What is the relationship between the reserve ratio and the money multiplier inverse or direct?
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THE PURPOSE of this paper is to examine some of the assumptions that are frequently implicit in monetary models of the economic system and to consider some of the lines along which further investigation of the operation of the banking system might be pursued. THE PURPOSE of this paper is to examine some of the assumptions that are frequently implicit in monetary models of the economic system and to consider some of the lines along which further investigation of the operation of the banking system might be pursued. Most analyses of the monetary mechanism proceed from an assumption that there is a relation, or a series of relations, between money and other assets available to the community. They examine the influence of these relations and of changes in the prime aggregate, money, on the rest of the economy. In general, they assume that the amount of money available to the community can be determined by the monetary authorities.1 This view is based on the traditional postulates regarding the operation of the banking system under a system of fractional reserve banking, which lead to the conclusion that the central bank has absolute control over its monetary liabilities.2 Deliberate changes in central bank monetary liabilities are assumed to result in proportionate changes in bank reserves. These changes in bank reserves, in turn, induce a secondary expansion or contraction by the banking system of an amount indicated by the ratio of currency in circulation to money and the ratio of customary or required reserves against deposits. These two ratios are considered to be reasonably stable, i.e., subject to only insignificant changes in the short run (in the absence of changes in legal reserve requirements). Hence it is assumed that the effect of given changes in central bank monetary liabilities on the total money supply is reasonably certain and predictable. It follows, from these assumptions, that a central bank can control the money supply in a fairly automatic and reliable fashion by producing changes in its monetary liabilities or, of course, by changing legal reserve requirements. Accordingly, limitations to central bank control of the money supply are attributed mainly to inability to manipulate monetary liabilities or to impose, vary, or enforce reserve requirements for banks. This inability may be the result of political or technical difficulties in offsetting changes in monetary liabilities arising from changes in foreign assets, or from credit given to the government as a result of fiscal policies. Limitations such as these are usually emphasized in discussions of monetary policy in less developed countries. For advanced countries, they are often considered insignificant.3 For such countries, discussions of monetary control are primarily concerned with the choice of instruments, the timing of measures, and their impact on effective demand for goods and services and on international capital movements. Inasmuch as a large part of banking theory has been developed in the United Kingdom and the United States, its assumptions are naturally related to the institutional setting in those countries. It might, therefore, be useful to examine the validity of the assumptions for a wider range of countries, in order to explore avenues along which the work being done toward integration of the banking mechanism into macro-economic analysis could be carried forward.4 It is assumed in this paper that central banks have absolute control over changes in their monetary liabilities. Attention is focused on their ability to control and predict the effect of these changes on the total money supply, i.e., on an examination of the stability of the ratio relating changes in money to changes in central bank monetary liabilities (the money multiplier). This ratio is determined by the ratios of currency to money and of required reserves plus working reserves to deposits.5 It is also influenced by changes in the nonmonetary liabilities of the banking system, excluding the central bank (e.g., time deposits and bank capital). If changes of this kind are ignored for the moment, the stability of the currency/money and reserve ratios will assure a fairly high reliability for predictions of the magnitude of secondary credit creation on the basis of a given change in central bank monetary liabilities. The validity of the assumption that these ratios are reasonably constant in the short run is a question of fact and can therefore be tested. The behavior of the two ratios and of the multiplier derived from them is reviewed here for selected countries6 and periods. First, the percentage changes in money that are attributable to changes in central bank monetary liabilities and to changes in the money multiplier are calculated for these countries. Then, the percentage changes in money attributable to variations in the three components of the multiplier (the ratio of currency to money, of required reserves to demand deposits, and of excess reserves to demand deposits) are estimated. Finally, the percentage changes in money which arise from (1) direct central bank action, i.e., through changes in its monetary liabilities and its required reserve ratio and (2) changes in behavior variables, i.e., the ratio of currency to money and the excess reserve ratio of banks, are separately identified. In conclusion, some implications of the estimated monetary impact of changes in the behavior variables are considered, and