The Variability of Velocity and Credit Ceilings

A TYPICAL FINANCIAL PROGRAM aimed at a desired balance of payments adjustment consistent with internal growth and employment objectives usually employs a range of policy instruments that may include an exchange rate adjustment, fiscal measures, control over the expansion of bank credit and other monetary policies, and perhaps some form of incomes policy. All financial programs supported by the International Monetary Fund have included control over credit expansion by domestic banks by means of credit ceilings. This paper discusses the implications for credit policy of changes in the income velocity of money; it neglects other policy elements of financial programs unless they have a direct bearing on velocity changes.


A TYPICAL FINANCIAL PROGRAM aimed at a desired balance of payments adjustment consistent with internal growth and employment objectives usually employs a range of policy instruments that may include an exchange rate adjustment, fiscal measures, control over the expansion of bank credit and other monetary policies, and perhaps some form of incomes policy. All financial programs supported by the International Monetary Fund have included control over credit expansion by domestic banks by means of credit ceilings. This paper discusses the implications for credit policy of changes in the income velocity of money; it neglects other policy elements of financial programs unless they have a direct bearing on velocity changes.

I. Introduction

A TYPICAL FINANCIAL PROGRAM aimed at a desired balance of payments adjustment consistent with internal growth and employment objectives usually employs a range of policy instruments that may include an exchange rate adjustment, fiscal measures, control over the expansion of bank credit and other monetary policies, and perhaps some form of incomes policy. All financial programs supported by the International Monetary Fund have included control over credit expansion by domestic banks by means of credit ceilings. This paper discusses the implications for credit policy of changes in the income velocity of money; it neglects other policy elements of financial programs unless they have a direct bearing on velocity changes.

Control over credit expansion by domestic banks is used to influence expenditure decisions, since the availability of credit has a strong impact on expenditures on domestic and foreign goods and services and, possibly, on net capital flows and, therefore, on the balance of payments. However, these decisions can also be influenced by the existence, and possible use for financing expenditures, of liquid assets held by the public. This use of accumulated liquid assets can be measured in terms of shifts in the income velocity of money. A reasonably accurate short-term projection of velocity is therefore important for the success of credit policies.

Section II describes some relationships between monetary and national income accounts in order to identify the changes in velocity that must be considered in determining credit policies. Section III discusses the effects of velocity changes under alternative forms of credit ceilings. Section IV reviews some considerations to be taken in the projection of liquid asset holdings.

The Appendix contains plots of the behavior of selected monetary statistics (money/income ratio, currency/deposit ratio, net domestic credit expansion, liquidity financing as a proportion of net domestic credit expansion) for a number of countries with which financial programs have been concluded.

II. The Link Between Monetary and National Income Accounts

In an open economy, changes in the stock of money can come about through changes in both the net domestic assets and the net foreign assets of the banking system, i.e.,



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This is the well-known monetary survey identity that may be used to test the internal consistency of financial policies in stabilization programs. According to this identity, a decline in net foreign assets of the banking system is equal to the excess of the expansion of net domestic bank assets over the increase in the stock of money during the same period; the inverse is true for any increase in the net foreign assets of the banking system. Ex post, this equality holds true at all times; however, for policy purposes it acquires the meaning of an equilibrium condition, since a certain desired change in the net foreign assets of the banking system can materialize only when it is consistent with the planned expansion of net domestic bank assets and with the demand for liquid assets by the public. For example, any excess of the expansion of net bank credit over the consistent amount is converted into foreign exchange at the banks, either because the initial credit-induced excess of liquidity results in increased expenditures on imports or because the public is induced to shift claims from domestic to foreign banks and firms, resulting in capital outflows. In the broadest sense, therefore, financial policies rely on creating those differences between the demand for liquid assets and the policy-controlled supply of liquid assets from domestic sources that will tend to induce the alterations in expenditures and capital flows necessary to achieve the desired change in net foreign assets.

This implies that a certain predictable relationship exists between the desired stock of liquid assets and national income. Such a link is provided in a simplified way by the velocity ratio or its inverse, the money/income ratio:


A credit program is to be formulated, and it is assumed here that both the change in real output and the behavior of the price level over the period of the program are known. This preliminary assumption does not imply that a dichotomy exists between the real and financial sectors of the given economy; it is only a working assumption for ease of exposition at this point.1 A forecast of the money/income ratio for the period of the program is made as k* through, let us assume for simplicity, an extrapolation of the past trend. The planned variables for the program now are, from (1),



MO0 = money stock at beginning of Δ period, and k* GNP = MO*.

However, for the same desired change in net foreign assets, ΔNFA*, the same actual change in gross national product (GNP) will be consistent with a larger expansion of bank credit if the money/income ratio increases over the projected value, i.e., if k > k*, and a smaller amount if the money/income ratio decreases, i.e., if k < k*.2

Define liquidity financing (LF)3 as



ΔMO is the actual change in the money stock, and k GNP = MO.

