Abstract
IN DISCUSSIONS on the ability of central banks to determine the quantity of money desired in any economic system, a distinction is often drawn between changes in money supply arising from changes in the monetary base (that is, the monetary liabilities of the central bank) and those emanating from the variations in the value of the money multiplier (that is, the ratio of money supply to the monetary base). Only the former type of change, attributable to variations in the monetary base, can reasonably be regulated by the central bank. Changes in money supply induced by changes in the value of the money multiplier tend to vary considerably.1 This is so because some of the determinants of the money multiplier, such as the public’s demand for currency, the banks’ demand for excess and borrowed reserves, and shifts between time and demand deposits, change over time. Unless the behavior of such variables is explained, it is not possible to know why the changes in the money multiplier come about at all. Of course, the theoretical importance of these behavioral relations has been recognized in the context of money multiplier analysis in particular and money supply theory in general, as described in Section I. Few attempts, however, have been made to relate them structurally and to estimate them in deriving the money supply function.2 The purpose of this paper is to specify and to estimate these behavioral relations in an integrated model of the money multiplier.
IN DISCUSSIONS on the ability of central banks to determine the quantity of money desired in any economic system, a distinction is often drawn between changes in money supply arising from changes in the monetary base (that is, the monetary liabilities of the central bank) and those emanating from the variations in the value of the money multiplier (that is, the ratio of money supply to the monetary base). Only the former type of change, attributable to variations in the monetary base, can reasonably be regulated by the central bank. Changes in money supply induced by changes in the value of the money multiplier tend to vary considerably.1 This is so because some of the determinants of the money multiplier, such as the public’s demand for currency, the banks’ demand for excess and borrowed reserves, and shifts between time and demand deposits, change over time. Unless the behavior of such variables is explained, it is not possible to know why the changes in the money multiplier come about at all. Of course, the theoretical importance of these behavioral relations has been recognized in the context of money multiplier analysis in particular and money supply theory in general, as described in Section I. Few attempts, however, have been made to relate them structurally and to estimate them in deriving the money supply function.2 The purpose of this paper is to specify and to estimate these behavioral relations in an integrated model of the money multiplier.
I. Public’s Demand for Currency and Banks’ Demand for Excess Reserves : Some Theoretical and Empirical Issues
A considerable amount of work, both theoretical and empirical, has been done regarding the analysis of the behavior of the public’s demand for currency and the banks’ demand for excess reserves. It will be fruitful to survey the existing literature briefly as a prelude to the money multiplier model presented in this paper. Such a survey will also help us to understand the basis of some of the assumptions underlying the model. Most of the work in this field has been in two directions—attempts to explain the behavior of public demand for currency and analysis of banks’ demand for excess reserves; both are, with few exceptions, in isolation from their implications for the operation of the money multiplier. The work of the Chicago School, more particularly that by Cagan,3 on the causes of changes in the U.S. currency/money ratio shows that between 1875 and 1955, while many variables such as expected income, direct tax rates, expected net rate of interest paid on deposits, urbanization, and retail trade could affect the currency ratio, only the first three seem to have exerted a major influence on its behavior.4 A similar approach is adopted by Macesich in his investigation of currency ratios in Canada.5 Khazzoom has also tested for a large sample of developing countries the demand for currency with respect to many independent variables, some of which are common to those chosen by Cagan.6 For want of sufficient statistical information, Khazzoom’s hypothesis has derived support only from his qualitative judgment that emphasis should be placed on such factors as monetization, banking growth, inflation, and income distribution.
The behavior of excess bank reserves evoked great interest in the postwar years, again in isolation from its relevance for the money multiplier. Of the many reasons for focusing attention on this factor, two were most prominent. First, the level of free reserves (that is, excess reserves minus borrowings by member banks) was considered to be the basis for judging the relative stringency or relaxation of monetary policy. For instance, if actual free reserves are in excess of desired levels, banks feel induced to expand their loan portfolio, leading thereby to a decline in interest rates,7 and vice versa when actual free reserves fall short of desired levels. The second reason has even wider implications. Banks are not merely passive agencies reacting to the public’s demand for their loans; they are also profit-maximizing entities. If banks possess excess reserves, it does not follow that they will automatically expand credit, nor are they necessarily satisfied to hold excess reserves if there is little or no demand for loans.8
A number of hypotheses were put forth to explain the demand of banks for excess reserves both in the panic periods (that is, when there is a banking crisis) and in the nonpanic or normal periods, and most of them were tested for U. S. data. For the panic period, the hypothesis—also known as shock-effect hypothesis—is that banks are more inclined to accumulate excess reserves because they expect larger outflows of reserves, owing first to runs on the banks and then to changes in reserve requirements. A variant of this hypothesis—inertia-effect hypothesis—like the shock-effect hypothesis relates reserve accumulation to a shift in the bank’s desired level of excess reserves, following the bankers’ expectation of large outflows of reserves. A major difference between the shock-effect hypothesis and its variant is that the former implies that banks tend to raise their excess reserves after every banking crisis, whereas the latter suggests that they do not accumulate excess reserves following a banking crisis unless there is a corresponding inflow of reserves. These hypotheses are tested by Morrison for the United States,9 and his evidence indicates that both have the power to explain a major portion of variations in excess reserves during the bank crisis period, viz., 1925–32, although this has been disputed by Frost.10 But the major limitation of these hypotheses is that they remain relevant only for explaining the abnormal behavior of banks.