suggestions for further study are made. The conclusion of these investigations is that the assumption of short-run stability in currency and excess reserves, and therefore in the money multiplier, is not warranted. Although in most years observed the monetary effects of changes in central bank monetary liabilities and in legal reserve requirements exceeded those of changes in behavior variables, in certain years the opposite was true for most of the countries reviewed. The conclusion is that continued observation of the currency and excess reserve ratios and their explicit inclusion in the analytical framework would improve monetary analysis and focus attention on the feasibility of introducing further refinements. General Survey of Behavior of Currency and Reserve RatiosThe ratios of currency to money (c) and of total reserves to total deposits (r), as well as data for the money multiplier (k) derived from these ratios, are given in Table 1 for the 12 countries in the sample. For Canada, the United Kingdom, and the United States, comparable data on which to base the ratios are available for some 30 years; for the other countries, such data are available for only a few postwar years. An attempt has been made to have the reserves data for each country measure the significant totals that guide commercial banks in their lending policy. Hence, the composition of reserves varies from country to country, depending on local institutional factors, whereas the value of c is more consistent from country to country. For each country, Table 1 shows the averages of the data for the periods covered, and the average absolute and relative deviations of c, r, and k. Changes in the annual averages of the two variables and in the money multiplier are shown in the charts on pages 147-49. Table 1. Ratio of Currency to Money, Ratio of Total Reserves to Total Deposits, and the Money Multiplier, Selected Countries1 1For sources and explanatory notes, see Appendix II. 21c+r(1−c) where c is the ratio of currency to money and r the ratio of total reserves to total deposits. Because of rounding, the average of the money multiplier may not be exactly equal to the multiplier derived from the averages of c and r. Table 1. Ratio of Currency to Money, Ratio of Total Reserves to Total Deposits, and the Money Multiplier, Selected Countries1
1For sources and explanatory notes, see Appendix II. 2 1c+r(1−c) where c is the ratio of currency to money and r the ratio of total reserves to total deposits. Because of rounding, the average of the money multiplier may not be exactly equal to the multiplier derived from the averages of c and r. For the postwar years, c is lowest in Canada, the United States, the United Kingdom, New Zealand, and Japan, and highest in Egypt, the Philippines, and the Federal Republic of Germany; Brazil, Colombia, Ceylon, and Italy are in an intermediate position. The highest r’s are those for the United Kingdom, Italy, Egypt, the Philippines, and Colombia; the lowest are those for Canada, Germany, and Japan. For the three countries for which data are available for about 30 years, c shows a higher average for the postwar period than for the interwar years. While the ratio has declined since the end of the war in the United States and Canada, it has risen steadily in the United Kingdom. As reserve ratios in the three countries moved downward toward prewar-predepression levels, k changed in the postwar period inversely to c; i.e., while lower than in the interwar period, it rose in the United States and Canada and declined in the United Kingdom. In most of the other countries reviewed, both c and r tended to move downward during postwar years, with a resulting upward tendency in k. For the purposes of this paper the average annual deviations are, however, of greater interest than the secular changes in k. During the postwar period, the average relative deviations in k were highest in Italy, Japan, and New Zealand (6 per cent), and lowest in Brazil, Colombia, and Germany (1 per cent or less). In countries where legal reserve requirements were unchanged, or were seldom adjusted during the period, or did not exist, as in Canada, Ceylon, Italy, Japan, the Philippines, and the United Kingdom, the average percentage deviations in k provide an indicator of the extent to which changes in the preferences of the public in respect to currency, demand deposits, and time deposits, and of banks in respect to excess reserves, tended to influence the money supply. During the postwar years the percentage deviation was smaller in c than in r in all the countries except the United Kingdom.7 On the other hand, the average value of c was greater than that of r, except in the United Kingdom and in New Zealand. Therefore, in most of the countries reviewed a given percentage change in c had a greater effect upon k than an equal percentage change in r, a conclusion also suggested by the fact that, with the notable exception of the United Kingdom, the average percentage deviation in k was always closer to that of c than to that of r. A numerical example may illustrate the monetary implications of apparently small variations in c and r. In the United States during 1947-1958, the average absolute deviations in c and r were about 0.01 each. These deviations produced an average deviation in k of 0.17, because c was about twice as large as r and in almost all years both ratios moved in the same direction so that their changes were not of an offsetting type. The average k was 3.31. Therefore, k varied roughly between 3.48 and 3.14. This implies that, given outstanding