It follows that liquidity financing can only be known ex post. That is, liquidity financing is defined as that unobserved expansion (contraction) in the stock of money at the projected money/income ratio k* which is the equivalent of the actual decrease (increase) in the money/income ratio over the projected value k*. Less formally, liquidity financing may be described as the monetary equivalent of unanticipated changes in the money/income ratio over the period of the program. Therefore, liquidity financing is positive as k* > k; it is negative as k* < k; and it is zero as k* = k.

Substituting (4) into (3) yields (5).


That is, if an unanticipated change in the money/income ratio does occur, only an adjustment of the credit ceiling by the amount of liquidity financing (positive or negative) would make the credit ceiling consistent with the desired change in net foreign assets, ΔNFA*. If the ceiling is not adjusted, the actual change in net foreign assets, ΔNFA, will be different from the desired change, ΔNFA*. As can be seen from (4), if the money/income ratio is forecast accurately—i.e., if k* = k—(5) reduces to (3).

Any model that attempts to explain short-term balance of payments developments in terms of, among other things, changes in domestic bank credit, contains (5) (or the simpler relation (3)) as a necessary consistency relation. However, without further assumptions, (5) is not, by itself, a “financial programing model.” Indeed, of the variables in relation (5), only the change in the expansion of net bank credit is under the control of the policymakers, whereas all others are influenced by the behavior of the public during the period of the program. A complete financial programing model, therefore, is any set of equations and assumptions, however simple or elaborate, that “explains” the values of all variables other than ΔNDA* in relation (5). Aside from the basic structure, these models are likely to be different from country to country.

By necessity, the financial programing model in many instances consists of information and projections that are not formalized in equations but are rather made consistent, ex ante, in an iterative process, with relation (3). This implies that the demand for money and therefore the velocity value (money/income ratio) for the end of the period must be projected reasonably accurately. The monetary survey identity can therefore be used as a consistency relationship in financial programing models when a particular behavior of velocity is made explicit and appears reasonable in light of experience and theoretical expectations. Without an understanding of the behavior of velocity, one should not use monetary survey figures to judge credit policy. In particular, without a supporting analysis it is not theoretically valid to base the credit program on an assumption of constancy of velocity or of trend stability of velocity between periods.

Often the projection of velocity for the period (i.e., the projection of the demand for monetary holdings) is the principal behavioral assumption in an exercise to test consistency and is therefore of great importance to the results of the credit program. This fact is widely realized and, in practice, constitutes the challenge of continually improving the projections of the demand for monetary holdings (see Section IV).

III. The Effects of the Variability of Velocity

Relation (5), which is usually the basic relation around which a financial programing model is built, does contain one financing item—namely, liquidity financing—that is not explicitly recognized in the monetary survey identity (1). This is the crux of the matter: the influence that control over the banking system’s net domestic assets has on its net foreign assets depends to an important degree on changes in velocity. When these velocity changes are foreseen approximately, adjustments can be made in the credit program. Unforeseen velocity changes, however, impair the attainment of the targets of the credit program, which is easily seen by reference to relation (5). Suppose that the ceiling on the net domestic assets of the banking system has been set, consistent with a certain net foreign asset target, on the assumption that velocity will not change over the program period. However, if in fact velocity does increase, liquidity financing will be positive, and, without a reduction of the planned expansion of credit, the additional financing item will be absorbed by unanticipated decreases in the net foreign assets of the banking system and, possibly, by some unanticipated increase in nominal GNP—perhaps largely through changes in price levels. The absorption of excess liquidity between the balance of payments and nominal GNP is an area that merits further study. It will depend in each specific case on marginal import propensities, the elasticity of capital flows with respect to domestic monetary variables, the degree of capacity utilization in the economy, and other variables. Conversely, if liquidity financing should turn out to be negative because of an unanticipated decline in velocity, there may be an unanticipated increase in the net foreign assets of the banking system and, possibly, some unanticipated decline in nominal GNP. That is, with positive (negative) liquidity financing, the planned level of the net domestic assets of the banking system is higher (lower) than is consistent with the original target for net foreign assets.