Perhaps a more fruitful and general approach to the excess reserves problem that can be applied in normal periods is to explain banks’ demand for reserves in terms of profit maximization. This approach is discernible in the work of Polak and White, Frost, and many others.11 Polak and White argue that a close relationship between excess bank reserves and interest rates reflects more realistically the banks’ demand for excess reserves, and their empirical tests bear this out in an observed close relationship between the ratio of net excess reserves (free reserves) to total deposits and the natural logarithm of the yield on short-term government securities. On the other hand, Frost presents, on both theoretical and empirical grounds, a more general example of banks’ demand for excess reserves. When interest rates are low, banks find it profitable to hold excess reserves, because the cost involved in constantly adjusting reserve positions tends to exceed the interest rate that would be earned by investing the excess reserves. But when interest rates are sufficiently high to more than compensate for the cost involved in adjusting reserve positions, banks tend to reduce their demand for them. Thus, Frost reconciles the Polak and White approach with Morrison’s liquidity-trap hypothesis.12 Teigen’s measurement of the response of money supply to changes in the market rate of interest is based upon the response of free reserves to changes in the market rate.13
The theoretical and empirical research into the behavioral pattern of the public’s demand for currency and the banks’ demand for excess reserves has helped incidentally to illuminate certain important relationships underlying money supply functions. That the money supply has an existence of its own as an economic variable determined by the public’s demand for currency, banks’ demand for excess reserves, etc., has been recognized explicitly in the work of Cagan, Brunner and Meltzer, and de Leeuw.14 There are no simple, mechanical relationships between reserve money, bank deposits, and money supply; such relationships are governed by changes in the public’s holding of currency and bank deposits and in the banks’ portfolio behavior. Cagan’s further work on the United States reveals that the currency/money ratio has been the major cause of the fluctuation in the money multiplier over a long timespan (1875–1960), but he has neglected the behavior of the bank-reserves/bank-deposit ratio.15 In the Brunner and Meltzer analytical framework, money supply variations
are explained in terms of the extended monetary base (i.e., the base plus the cumulated sum of reserves “liberated” from or “impounded” into required reserves by fiat changes in requirement ratios or due to the redistribution of existing deposits between different classifications), the public’s desired wealth allocation to currency and time deposits, and the banks’ desired portfolio of excess reserves.16
Following this reasoning, Brunner and Meltzer regressed money supply on: the extended monetary base; the public’s marginal propensity to hold currency and time deposits with respect to money wealth; the banks’ marginal propensity to hold excess reserves with respect to deposit liabilities; the discount rate; treasury bill rate; and the long-term bond rate.17 While this approach of Brunner and Meltzer presented a more complete model of the money multiplier by allowing for leakages other than legal reserve requirements and currency drain, it did not attempt in an explicit manner to specify and to estimate structurally the public’s demand for currency and the banks’ demand for excess reserves. Apart from this, their analytical system assumes an independence between what they call an extended monetary base and other variables, such as the public’s demand for currency, shifts between time and demand deposits, and banks’ demand for reserves.
It is to fill some of these gaps in the money multiplier analysis that a fuller structural model specifying behavioral variables is formulated in this paper.
II. The Model
The theoretical model presented here is an expanded version of the Warren Smith model, formulated to explain demand for free reserves, money, and time deposits in the U. S. economy.18 Smith’s model makes no reference to the determinants of two variables: the central bank’s holdings of foreign reserves and the demand for currency. Besides, his model does not specify separate demand functions for excess reserves, borrowed reserves, and demand deposits. The enlarged version in this paper provides explicitly for the determinants of all these variables. While the theoretical model so constructed is sufficiently general to reflect the behavioral pattern of the money multiplier in both the developed and less developed countries, subject, of course, to modification and empirical validation, this model is adapted and tested only with U. S. quarterly data.
Any model is a simplification of the economic system, and it must be kept manageable. Hence, some of the less important relationships have to be left out. It should be made explicit that income is exogenous in the model, implying that the real sector adjusts so slowly that feedback effects of the financial sector on the real sector can be ignored. In view of the partial model, as presented here, some degree of specification bias in the structural estimates is to be expected.
There are in all 12 equations in the model, the first 4 of which are either accounting identities or definitions; 6, equations (5) through (10), are stochastic equations; and the remaining 2, equations (11) and (12), are expectation-generating functions. All these are explained below in detail.