central bank monetary liabilities of, say, $50 billion, the total of money might have varied between $174 billion and $157 billion, or by $17 billion, without any change in central bank monetary liabilities. With an average total for money of, say, $166 billion (50 × 3.31), the variation would have ranged from about +5 per cent to −5 per cent of the money supply.8 The potential percentage change in the money supply as a result of variations in k will be equal to L(k±ADk)M−1, where L denotes monetary liabilities of the central bank, k the average multiplier, ADk the absolute average deviation of k, and M money. Effects of Changes in Money Multiplier on MoneyThe order of magnitude of variations in k indicated by Table 1 suggests that it would be instructive to attempt a separation of the observed changes in money into those attributable to changes in central bank monetary liabilities and those arising from changes in the money multiplier. For the present exposition, it is statistically convenient to define the money multiplier as being equal to the ratio of money (M) to central bank monetary liabilities to the private sector and banks (L). As proved in Appendix I, Section 1, this expression, M/L, of the money multiplier is in fact, at any given point of time, the same as the more conventional expression, 1c+r(1−c) .9 In Table 1 and in the charts, k is expressed in terms of the ratio of total reserves to total deposits; at this point, and throughout the rest of this paper, it is calculated in terms of the ratio of total reserves to demand deposits.10 The total change in money may be separated into its two components: (1) the change arising from changes in central bank monetary liabilities (ΔM′t); and (2) the change arising from changes in the money multiplier (ΔM″t). That is,
As shown in Appendix I, Section 2, these two components can be very closely approximated by the expressions
These are expressed in absolute values. It is, however, of greater practical interest to express ΔM′ and ΔM″ as percentages of money in the previous period, in order to show the effect of changes in L and k on the percentage change in money. The percentages of the components for each year during the period 1952-58 and the average percentages (ignoring signs) for the whole period are given in Table 2 for 11 countries. The average k-effect on the money supply ranged from 11.5 per cent in New Zealand to 1.3 per cent in the United States, while the average L-effect ranged from 22.2 per cent in Brazil to 1.6 per cent in the United States. In all countries, the average percentage change in money due to the change in k (ΔM″t/Mt-1) was smaller than the variation associated with the change in central bank monetary liabilities (ΔM′t/Mt-1), although in most countries (the only exceptions being Brazil, Colombia, and Germany) this relation did not hold in every individual year. As might be expected, the excess of the average L-effect over the average k-effect was smallest in countries with relatively low rates of monetary expansion, such as Egypt, the United States, Canada, Ceylon, and the Philippines, and largest in countries with high rates of expansion, such as Brazil, Colombia, Germany, and Italy. This observation confirms the a priori expectation that the monetary effects of changes in the multiplier will be less significant when changes in central bank monetary liabilities are relatively large and will be more important when such changes are comparatively small. In other words, it would be most unusual for inflationary movements to be attributed to, although they could well be aggravated by, the k-effect. Table 2. Percentage Changes in Money Attributable (1) to Changes in Central Bank Monetary Liabilities and (2) to Changes in Money Multiplier, Selected Countries, 1952-581  1For sources and explanatory notes, see Appendix II. ΔM′t/Mt-1 represents the percentage change in money that is due to the change in central bank monetary liabilities, and ΔM″t/Mt-1 the percentage change in money due to the change in the money multiplier. ΔMt/Mt-1 represents the total percentage change in money. 2Average ignoring plus and minus signs. Table 2. Percentage Changes in Money Attributable (1) to Changes in Central Bank Monetary Liabilities and (2) to Changes in Money Multiplier, Selected Countries, 1952-581
1For sources and explanatory notes, see Appendix II. ΔM′t/Mt-1 represents the percentage change in money that is due to the change in central bank monetary liabilities, and ΔM″t/Mt-1 the percentage change in money due to the change in the money multiplier. ΔMt/Mt-1 represents the total percentage change in money. 2Average ignoring plus and minus signs. The inverse relationship between the changes in M′ and M″ which can frequently be observed appears to indicate that the k-effect often tends to compensate changes arising from the L-effect. This inverse relationship occurred most frequently in New Zealand, the United States, the Philippines, and Ceylon. However, inasmuch as the k-effect also reflects changes in the required reserve ratio, interpretation of the inverse relationships requires that the effects of changes in the currency/money and excess reserve ratios be isolated. Effects of Changes in Currency and Reserve Ratios on MoneyAfter the percentage change in money attributable to changes in the money multiplier is established, an attempt may be made to quantify the effects of changes in the currency/money ratio and in the ratios of required and of excess reserves to demand deposits on the multiplier, and ultimately on money. This is done in Table 3, which shows the