to the transactions of business companies (cf., abstract of a paper by A. H. Meltzer, Econometrica, Vol. 29 [1961], p. 456). “Economies of scale” were found for cash holdings as the size of company rises within the “small” and “medium” ranges, but not for the economically dominant “large” size group.

9

Karl Brunner, “Some Major Problems in Monetary Theory,” American Economic Review, Vol. LI, Papers and Proceedings, May 1961, p. 56. The formula was logmoney+timedepositspopulation=.30.23loginterest+.89logGDPpopulation. R = .993. Standard error of the interest coefficient = .06.

10

Milton Friedman, “The Demand for Money: Some Theoretical and Empirical Results,” Journal of Political Economy, Vol. LXVII (1959), pp. 327-51.

11

Paul F. McGouldrick, “A Sectoral Analysis of Velocity,” Federal Reserve Bulletin, December 1962, pp. 1557-71, found that the share of heavy industry in total money transactions is relatively high in prosperity. This sector uses money much more “efficiently” than, say, consumers, whose share declines in prosperity.

12

M. J. Bronfenbrenner and T. Mayer, op. cit., p. 829. These investigators may have been led to de-emphasize the influence of the wealth variable because of the currently prevalent argument that desired money holdings may not be directly a function of the cost of holding money (the interest income forgone) but instead a function of the value of total wealth held, with the market value of wealth itself an inverse function of the level of interest rates. If so, the wealth variable would in part duplicate the interest variable. Because the interest rate presumably has little influence on the market value of wealth, and because many wealth holders may be affected more by the cost or face value than by the current market value of their assets, the concern over this duplication seems exaggerated.

13

Minor refinements include allowances for Treasury and other deposits in the Federal Reserve System. Currency held by the member banks as vault cash will be shown to be of minor significance. (Such currency is now counted in legal reserves. Allowance for it would not greatly affect the size of the elasticity—see footnote 14, below—since any portion that the banks are not certain will remain available to meet reserve requirements is probably, in the aggregate, a small and stable fraction of deposits.) When deposits are expanding to levels not previously attained, the banks may feel obliged to raise new capital, and they must use a small fraction of such capital to purchase Federal Reserve shares. This hidden “reserve requirement” is very small, however, and in any case has only limited relevance where there is a tendency for deposits to fall below previous levels. Nonmember bank deposits at the Federal Reserve are unimportant in themselves but introduce the question of the one sixth of the public’s demand deposits that are held in nonmember banks. Allowance for these is made difficult because of the uncertainties about, and inconsistencies in, the reserve requirements of these banks. (In some cases, requirements are equal to those set by the Federal Reserve but are satisfied by deposits maintained in large-city commercial banks.) These banks tend to be small and remote from commercial or financial centers. It is plausible that they do not adjust their credit supplies to the interest rate as sensitively as do member banks. Furthermore, their depositors likewise may tend to have exceptionally low interest elasticities of demand for money. Because of these considerations, the one sixth of the public’s demand deposits held in nonmember banks is disregarded here.

14

The time and savings components of the unchanging deposits, OD0, may seem to require smaller free reserve ratios, at any given level of interest rates, than do the demand deposits held by the public, DDs. However, the unchanging deposits include interbank demand deposits, and these may require very high free reserves because they tend to be the deposit-owning bank’s first line of reserves. In the absence of means for distinguishing the free reserve ratios associated with OD0 and with DDs, it therefore seems permissible to assume that they are equal. The interest elasticity would not be greatly affected if the observed free reserves were allocated under the assumption that frDD = 2 0D.

15

The derivation of ηs is achieved by the following steps: Substituting (2) and (3) into (1): DDs=RCo(ODo)rrODODo(a+bi)rrDD+a+bi(3a)

Differentiation of (3a) yields dDDsdi=bOD0.rrDD+RCoODo.rrOD(rrDD+a+bi)2(3b)

Dividing by (3a) and multiplying by i yield the following for the interest elasticity of supply: ηs=brrDD+ai+b.RC0OD0(rrOD)+OD0(rrDD)RC0OD0(rrOD)OD0(a+bi)=brrDD+ai+b.{1+OD0(rrDD+a+bi)RC0OD0(rrOD)OD0(a+bi)}(3c)

From (3a) it is seen that the fraction inside the braces in (3c) equals OD0DDs. Substitution of that expression in (3c) yields the formula for supply elasticity presented above.

16

Derived from Federal Reserve Bulletin, June 1962, p. 709.

17

A. J. Meigs, op. cit., p. 75. Meigs employs monthly data, using them to estimate the speed with which banks return to their desired free reserve ratios after a change in their excess reserve holdings has occurred.

18

Federal Reserve Bulletin, June 1962, p. 709. The figure for each deposit group was between $92 billion and $93 billion.