Notation
| Af = | net foreign assets, inclusive of gold, held by central bank |
| C = | currency outside banks |
| D = | demand deposits |
| k1 = | required reserve ratio for demand deposits |
| k2 = | required reserve ratio for time deposits |
| M = | money supply |
| expected rate of inflation | |
| rs = | interest rate on short-term treasury bills |
| rf = | foreign interest rate |
| rti = | interest rate on time deposits |
| Rb = | central bank net credit to financial institutions |
| Rex = | excess reserves of banks |
| required reserves for demand deposits | |
| required reserves for time deposits | |
| S = | net holdings of government securities by central bank |
| T = | time deposits |
| X = | exchange rate |
| Ye = | “expected” or “permanent” income |
| u1 … u6 = | error terms |
| — | indicates variable is determined outside the model, that is, determined exogenously |
| Af = | net foreign assets, inclusive of gold, held by central bank |
| C = | currency outside banks |
| D = | demand deposits |
| k1 = | required reserve ratio for demand deposits |
| k2 = | required reserve ratio for time deposits |
| M = | money supply |
| expected rate of inflation | |
| rs = | interest rate on short-term treasury bills |
| rf = | foreign interest rate |
| rti = | interest rate on time deposits |
| Rb = | central bank net credit to financial institutions |
| Rex = | excess reserves of banks |
| required reserves for demand deposits | |
| required reserves for time deposits | |
| S = | net holdings of government securities by central bank |
| T = | time deposits |
| X = | exchange rate |
| Ye = | “expected” or “permanent” income |
| u1 … u6 = | error terms |
| — | indicates variable is determined outside the model, that is, determined exogenously |
Equation (1) identifies the sources and uses of base money. Sources of base money are (a) central bank’s net holdings of government securities, 5; (b) its net lending to the financial institutions, Rb; and (c) its net holdings of foreign assets, Af Uses of base money are (a) currency held by the nonbank sector, C; (b) required reserves for demand deposits,
Equations (5) through (10) are behavioral relations explaining the banks’ demand for excess and borrowed reserves, the public’s demand for currency, demand deposits, and time deposits, and the central bank’s net holdings of gold and foreign exchange. The last two equations generate the “Almon” variables Ye and
In equation (5), it is assumed that banks’ demand for excess reserves is negatively related to the short-term market interest rate.20 That is, a higher market interest rate with an unchanged discount rate means an increase in the opportunity cost of holding excess reserves; hence, banks will tend to reduce excess reserves. Equation (6) assumes that bank borrowing is related positively to the short-term rate; that is, for a given discount rate, an increase in the market yield on treasury bills will tend to encourage borrowing, either for purchasing treasury bills or, if the rise in market rates is a consequence of an open market sale, for replenishing reserves.
Equations (7) through (9) suggest that economic variables, such as interest rates, permanent income, and expected rate of inflation, influence the public’s demands for currency, demand deposits, and time deposits. It is to be expected that the demand functions are related positively to permanent income and related negatively to the interest rate and the expected rate of inflation.
Equation (10) assumes that the central bank’s net holdings of foreign reserves result from both trade and capital flows. These flows are considered to be determined by domestic and foreign interest rates, permanent income, expected rate of inflation, and the exchange rate. A rise in the domestic interest rate relative to the foreign interest rate will tend to increase foreign reserves through capital inflows. On the other hand, increases in permanent income and the expected rate of inflation may induce an outflow of external reserves through increased imports and reduced exports. If the exchange rate expressed in units of domestic currency per unit of, say, gold goes up, exports and imports may be expected to rise and to fall, respectively, thereby bringing about an increase in the flow of external reserves.
III. Statistical Estimation of the Model
All behavioral equations, except equation (10), were fitted to U. S. seasonally unadjusted, quarterly data (the first quarter of 1958 through the fourth quarter of 1970). For institutional reasons the equation for external reserves, equation (10), is not appropriate for the United States. As has been pointed out,
The neglect of the balance of payments, in particular in U. S. studies [italics ours], partly reflects the institutional fact that, in the United States changes in the balance of payments (on an official settlements basis) do not normally affect base money in the system and partly reflects the small role played by the external sector in its domestic impact.21
All data used were in current prices; where only monthly series were available, they were converted into quarterly data. All regressions were corrected for seasonal shifts through inclusion of dummy variables (which, however, are omitted below).22
Preliminary ordinary least-squares regressions using the levels of the variables yielded substantially low values for the Durbin-Watson statistic (in the order of 0.3–0.4), suggesting serial correlation of the residuals of each equation. Accordingly, the original equations were transformed to take account of first-order serial correlation; such transformed equations were nonlinear in the estimated parameters and thus were estimated nonlinearly.23 The asterisk in the regressions below indicates that the variable has been transformed to take account of serial correlation in the residuals, for example, M* = Mt – ρMt–1, where | ρ | < 1 is the autoregressive coefficient.