percentage changes in money attributable to changes in the ratio of currency to money (ΔMc/Mt-1), of required reserves to demand deposits (ΔMr′/Mt-1), and of excess reserves to demand deposits (ΔMr″/Mt-1), the sum of which equals the percentage change in money attributed to the change in k (ΔM″t/Mt-1) in Table 2). The separation of changes in money into these three component parts is based on the formulation outlined in Appendix I, Section 3. In computing the effects of changes in c, r′, and r″ on money, a statistical discrepancy must be recognized. It was shown that, at a given point of time, the multiplier expressed in terms of M/L is equal to the one expressed in terms of c and r. Statistically, however, they are not exactly equal. (Table 5 in Appendix II shows both ratios as statistically observed.) The discrepancy is due in part to the use of time series derived from different sources. The series for M, L, and c were obtained mainly from International Financial Statistics (published by the International Monetary Fund), and the data on required and excess reserves from national sources.11 Whereas the statistical discrepancy is quite small in percentage terms for most years, the observed changes in k measured in terms of M/L or c and r, respectively, were in opposite directions in a few years. In such cases it is not possible to estimate the effect of changes in c, r′, and r″ on the observed money supply.12 Table 3. Percentage Changes in Money Attributable to Changes in Ratios of (1) Currency to Money, (2) Required Reserves to Demand Deposits, and (3) Excess Reserves to Demand Deposits, Selected Countries, 1952-581 1For sources and explanatory notes, see Appendix II. ΔMc/Mt-1 represents the percentage change in money that is due to the change in the currency/money ratio; ΔMr′/Mt-1, the change due to the change in the ratio of total required reserves to demand deposits; and ΔMr″/Mt-1 the change due to the change in the ratio of excess reserves to demand deposits. The sum of the three percentages, ΔMr″/Mt-1 equals the corresponding item in Table 2. 2Average ignoring plus and minus signs. Table 3. Percentage Changes in Money Attributable to Changes in Ratios of (1) Currency to Money, (2) Required Reserves to Demand Deposits, and (3) Excess Reserves to Demand Deposits, Selected Countries, 1952-581
1For sources and explanatory notes, see Appendix II. ΔMc/Mt-1 represents the percentage change in money that is due to the change in the currency/money ratio; ΔMr′/Mt-1, the change due to the change in the ratio of total required reserves to demand deposits; and ΔMr″/Mt-1 the change due to the change in the ratio of excess reserves to demand deposits. The sum of the three percentages, ΔMr″/Mt-1 equals the corresponding item in Table 2. 2Average ignoring plus and minus signs. For the periods observed, the average effect of changes in Mc (disregarding sign) ranged from 6 per cent in Brazil and 5 per cent in Japan (the only countries where c always declined) to less than 1 per cent in the United States and Germany. The effect of changes in excess reserves (Mr″) ranged from 11 per cent in New Zealand and 5 per cent in Brazil and Italy to less than 1 per cent in the United States and Germany.13 Ceylon is the only country where the excess reserve ratio declined in almost all years observed; in most years this trend counteracted the contractive effects of changes in c and r′ and in 1952-54, of changes in monetary liabilities. In interpreting the effect of changes in the ratio of required reserves to demand deposits (Mr′), it should be noted that for countries which did not change legal reserve requirements, or which changed them only slightly during the years observed (e.g., Italy, the Philippines, and Ceylon), the (Mr′) effect might be expected to be zero. However, inasmuch as r′ refers to the ratio of total required reserves to demand deposits, it may change without changes in the legal ratio, when the proportion between demand and time deposits changes. Similarly, if reserve requirements are related to the capital of banks, as in Italy, or to the location of banks, as in the United States and Germany, the effective required reserve ratio may change without any formal change in the nominal ratio. The average effect of changes in the required reserve ratio ranged from 6 per cent in New Zealand (mainly because of frequent changes in reserve requirements) and 4 per cent in Italy (mostly contractive and due, probably, to the significant rise in bank capital accounts) to about 1 per cent in Brazil, Ceylon, Egypt, and the Philippines. In Germany and the United States, where reserve requirements were frequently changed, the Mr′ effect exceeded that of the other two variables and was the opposite of the L effect, in almost all years observed. In some cases, at least, these disparate movements reflect conscious decisions by the monetary authorities to bring about an immediate short-term change in their liabilities, contrary in effect to the longer-term decisions regarding changes in reserve requirements. Effects of Changes in Policy and in Behavior VariablesOn the basis of the preceding discussion, it is possible to distinguish between changes in money that are attributable to the policy decisions of the monetary authorities and those attributable to the behavior of the private sector, i.e., of banks and the nonbank public. Changes in central bank monetary liabilities and in the ratio of required reserves to demand deposits will be considered as policy variables. Changes in the ratios of currency to money and of excess reserves to demand