19

As noted above, this formula does not provide for the amount of vault cash which banks must hold for operating purposes. However, as the definition of minimum required reserves has been changed to include vault cash, these holdings may reasonably be ignored; they are now part of the reserve base. Some smaller banks may not treat vault cash as a complete substitute for deposits at the Federal Reserve, because of its erratic behavior. (See “The Vault Cash Provision: Has It Changed the Way Banks Manage Their Reserves?” Federal Reserve Bank of Philadelphia, Business Review, September 1961, pp. 11-15.) Ample allowance for the extra desired “excess” reserve holdings that may now exist because of this consideration could be provided by raising the constant term, a, from .005 to .015 or .02 (Polak and White, op. cit., p. 427, fn. 30, found that the vault cash/deposits ratio had been very stable regardless of the level of the short-term interest rate, so that the constant term is the one to be modified).

With the constant term raised to .02, the elasticity is reduced from .085 to .077. This is within the range of .07-.08 found by Polak and White (op. cit., p. 428) for a period ending five years earlier than the period covered by Meigs.

20

The rise in the long-term rate would actually be less than the rise in the short-term rate, for economic conditions justifying high long-term rates would be absent when the short-term rate was being raised merely for transitory balance of payments reasons. The relevant total yield on long-term securities—that commensurable with the short-term rate—would be the long-term interest yield plus the value of the prospect of a capital gain to be obtained when long-term rates fall back again. (The same consideration operates to hold even cyclical rises in long-term rates below the accompanying rises in short-term rates, although not so strongly.)

21

This analysis of the influence of the long-term market on the elasticity of the public’s demand curve for deposits could also be applied to the elasticity of the bank’s supply of credit (of deposits), but the observed supply elasticity is already so low that any resulting changes in it would be insignificant.

A study prepared for the Commission on Money and Credit took some account of the interaction between the short- and long-term markets (by including portions of short- to medium-term and of long-term security holdings, along with varying portions of the stock of money plus time deposits, as determinants of the level of the U.S. Treasury bill rate); this permitted the making of a most probable, rather than merely an upper-limit, estimate of the necessary amount of open market sales. (See Arthur M. Okun, “Monetary Policy, Debt Management and Interest Rates: A Quantitative Appraisal,” Cowles Foundation Discussion Paper No. 125, mimeographed, preliminary, esp. 22, 34, 38-39, 43, 44.)

Two estimates of equal statistical reliability were made on the basis of different definitions of the variable representing the stock of money and time deposits. Although noting that the two estimates were “distressingly far apart,” the investigator did not express his preference in this preliminary version of his report. While the estimated open market sales derived from the definition that seems to have greater economic meaning tends to confirm the findings of the present study, the other definition indicates a need for volumes of open market sales which might be impractical.

22

Federal Reserve Bulletin, January 1963, p. 31. Until 1961, the large New York banks refused to pay any interest on the time deposits of business corporations. They then made time deposits especially attractive to big companies by creating a marketable interest-bearing security, the “negotiable certificate of (time) deposit.”

23

This is the situation in the United Kingdom. Moreover, if the Bank rate is raised by the amount of the desired rise in Treasury bill rates, the yield on U.K. time deposits (which is linked to Bank rate) will rise by substantially as much as the yield on Treasury bills, so that time deposits can be expected to claim a good share of the funds diverted from British demand deposits. Other things equal, therefore, the amount of open market sales required to offset the consequences of lower demand deposits will be even smaller in the United Kingdom than in the United States.

Less restriction than in the United States is also indicated for Germany, even though German reserve requirements are (somewhat) lower for time than for demand deposits: First, a major part of the reduction in demand deposits must be reflected in transfers to time deposits because (Lutz, op. cit., p. 298) the domestic nonbank public in Germany has little access to other money market investments (except long-term bonds). Second, the yield on German banks’ time deposits rises less than the Bundesbank discount rate, and the net yield obtainable rises still less because the demand deposits themselves receive a (low) interest rate that is linked to the discount rate. A given rise in the Treasury bill rate therefore has an attenuated effect on the size of desired demand deposits even with the same rise for the discount rate.

The reduction of the effect on demand deposits may be counterbalanced by the appearance of an effect on currency: those financially sophisticated enough to be influenced by the level of interest rates obtainable on idle money may hold some of their idle money in the form of currency when the rate of interest is low, because demand deposits in Germany lack the attraction of being a convenient means of making check payments. And a shift from currency to time deposits strengthens the banks’ reserve position by almost the full amount of the funds shifted.

24

Other relevant considerations are the influence of the development of other convenient and safe short-term outlets for funds (such as finance company commercial paper) which compete with the banks’ negotiable certificates of time deposit, and the possible effects on the demand for currency of the high rates on savings deposits now obtainable when money is made tight.