Several assets compete with currency and demand deposits: treasury bills, savings deposits, time deposits, savings and loan association shares, and mutual savings bank deposits. In theory, all rates paid on these substitutes should enter as separate arguments in the demands for currency and demand deposits. However, inclusion of all the rates, assuming that they are available, introduces the empirical problem of isolating the effects of specific interest rates when all rates are highly collinear in time-series analyses. There are at least two ways to avoid the problem of multicollinearity. First, an index of rates paid on other assets can be constructed, as Christ has attempted.24 Although such an index is superior to one that completely leaves out some of the rates, it is still incapable of distinguishing the separate substitution effects for different assets. Second, a better approach is to pool cross-state data for the entire sample period, as Feige has done.25 However, in the absence of cross-state data for the period 1958–70, there was simply no choice but to use one rate on money substitutes (three-month treasury bill rate) and ignore other rates, in order to avoid the multicollinearity problem.
With regard to the demand for time deposits, the definition of time deposits does not include the new certificates of deposit, which are interest sensitive; thus, even abstracting from the multicollinearity problem, the noninclusion of the yield on fixed deposits is not entirely unrealistic.
The time period, t, is one quarter. The estimates of αi and βi respectively, are the weights attached to current and past values of
The estimated equations are as follows:
note: t-statistics are shown in parentheses;
All the coefficients are of the correct expected signs and of reasonable order of magnitude. The yield on treasury bills does affect the banks’ demand for excess and borrowed reserves in the expected direction; the market interest rate and permanent income do influence the demand for currency, the demand for demand deposits, and the demand for time deposits. The Durbin-Watson statistics in three out of five equations are, by and large, respectable, considering the time-series nature of the data used; so are the SEEs. The
The required reserve ratios, k1 and k2, were calculated as follows. In the absence of a breakdown of total required reserves into its two components (required reserves for demand deposits plus required reserves for time deposits), total demand deposits were multiplied by an average reserve ratio prescribed for demand deposits, calculating thereby the amount of required reserves for demand deposits. Legal reserve requirements so computed for demand deposits were then subtracted from total required reserves in order to arrive at required reserves for time deposits. These estimated required reserves for each type of deposit were related separately to demand and time deposits, respectively. These ratios are represented by symbols k1 and k2, respectively. The average value of kx was found to be 0.18 and that of k2, 0.03; however, the estimated average legal reserve ratio for demand deposits assumes an existing distribution of demand deposits among banks, with regard to both size and location. This implies that any change in that distribution will change the estimated values of kx and k2.
IV. Policy Implications of the Model
The money multiplier derived from the model is given by the following expression. Its algebraic derivation is described fully in the Appendix.
The nonzero estimates of the partial derivatives contained in equation (13) indicate that the behavioral variables, viz., demand for excess and borrowed reserves, demand for currency, demand for demand deposits, and demand for time deposits, are all sensitive to the short-term market interest rate. Note that, given the negative signs of the partial derivatives in (13), there is no ambiguity at all as to the positiveness of dM/dS. Equation (13) identifies five leakages, all of which severally or in combination tend to lower the size of the money multiplier.
The money multiplier expression, equation (13), reveals that the size of the money multiplier is a function of the partial derivatives and the reserve ratios k1 and k2. It is obvious, by inspection, that the money multiplier is a decreasing function of k1 k2, ∂T/∂rs, ∂Rex/∂rs, and —∂Rb/∂rs. Take, for example, the demand for time deposits. Net open market purchase will tend to lower market interest rates, which in turn will tend to increase the absolute level of demand for time deposits, the increase being equal to the change in the interest rate multiplied by ∂T/∂rs. But, since the size of money multiplier depends only on the ratio of the change in the demand for time deposits to the change in the interest rate, the multiplier will not decrease unless that ratio increases with the decline in the interest rate. In the present linear model, that ratio (and all the others) is assumed to be constant, so that the only way the authorities can affect the size of the multiplier is by changing the reserve ratios k1 and k2. A possibility may still arise (for instance, in a nonlinear model) that the interest rate coefficients themselves change as a result of the policy actions of the authorities.
On the other hand, the effects of changes in ∂C/∂rs and ∂D/∂rs on the size of the money multiplier are ambiguous, because both these terms appear in the numerator as well as in the denominator. The multiplier would shrink if, and only if, the change in the terms appearing in the denominator is larger than that appearing in the numerator.
Suppose that the only leakage is the reserve requirement against demand deposits, that is, there is no currency drain, no interest sensitivity of excess or borrowed reserves, and no interest-induced substitution between bills and time deposits, then the money multiplier reduces to the simplest form:
Any one or a combination of nonzero values of ∂T/∂rs, ∂Rex/∂rs, and ∂Rb/∂rs will reduce dM/dS below “1/k1.”