deposits will be referred to as behavior variables. A separation along these lines is given in Table 4, where ΔMp represents the change in money arising from central bank action, expressed as a percentage of money in the preceding year, and ΔMa represents the change arising from behavior variables, expressed in the same terms. The calculation of ΔMp and ΔMa is shown in Appendix I, Section 4. In part, at least, this separation must be arbitrary. If the monetary authorities have adequate knowledge, they will take account of the effects of the behavior of the private sector. A completely satisfactory monetary policy must be, in large part, a stimulation or counteraction of private behavior, designed to bring about monetary changes that are considered to be in the national interest. In addition, this distinction cannot be entirely unambiguous. As was noted earlier, central bank control of the movements of its monetary liabilities may be subject to limitations, especially in less developed economies in the short run; also, changes in the ratio of required reserves to demand deposits may occur without formal variations in legal reserve ratios, e.g., on account of shifts from demand to time deposits, or vice versa. At times, such shifts may be associated with the interest policy of the authorities. Changes in the excess reserve ratio of banks, on the other hand, may be related to “moral suasion” or “ear-stroking”14 on the part of the authorities. Table 4. Percentage Changes in Money Attributable to Policy and to Behavior Variables, Selected Countries, 1952-581 1ΔMp/Mt-1 represents the percentage change in money that is due to changes in central bank monetary liabilities (ΔM′t/Mt-1 in Table 2) and changes in the required reserve ratio (ΔMr′/Mt-1 in Table 3); ΔMa/Mt-1 refers to the percentage change in money due to changes in the currency/money and excess reserve ratios (ΔMc/Mt-1 and ΔMr″/Mt-1 in Table 3). The total percentage change in money, ΔMt/Mt-1, equals the corresponding item in Table 2. 2Average ignoring plus and minus signs. Table 4. Percentage Changes in Money Attributable to Policy and to Behavior Variables, Selected Countries, 1952-581
1ΔMp/Mt-1 represents the percentage change in money that is due to changes in central bank monetary liabilities (ΔM′t/Mt-1 in Table 2) and changes in the required reserve ratio (ΔMr′/Mt-1 in Table 3); ΔMa/Mt-1 refers to the percentage change in money due to changes in the currency/money and excess reserve ratios (ΔMc/Mt-1 and ΔMr″/Mt-1 in Table 3). The total percentage change in money, ΔMt/Mt-1, equals the corresponding item in Table 2. 2Average ignoring plus and minus signs. Table 4 indicates that, on the average, changes in money arising from direct central bank action exceeded those arising from behavior variables in all countries except Egypt and Italy. In certain years, however, the latter exceeded the former in all countries except Brazil and Germany. In addition to Egypt and Italy, changes in behavior variables were relatively most significant in New Zealand, Canada, and Japan, and least significant in Germany, Brazil, and the United States. Even in Germany, however (ignoring signs), they amounted on the average to about 10 per cent of the average rate of change in money, in Brazil to about 20 per cent, and in the United States to about 30 per cent. The monetary effects of policy and behavior variables were of an offsetting type in all years in New Zealand and in most years in Ceylon and Egypt. In most of the other countries, an opposite movement can be observed in certain years. In Germany and Italy, where policy variables had an expansion effect in all years, the behavior variables contributed to the monetary expansion in most years. Implications for Monetary AnalysisThe year-to-year variations in the proportionate effects of direct central bank action indicated in the sample of countries examined here suggest that the management of the quantity of money is not quite as mechanistic an affair as is frequently supposed. For instance, roughly equal percentage changes in money supply due to policy variables, in 1954 and 1955 in New Zealand, in 1957 and 1958 in Brazil, in 1953 and 1954 in Egypt, and in 1955 and 1957 in Germany, were associated with appreciably different rates of monetary expansion, i.e., 11 and 1 per cent in New Zealand, 24 and 33 per cent in Brazil, 1 and −3 per cent in Egypt, and 11 and 9 per cent in Germany. The quantitative implications of this survey and the methodology developed in it may indicate two avenues toward further refinement in monetary analysis. First, the analysis and presentation of sources of changes in money in terms of consolidated balance sheets of the monetary system, i.e., summations of central bank and commercial banks’ balance sheets, preclude an identification of monetary changes that are due to direct central bank action and those due to behavior variables (and possibly indirect central bank action). An analysis in terms of separate sets of balance sheets for the central bank and the banking system, which shows variations in absolute terms, overcomes this limitation only in part. On the other hand, an explicit allocation of monetary changes to policy and to behavior factors, based on the calculation of the respective ratios, does provide useful information which is not explicitly shown in the conventional forms of presentation mentioned above. Monetary analyses in such terms, which are of course susceptible to considerable further refinement, would, for instance, facilitate the assessment of the effects of changes in legal reserve requirements—an instrument of monetary control especially important and increasingly used in the less developed economies. The same may hold in respect to the evaluation of the effects of quantitative over-all credit ceilings for commercial banks. Further refinement and adaptation of available data could proceed in several directions. For instance, in individual country surveys it might be useful to estimate the effects of changes in the behavior variables and also in the required reserve ratio (inasmuch as it is related to the demand/time deposit ratio) on the basis of end-of-quarter or even end-of-month data. Since such information tends to be available without a significant time lag, its use would permit an early assessment of the banks’ and the public’s reaction to other monetary and general economic developments. This would place the authorities in a position where they could more reliably estimate the probable reactions to contemplated measures of monetary policy. After relaxing the earlier assumption of absolute central bank control of its monetary liabilities, the relationship between changes in specific central bank asset items and central bank monetary liabilities, which also may reflect behavior factors, could also be assessed. For instance, it might be possible to show how far and how rapidly banks adjust their net borrowing from the central bank to changes in their reserves that are due to, say, an external surplus, and thus influence the changes in central bank monetary liabilities. A survey of the relationship between average and marginal currency and reserve ratios eventually might provide a basis for relaxing the assumption of equality between the two ratios and consequently permit a further improvement of the analysis. The second implication of this survey is, of course, that it focuses attention on the necessity of explaining variations in the currency/money ratio,15 the excess reserve ratio, and the ratio of demand to time deposits. The explicit incorporation of these ratios in a framework of monetary-analysis and their continued observation would, apart from the implications indicated in the previous paragraph, facilitate the explanation of changes. Inasmuch as these ratios reflect behavior patterns (notwithstanding the likelihood that they may well be functionally related to certain central bank actions), their movements may be related to influences affecting still more important behavior coefficients, e.g., the income velocity of money.16 APPENDICESI. Methodological Notes1. The money multiplier in terms of M/LThe money multiplier is usually expressed in terms of the ratios of currency to money and of reserves to deposits, on the assumption that average and marginal ratios are equal. This assumption has been retained in this paper. Therefore k=1CM+RD(1−CM ),(1.1) where C represents currency in circulation outside banks, M money, R bank reserves, and D demand deposits. If both numerator and denominator are multiplied by M, we obtain MC+ RD(M−C),(1.2) which equals C+DC+RDD= ML=k.(1.3) 2. The attribution of changes in money to changes in central bank monetary liabilities and changes in the money multiplier (Table 2)The changes in money (M) attributable to changes in central bank monetary liabilities (L) and to changes in the money multiplier (k) may be allocated as follows: ΔMt= Mt−Mt−1;(2.1) as kt−1=Mt−1 Lt−1, Mt−1=kt−1Lt−1.(2.2) Therefore, ΔMt=Mt−kt−1Lt−1.(2.3 ) As Mt = (kt-1 + Δkt) (Lt-1 + ΔLt) or Mt=kt−1Lt− 1+ΔktΔLt+kt−1ΔLt+Lt−1Δkt,(2.4) equation (2.3) is reduced to ΔMt =ΔktΔLt+kt−1ΔLt+Lt−1Δ kt,(2.5) or ΔMt=(Lt−1+ΔL t)Δkt+ΔLtkt−1=LtΔkt+ΔLtkt−1.(2.6) Equation (2.6) shows that the change in money in period t is equal to total central bank monetary liabilities multiplied by the change in k plus the change in central bank monetary liabilities multiplied by the k of the previous period. The change in money that is due to the change in central bank monetary liabilities is equal to ΔM′t=ΔLtkt−1,(2.7) while the change in money due to the change in k is equal to ΔM″ t=LtΔkt.(2.8) The total change in money is ΔMt =ΔM′t+ΔM″t.(2.9) It follows that the ratios of ΔM′/ΔM and ΔM″/ΔM show the relative effects of changes in L and k, respectively, on the absolute change in money. In textbook presentations of the process of secondary credit creation, k is usually assumed to be constant, so that ΔM″ = 0 and ΔM′/ΔM = 1. From equation (2.8) it follows that ΔM″t = (Lt-1Δkt) + (ΔLtΔkt), where ΔLtΔkt is likely to be much smaller than Lt-1Δkt. The cross product ΔLtΔkt was therefore allocated entirely to ΔM″t. In order to allocate this cross product in a perhaps more neutral fashion, equations (2.7) and (2.8) could be modified to ΔM′ t=ΔLtkt−1+ΔLtΔkt2 (2.7.1) and ΔM″t=Lt−1Δkt+ΔLtΔkt2.(2.8.1) 3. The attribution of changes in money to changes in the ratios of currency to money, of required reserves to demand deposits, and of excess reserves to demand deposits (Table 3)The changes in money attributable to changes in the currency and reserve ratios respectively may be allocated as shown below (k representing the money multiplier, c the ratio of currency to money, and r the ratio of reserves to demand deposits). The change in k arising from changes in c or r is given by the derivative, Δk=∂k∂cΔc+∂k∂rΔ r+∂2k∂c∂rΔc.Δr.(3.1) This expression permits an allocation of the change in k to changes in c and r, respectively. The allocation for finite changes in c and r can, however, be only approximate. The margin of error will be a direct function of the magnitude of changes in the two ratios. Moreover, any allocation of the cross product ∂2k∂c∂rΔc. Δr is necessarily arbitrary. Inasmuch as this value is likely to be very small, it may be ignored.17 Equation (3.1) may then be written as Δk=−(1−r)Δc[c+r(1−c)]2−(1−c )Δr[c+r(1−c)]2.