Thus, when the behavioral responses cannot be set aside in view of their intrinsic importance, as is shown in this model, the relevant expression for the money multiplier is given by equation (13), and since it has many more terms in the denominator than equation (13a), its value is necessarily lower. Allowing for currency drain and reserve drain (k1∂D/∂rs ≠ 0), the multiplier 28 becomes
Evaluation of equations (13) and (13b) yields the following rough orders of magnitude for the two multipliers in the United States:
Starting with the “conventional” multiplier, equation (13b), let us allow for substitution only between time deposits and treasury bills. Then the value of the multiplier becomes
Let us allow for only the interest sensitivity of bank borrowing. Then the value of the multiplier is
The multiplier value 1.78 comes close to that given by equation (13) above, (which is equal to 1.42). In other words, the leakage owing to bank borrowing is practically the single most important leakage that reduces the money multiplier below its “conventional” level given by equation (13b).
The policy implications are clear. The authorities have these alternatives: (a) If they have confidence in the estimate of the value of the multiplier, they can adjust the magnitude of their open market operations to the desired changes in the money supply; (b) if there are limitations on the magnitude of open market operations (if substantial fluctuations in market interest rates are to be avoided by the authorities), they can implement a more aggressive discount rate policy, perhaps supplemented by quantitative ceilings on bank borrowing, in order to discourage or encourage bank borrowing, depending upon the circumstances.
Also, to the extent that marginal responses to changes in interest rates (the partial derivatives in equation (13)) are influenced by the actions of the authorities, changes in the value of the money multiplier can be considered to be responsive to central banking policy. This implies that changes in the reserve money or the extended monetary base effected by central banking policy may not be altogether independent of the changes in the value of the money multiplier. Thus, the distinction usually drawn between changes in money supply arising from variations in reserve money and those stemming from variations in the value of the multiplier can be questioned.29 Central banking policy may have a much more pervasive influence on money supply than is usually supposed.
V. Concluding Remarks
While these findings may be useful to generalize money multiplier analysis, with its attendant policy implications, they do not answer two questions. The first is whether the model can enable the central banking authority to predict a desired change in the money supply. An affirmative answer depends upon two conditions: (a) stability in the value of the multiplier, which in turn depends upon the stability of the estimated coefficients of the model; and (b) accurate forecasts of changes in the exogenous variables, such as expected income and expected inflation, and of changes in the policy variables, such as required reserve ratios and open market operations. The first issue must await extensive stability tests on the estimated coefficients of this model. The second issue requires a more complex and comprehensive model covering both the real and monetary sectors and more elaborate and sophisticated price-adjustment equations. Further, additional equations explaining variations in reserve ratios, discount rate, and open market operations may be needed. In the United States, open market policy has both a “defensive” and an “initiative” aspect. The former is undertaken in order to offset gold flows, changes in float, and other such factors that affect reserve money in a manner not desired for stabilization purposes. The initiative type of open market policy is designed as a response to certain macroeconomic goals of the economy. A net change in unborrowed reserves plus currency can be considered to have been motivated mainly by the initiative type of open market operations. In that case, it is logical and also realistic to take a change in the reserve base as endogenously determined, which has not been done in this paper.30
The second question is whether the significance of the coefficients in this model can hold good for explaining the behavior of the money multiplier in other developed and developing countries. It is likely that the model will have to undergo many adaptations to take into account the features of any countries where it is applied. For instance, in the application of this model to U. S. data, the equation for external reserves has been dropped for institutional reasons. This equation may be important in other developed or developing countries. Until such empirical investigations are made, a final verdict on the money multiplier analysis and its relevance for policy issues has to be held in abeyance.
APPENDIX
Derivation of the Money and Interest Rate Multipliers
Substitute equations (2) and (3) and (5) through (10) into equation (1) and repeat the definitional equation for money supply, equation (4):
Equations (A.1) and (A.2) are a system of two simultaneous equations in two unknown variables—the interest rate, rs, and money supply, M. Differentiate this system totally with respect to the open market variable 5, treating all the other policy variables as constant. The result, in rearranged form, is
Solve system (A.3) and (A.4) for dM/dS and drs/dS, using Cramer’s Rule:
where J = ∂C/∂rs + k1∂D/∂rs + k2∂T/∂rs + ∂Rex/∂rs – ∂Rb/∂rs – ∂Af/∂rs < 0 is the determinant of the Jacobian matrix, in which the implicit coefficients of dM/dS are zero in (A.3) and unity in (A.4). In the text, ∂Af/∂rs = 0 by assumption.
Une théorie du comportement du multiplicateur de la monnaie aux Etats-Unis : un test empirique
Résumé
Dans la présentation habituelle du multiplicateur de la monnaie, aucun effort n’est fait pour expliquer les variations de valeur résultant pour celui-ci des changements accusés dans le comportement de certains facteurs tels que la demande de monnaie de la part du public, la demande des banques de réserves excédentaires et de réserves empruntées, et les mouvements entre les dépôts à terme et les dépôts à vue. La présente étude a pour objet de spécifier et d’évaluer ces relations de comportement dans un modèle intégré du multiplicateur de la monnaie.