(3.2) The approximation can, however, be improved somewhat by expressing the remaining values of equation (3.1) in terms of the average c and r in two periods. Therefore Δk=12[(∂k∂c )rt−1,ct−1+(∂k∂c)rt,ct] Δc+12[(∂k∂r)ct−1,rt−1+(∂ k∂r)ct,rt]Δr.(3.3) The two values on the right side of equation (3.3) represent the approximate extent to which the change in k is attributable to changes in c and in r. Inasmuch as r is defined as the ratio of total reserves to demand deposits, it is equal to the sum of the ratios of required reserves (r′) and of excess reserves (r″) to demand deposits. In order to identify the effect of changes in excess reserves on k, equation (3.3) may be written as follows: Δk=12[(∂k ∂c)rt−1,ct−1+(∂k∂c)rt,ct ]Δc+12[(∂kr∂)ct−1,rt−1+ (∂k∂r)ct,rt]Δr′+12[( ∂k∂r)rt−1,ct−1+(∂k∂r)rt, ct]Δr″(3.4) Since the ratio M/L appears to be a statistically more manageable and convenient concept than the multiplier expressed in terms of c and r, the three products on the right side of equation (3.4) are expressed as percentages of the left side. These percentages are then applied to the observed change in M/L in order to obtain an estimate of the effects of changes in c, r′ and r″ on M/L. The three products are then multiplied by the amount of central bank monetary liabilities during the current period (Lt). The products obtained are expressed as percentages of the observed money supply in the previous period (Table 3). 4. The attribution of changes in money to changes in policy and in behavior variables (Table 4)The monetary effect of direct central bank action is shown by the equation, ΔMp=ΔLtkt− 1+Δkr′Lt;(4.1) that is, it is equal to the sum of the product of the change in central bank monetary liabilities and the multiplier of the previous period plus the product of the change in the multiplier due to the change in the required reserve ratio and total central bank monetary liabilities during the current period. The change in money due to changes in behavior variables will be ΔMa=Lt(Δkc+Δk r″),(4.2) that is, the sum of the changes in the multiplier due to changes in the currency/money and excess reserve ratios multiplied by total monetary liabilities. (The values for Δkr′, Δkr″, and Δkc are obtained from the right side of equation 3.4.) The sum of the two percentages equals the observed percentage change in the money supply, i.e., ΔMt/Mt−1=ΔMp/Mt−1+ΔMa/Mt−1.(4.3) Table 4 shows ΔMp and ΔMa as percentages of the observed money supply of the previous period, and the sum of these percentages, i.e., the observed percentage change in money in the current period. II. Sources and Explanatory NotesSourcesData on money, currency, and demand deposits were obtained from International Monetary Fund, International Financial Statistics, except those for Canada, which are from Bank of Canada, Statistical Summary; for the United Kingdom, from F. W. Paish, “Gilt-Edged and the Money Supply,” The Banker (London), January 1959; and for the United States, from Board of Governors of the Federal Reserve System, Banking and Monetary Statistics and Federal Reserve Bulletin. Data on total deposits and reserves were obtained from the following sources: for Brazil, from Superintendencia da Moeda e do Crédito, Boletim; for Canada, from Bank of Canada, Statistical Summary; for Ceylon, from Central Bank of Ceylon, Annual Report; for Colombia, from Banco de la República, Revista; for Germany, from Deutsche Bundesbank, Monthly Report; for Italy, from Banca d’Italia, Assemblea Generale Ordinaria dei Partecipanti; for New Zealand, from Reserve Bank of New Zealand, Bulletin; for the Philippines, from Central Bank of the Philippines, Statistical Bulletin; for the United Kingdom, from The Banker; for the United States, from Board of Governors of the Federal Reserve System, Banking and Monetary Statistics and Federal Reserve Bulletin; and for Egypt and Japan, from International Financial Statistics. Data on central bank monetary liabilities were obtained from International Financial Statistics; and data on supplementary reserves for Italy, New Zealand, and the Philippines were obtained from the respective country sources noted above. Explanatory notesTable 1. Money and currency data are averages of end-of-month figures, except those for Japan and Italy, which are averages of end-of-quarter figures, and for Canada, whose currency data are monthly averages of notes held outside banks. For Brazil and Egypt, private monetary deposits with the central bank are included in currency because changes in such deposits have the same effect on commercial bank reserves and the money multiplier as changes in currency. The deposit and reserve data are averages of end-of-month figures, with the following exceptions: For Canada, the deposit data are averages of daily figures and the reserve data are averages of end-of-month figures prior to 1954; from then on, they refer to monthly averages of Wednesday data. For Egypt, the reserve data are averages of end-of-year figures. For Italy and Japan, reserve and deposit data are averages of end-of-quarter figures. For the United States, the data are end-of-June figures prior to 1923, and averages of December-June-December figures thereafter. Reserve data include till cash and balances with the central bank; for Colombia, Italy, and the Philippines, in addition, reserves in the form of government securities are included; for the United Kingdom, reserves include till cash, call loans, and treasury bills of the clearing banks; for Japan, reserves refer to the Bank of Japan monetary liabilities to banks and other financial institutions as shown in International Financial Statistics. Table 2. Central bank monetary liabilities exclude monetary liabilities to governments and, in the United States, to foreigners. For Brazil, Ceylon, Germany, Japan, and the Philippines, the data are averages of end-of-quarter figures; for Canada, Egypt, and the United States, averages of end-of-year figures; for New Zealand, averages of end-of-month figures. For Italy, the figures combine end-of-year averages of central bank monetary liabilities and end-of-quarter averages of the noncash reserves referred to in the note to Table 1; for the Philippines, monetary liabilities include an estimated quarterly average of government security holdings included in reserve data. Tables 3 and 4. The figures are based on the data used for Tables 1 and 2, respectively. Table 5 shows the money multiplier calculated in terms of the ratio of money to central bank monetary liabilities and in terms of the ratios of currency to money and of total reserves to demand deposits, as well as the first multiplier calculated as a percentage of the second. Table 5. Money Multiplier in Terms of (1) the Ratio of Money to Monetary Liabilities and (2) the Currency and Reserve Ratios, Selected Countries, 1952-58 Table 5. Money Multiplier in Terms of (1) the Ratio of Money to Monetary Liabilities and (2) the Currency and Reserve Ratios, Selected Countries, 1952-58
Other PublicationsBalance of Payments YearbooksThe Balance of Payments Yearbook, Volume 12, is being published as a series of loose-leaf sections; the first sections were issued in June 1960, and the last will be issued in May 1961. The volume will contain basic statistics, with explanatory notes, for the years 1955-59. These data will bring to date the basic statements given in Volumes 5 and 8 (the two base volumes previously issued in the Yearbook series), and the three volumes, when used together, will provide a comprehensive record of the international transactions of some 75 countries covering the period 1947-59. For the majority of countries, regional details of the basic data for 1959 will be shown in Volume 12, and figures for the first halves of 1959 and 1960 will be given for the countries that report such data. In addition, summary statements expressed in U.S. dollars and covering several years will be given for all the countries. The analytic material presented in earlier volumes will be brought to date, and similar data for other countries will be added. Volume 5 is out of print. Volume 8 may be purchased for US$5.00 or the approximate equivalent in the currencies of most countries. For Volume 12, the subscription rate is US$7.50 or its equivalent; a binder for filing the loose-leaf sections may be purchased for US$3.50. International Financial StatisticsThis monthly bulletin is a standard source of statistics on domestic and international finance. It assembles for most countries annual, quarterly, and monthly data significant for the study of inflation and deflation, and balance of payments surpluses and deficits. It outlines the transactions of the principal sectors of the economy: the banking sector, the insurance and other financial institutions sector, the government sector, and the foreign sector. It provides data on exchange rates, international reserves, interest rates, prices, and international trade. A series of notes indicates the economic significance of the material presented in the tables and explains the methods used in their compilation. The comparative study of the material is facilitated by the adoption of a uniform method of charting the major series, and country data are also assembled on a comparable basis in international tables. The annual subscription rate for 12 issues postpaid is US$10.00 or the approximate equivalent in the currencies of most countries. Single copies, US$1.50. Airmail subscription rates will be quoted on application. Address orders to The Secretary International Monetary Fund 19th and H Streets, N.W., Washington 25, D.C. What is the relationship between reserve ratio and money multiplier?The bank's reserve requirement ratio determines how much money is available to loan out and therefore the amount of these created deposits. The deposit multiplier is then the ratio of the amount of the checkable deposits to the reserve amount. The deposit multiplier is the inverse of the reserve requirement ratio.
Is there an inverse relationship between the required reserve ratio and the money supply?There is an inverse relationship between the required reserve ratio and the money supply. The discount rate is sometimes also known as the primary credit rate. . In 2007, the Fed began using an additional monetary policy tool called the term auction facility program.
What kind of relationship is found in between liquidity reserve ratio and money multiplier?The size of the multiplier depends on the percentage of deposits that banks are required to hold as reserves. When the reserve requirement decreases, the money supply reserve multiplier increases, and vice versa.
Is the money multiplier the inverse of the deposit ratio?The deposit multiplier is the inverse of the reserve requirement ratio. For example, if the bank has a 20% reserve ratio, then the deposit multiplier is 5, meaning a bank's total amount of checkable deposits cannot exceed an amount equal to five times its reserves.
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