Le modèle théorique offert dans la présente étude est une version élargie du modèle de Warren Smith, formulé de façon à expliquer la demande de réserves disponibles, de monnaie et de dépôts à terme dans l’économie américaine. Le modèle présenté ici prévoit cependant de façon explicite les déterminantes de variables telles que les fonctions de la demande de réserves excédentaires, de réserves empruntées, de dépôts à vue, de monnaie fiduciaire et de réserves de change, qui sont exclues du modèle de Smith. Alors que le modèle théorique ainsi construit est suffisamment général pour refléter la structure de comportement du multiplicateur de la monnaie dans les pays développés et dans les pays moins développés, le modèle est ajusté et vérifié uniquement à l’aide des données trimestrielles pour les Etats-Unis.
Le multiplicateur de la monnaie obtenu à partir du modèle est donné par l’équation ci-après:
Les estimations non nulles des dérivées partielles contenues dans cette équation indiquent que les variables de comportement, c’est-à-dire la demande de réserves excédentaires et de réserves empruntées, la demande de monnaie fiduciaire, la demande de dépôts à vue et la demande de dépôts à terme, sont toutes sensibles au taux d’intérêt à court terme sur le marché. Le multiplicateur identifie cinq fuites qui, considérées séparément ou conjointement tendent toutes à réduire la grandeur du multiplicateur de la monnaie. Ceci contraste avec un multiplicateur classique de la monnaie ne comportant que deux fuites, les retraits de comptes bancaires et les réserves obligatoires. C’est ce qui explique que la grandeur du multiplicateur de la monnaie obtenu à partir du modèle présenté dans cette étude soit inférieure à celle du multiplicateur classique de la monnaie.
L’implication, sur le plan de la politique monétaire, est que dans la mesure où la réaction marginale aux modifications des taux d’intérêt (les dérivées partielles de l’équation du multiplicateur) ressent l’effet des mesures prises par les autorités, les changements de la valeur du multiplicateur de la monnaie peuvent être considérés comme des réactions à la politique adoptée par les banques centrales. Ceci laisse entendre que les changements qui se produisent dans la monnaie centrale ou dans la base monétaire élargie par suite de la politique des banques centrales peuvent ne pas être entièrement indépendants des changements accusés par la valeur du multiplicateur de la monnaie. Ainsi, l’on peut contester la distinction qui est faite d’ordinaire entre les variations de la masse monétaire résultant de variations de la monnaie centrale et celles provenant des variations de la valeur du multiplicateur. La politique suivie par les banques centrales peut exercer sur la masse monétaire une influence beaucoup plus pénétrante qu’on ne le suppose habituellement.
Una teoría de comportamiento del multiplicador del dinero en los Estados Unidos: comprobación empírica
Resumen
En la presentación corriente del multiplicador del dinero no se intenta explicar las variaciones de su valor como resultado de variaciones en el comportamiento de factores tales como la demanda de moneda por parte del público, la demanda de reservas en exceso y reservas tomadas a préstamo por parte de los bancos, y los desplazamientos entre los depósitos a plazo y a la vista. Este estudio tiene por objeto especificar y estimar esas relaciones de comportamiento en un modelo integrado del multiplicador del dinero.
El modelo teórico que se presenta en este trabajo es una versión ampliada del modelo de Warren Smith, formulado para explicar la demanda de reservas disponibles, de dinero y de depósitos a plazo, en la economía de EE. UU. No obstante, el modelo aquí presentado tiene en cuenta explícitamente las determinantes de variables tales como las funciones de demanda de reservas en exceso, de reservas tomadas a préstamo, de depósitos a la vista, de moneda y divisas, que quedan excluidas del modelo de Smith. Aunque el modelo teórico construido de esta manera es suficientemente general como para constituir una indicación de la tendencia del comportamiento del multiplicador del dinero, tanto en los países desarrollados como en los menos desarrollados, se ha adaptado y comprobado empleando solamente datos trimestrales de EE. UU.
El multiplicador del dinero calculado a partir del modelo lo da la expresión siguiente:
Las estimaciones distintas de cero de las derivadas parciales que contiene esta ecuación indican que las variables de comportamiento, es decir, la demanda de reservas en exceso y reservas tomadas a préstamo, la demanda de moneda, la demanda de depósitos a la vista y la demanda de depósitos a plazo, son sensibles al tipo de interés a corto plazo del mercado. El multiplicador identifica cinco fugas, y todas ellas, separadamente o en combinación, tienden a reducir la magnitud del multiplicador convencional del dinero, que tiene sólo dos fugas: el agotamiento gradual de la moneda, y el coeficiente de reserva obligatoria. Debido a ello, la magnitud del multiplicador del dinero calculada según el modelo de este estudio es más pequeña que la del multiplicador convencional del dinero.
La significación en cuanto a política es que, dado que las acciones de las autoridades influyen en la reacción marginal ante las variaciones de los tipos de interés (las derivadas parciales que aparecen en la ecuación del multiplicador), se puede considerar que las variaciones en la magnitud del multiplicador del dinero reaccionan ante la política de banca central. Esto significa que puede ser que las variaciones de la base monetaria o el aumento de la misma ocasionados por la política de banca central no sean totalmente independientes de las variaciones en la magnitud del multiplicador del dinero. Por lo tanto, cabe poner en duda la distinción que se suele hacer entre las variaciones de la oferta monetaria que se deben a variaciones de la base monetaria y las que provienen de variaciones en la magnitud del multiplicador. La política de banca central puede tener sobre la oferta monetaria una influencia mucho mayor de lo que se suele suponer.
Mr. Khatkhate, Advisor in the Central Banking Service, is a graduate of the Universities of Bombay and Manchester. He was formerly Director of Research in the Reserve Bank of India. He has contributed numerous articles on planning, trade, and monetary policy to academic journals.
Mr. Villanueva, economist in the Central Banking Service, is a graduate of the University of the Philippines and of the University of Wisconsin. He is the author of several articles on mathematical growth models and quantitative monetary policy in academic journals.
Joachim Ahrensdorf and S. Kanesa-Thasan, “Variations in the Money Multiplier and Their Implications for Central Banking,” Staff Papers, Vol. VIII (1960), pp. 126–49; V. V. Bhatt, “The Creation of Bank Money: A Comparative Study,” The Bankers’ Magazine (London), November 1961, pp. 322–28; P. R. Narvekar, “The Creation of Bank Money: A Comment,” The Bankers’ Magazine (London), March 1963, pp. 201–205; S.L.N. Simha, V. V. Bhatt, A. G. Chandavarkar, and D. R. Khatkhate, “Analysis of Money Supply in India—II,” Reserve Bank of India Bulletin (Bombay), August 1961, pp. 1214–19; Richard Goode and Richard S. Thorn, “Variable Reserve Requirements Against Commercial Bank Deposits,” Staff Papers, Vol. VII (1959), pp. 9–45; Rattan J. Bhatia, “Factors Influencing Changes in Money Supply in BCEAO Countries,” Staff Papers, Vol. XVIII (1971), pp. 389–98.
Karl Brunner and Allan H. Meltzer, An Alternative Approach to the Monetary Mechanism, Committee on Banking and Currency, House of Representatives Subcommittee on Domestic Finance (88th Congress, 2nd Session, August 17, 1964); Karl Brunner and Allan H. Meltzer, “Some Further Investigations of Demand and Supply Functions for Money,” The Journal of Finance, Vol. XIX (1964), pp. 240–83; David I. Fand, “Some Implications of Money Supply Analysis,” American Economic Association, Papers and Proceedings of the Seventy-Ninth Annual Meeting (The American Economic Review, Vol. LVII, May 1967), pp. 380–400.
Phillip Cagan, The Demand for Currency Relative to Total Money Supply, Occasional Paper No. 62, National Bureau of Economic Research, Inc. (New York, 1958).
Ibid., p. 25.
George Macesich, “Demand for Currency and Taxation in Canada,” The Southern Economic Journal, Vol. XXIX (1962), pp. 33–38; see also Frank Brechling, “The Public’s Preference for Cash,” Banca Nazionale del Lavoro, Quarterly Review (September 1958), pp. 377–93.
J. Daniel Khazzoom, The Currency Ratio in Developing Countries (New York, 1966).
Peter A. Frost, “Banks’ Demand for Excess Reserves,” Journal of Political Economy, Vol. 79 (July/August 1971), p. 806.
This is the approach popularized by James Tobin, “Commercial Banks as Creators of ‘Money’,” in Banking and Monetary Studies, ed. by Deane Carson (Homewood, Illinois, 1963). See also, for excellent exposition of this and other views on the behavior of banks, Thomas Mayer, Monetary Policy in the United States (New York, 1968), pp. 80–82.
George Randolph Morrison, Liquidity Preferences of Commercial Banks (University of Chicago Press, 1966).
Frost, “Banks’ Demand for Excess Reserves” (cited in footnote 7), p. 819.
J. J. Polak and William H. White, “The Effect of Income Expansion on the Quantity of Money,” Staff Papers, Vol. IV (1955), pp. 398–433; Frost, “Banks’ Demand for Excess Reserves” (cited in footnote 7), p. 819. There has also been extensive discussion about the banks’ behavior as a whole, which comprehends not only their demand for excess reserves but also their borrowing and lending. The main issue investigated empirically is whether banks borrow for need or for profit, and a general conclusion is that they borrow for both. In this connection, see Stephen M. Goldfield, Commercial Bank Behavior and Economic Activity (Amsterdam, 1966), p. 151; Brunner and Meltzer, “Some Further Investigations of Demand and Supply Functions for Money” (cited in footnote 2); Stephen M. Goldfield and Edward J. Kane, “The Determinants of Member-Bank Borrowing: An Econometric Study,” The Journal of Finance, Vol. XXI (1966), pp. 499–514; and Alexander James Meigs, Free Reserves and the Money Supply (University of Chicago Press, 1962).
Frost, “Banks’ Demand for Excess Reserves” (cited in footnote 7), p. 821.
Ronald L. Teigen, “Demand and Supply Functions for Money in the United States: Some Structural Estimates,” Econometrica, Vol. 32 (1964), pp. 476–509.
Brunner and Meltzer, An Alternative Approach to the Monetary Mechanism (cited in footnote 2), pp. 1–77; Brunner and Meltzer, “Some Further Investigations of Demand and Supply Functions for Money” (cited in footnote 2), pp. 240–83; Frank de Leeuw, “A Model of Financial Behavior,” in The Brookings Quarterly Econometric Model of the United States, ed. by James S. Duesenberry, Gary Fromm, Lawrence R. Klein, and Edwin Kuh (Chicago, 1965), pp. 465–530; Fand, “Some Implications of Money Supply Analysis” (cited in footnote 2).
Philip Cagan, Determinants and Effects of Changes in the Stock of Money, 1875–1960 (Columbia University Press, 1965).
Brunner and Meltzer, An Alternative Approach to the Monetary Mechanism (cited in footnote 2), p. 32.
Brunner and Meltzer, “Some Further Investigations of Demand and Supply Functions for Money” (cited in footnote 2), p. 271.
Warren L. Smith, “Time Deposits, Free Reserves, and Monetary Policy,” in Issues in Banking and Monetary Analysis, ed. by Giulio Pontecorvo, Robert P. Shay, and Albert G. Hart (New York, 1967).
For a description of the Almon polynomial distributed lag, see Shirley Almon, “The Distributed Lag Between Capital Appropriations and Expenditures,” Econometrica, Vol. 33 (1965), pp. 178–96.
For an explanation of this relationship based on optimizing behavior of banks, see Franco Modigliani, Robert Rasche, and J. Philip Cooper, “Central Bank Policy, the Money Supply, and the Short-Term Rate of Interest,” Journal of Money, Credit and Banking, Vol. II (1970), pp. 180–98.
Victor Argy, “The Determinants of the Money Supply” (unpublished, International Monetary Fund, September 4, 1970).
The complete set of data is available in typescript on application to the Central Banking Service, International Monetary Fund, 19th and H Streets, N. W., Washington, D. C. 20431 U. S. A.
The nonlinear program used was the LSAUTO of Data Resources, Inc. No attempt was made to reduce simultaneous equation bias.
Carl F. Christ, “Interest Rates and ‘Portfolio Selection’ among Liquid Assets in the U. S.,” Chapter 8 in Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld (Stanford University Press, 1963), pp. 201–18.
Edgar L. Feige, The Demand for Liquid Assets: A Temporal Cross-Section Analysis (Englewood Cliffs, New Jersey, 1964). Feige’s sample period was 1949–59, covering the then 48 United States (plus the District of Columbia). His interest rates were computed as actual, as opposed to the announced nominal, interest payments (derived from income and expense statements of the financial institutions) divided by the average balance of the asset during a period. According to him, the actual interest payment is used because it represents more clearly the real market opportunities facing the saver.
Almon, “The Distributed Lag Between Capital Appropriations and Expenditures” (cited in footnote 19).
The estimates of αi and βi are
α0 = 0.5468
α1 = 0.3563
α2 = 0.2006
α3 = 0.0799
α4 = −0.0058
α5 = −0.0567
α6 = −0.0727
α7 = −0.0538
β0 = 0.5894
β1 = 0.3718
β2 = 0.1953
β3 = 0.0599
β4 = −0.0342
β5 = −0.0873
β6 = −0.0993
β7 = −0.0702
This multiplier may be rewritten as
Rewritten in this way, it is analogous to the usual expression of the money multiplier in terms of the currency to money ratio, that is,
which measures the response of the supply of money to a change in the monetary base in a rather mechanistic manner. On the other hand, the money multiplier given by equation (13b) or (13) measures the response of the quantity of money to a change in the base, taking account of behavioral responses of both supply of and demand for money.
Jordan, for example, refers to factors influencing money supply as changes in components of the “money multiplier” and changes in the monetary base. By this he implies that these two factors are separate and not interdependent. Jerry L. Jordan, “Elements of Money Stock Determination,” Review, Federal Reserve Bank of St. Louis (October 1969), pp. 10–19.
Teigen has explained open market policy and discount rate policy in terms of several variables, such as the gap between actual and potential GNP, unemployment, rate of price change, growth rate of real output, and the balance of payments. See Ronald L. Teigen, “An Aggregated Quarterly Model of the U. S. Monetary Sector, 1953–1964,” in Targets and Indicators of Monetary Policy, ed. by Karl Brunner (San Francisco, 1969), pp. 175–218.