The Appendix contains charts for a selected group of countries in which the amount of liquidity financing is shown as a percentage of the actual change in banking system credit. Liquidity financing has been computed by applying formula (4); a trend has been fitted to the money/income ratios observed over a 10-year to 15-year period and the deviations from trend are taken to represent the difference between projected and actual money/income ratios (k*k). It must therefore be stressed that the calculations are very rough and at best indicative of orders of magnitude, since in practice the projection of the demand for liquid assets is usually more sophisticated than assumed here. With these reservations, the charts show that liquidity financing amounted, in some countries, to an equivalent of 100 per cent or more of the actual change in net domestic assets of the banking system. An independent survey of a small number of financial programs was made in which the demand for liquid assets actually projected was compared with the observed stock of liquid assets at the end of the program period. With this more realistic method of computing, it was also found that liquidity financing was quantitatively important in the sense of amounting, in some cases, to a very significant proportion of the change in net domestic assets of the banking system, actually realized or allowed under the ceiling. This resulted in some programs because the extent of the velocity shift was underestimated and in others because a shift was altogether unexpected. The charts also show the relatively heavy occurrence of liquidity financing at the time of the implementation of financial programs supported by the Fund. This subject is taken up more fully in Section IV, where the problem of simultaneity in the projection of the demand for money is discussed.

The quantitative effects of even small errors in forecasting the holdings of liquid assets may be considerable. On the extreme assumption that any error in the projection of holdings of liquid assets is fully and immediately reflected in equivalent changes in the gross reserves of the central bank, the foreign exchange loss resulting from an error of overprojecting such holdings by 1 per cent would range between ½ per cent and 30 per cent of the gross reserves of the central banks of Fund member countries. However, because of the partial absorption of excess credit through increases in price levels, the amount of excess credit may not immediately spill over into reserve losses to the maximum extent possible.

Changes in velocity measured on an annual basis usually occur in all credit programs. (See the charts in the Appendix for plots of the money/income ratio and for annual percentage changes in this ratio in selected countries.) Of interest here are those programs where substantial changes in velocity have not been anticipated. These cases are of concern because unexpectedly large positive liquidity financing (unexpected increases in velocity) reduces the effectiveness of credit controls and may prolong the adjustment process—necessitating far-reaching measures, including possible exchange rate action, later on. Conversely, with unexpectedly large negative liquidity financing (unexpected decreases in velocity), adherence to the original credit ceilings may cause a temporary and unnecessary credit squeeze. However, in this case the ceilings can easily be modified without damage to the stabilization program, whereas adherence to the original ceiling will always cause damage when there is a large unanticipated increase in velocity. While there is the theoretical possibility of reducing the credit ceiling when velocity increases unexpectedly, it is almost always impossible to achieve such reductions in practical circumstances.

Given an unexpected shift in velocity, its ultimate effect on financing expenditures will depend on the type of credit ceiling employed. For a banking system ceiling, relation (5) is directly applicable. For example, if an unanticipated increase in velocity does occur, liquidity financing is injected with no offsetting reduction in banking system credit, since banks can expand credit to the ceiling by borrowing from the central bank when faced with smaller-than-expected increases in deposits or a cash drain.

Ceilings on the net domestic assets of the central bank may be distinguished according to whether the reserve deposits of the commercial banks are excluded or included from the definition of the ceiling. If their reserve deposits are excluded from the ceiling, any decrease in the banks’ reserve deposits with the central bank does not affect the margin for expanding central bank credit under the ceiling. If their deposits are included in the ceiling, any decrease in their reserve deposits decreases the margin.4

These technical features of alternative ceilings on central bank credit have a bearing on the ultimate effects of liquidity financing in financial programs. If velocity increases unexpectedly, and there is no change in the currency/deposit ratio, the resulting increase in liquidity financing will be the same as for the banking system ceiling. This would not be so, however, if the rise in velocity were accompanied (as it often is) by a rise in the currency/deposit ratio. (See the charts, in the Appendix, for plots of the currency/deposit ratio in selected countries.) Under either form of central bank ceiling, the increase in the currency/deposit ratio will decrease the credit-creating potential of the commercial banks for each unit of increase in the domestic assets of the central bank. In these circumstances, however, the aggregate increase in bank credit will be less under a central bank ceiling that includes (nets out) the reserve deposits of commercial banks than under one that excludes them. This is so because the scope for expanding the net domestic assets of the central bank under a ceiling that nets out the reserve deposits of commercial banks is reduced by any decline over the projected rate of increase in reserve deposits that results from a decline in the rate of increase in deposits with the commercial banks.

These implications of alternative forms of credit ceilings may have an influence on the choice of the type (not level) of ceiling in a particular financial program, when that choice has not already been dictated by other considerations. In a situation where an increase in velocity accompanied by some of the usual increase in the currency/ deposit ratio is confidently expected, but where the extent of the increase is difficult to project, it is preferable to use a central bank ceiling with banks’ reserve deposits netted out. This is so because of this ceiling’s requirement of an automatic offset to unanticipated positive liquidity financing through a reduction in the expansion of the net domestic assets of the central bank. In case of an unexpected decline in velocity accompanied by a decrease in the currency/deposit ratio, the central bank ceiling with banks’ reserve deposits netted out allows a larger aggregate expansion of bank credit than any other form of ceiling.

IV. The Projection of Holdings of Liquid Assets

The analysis so far has shown that the velocity concept is an important element in the theoretical framework of credit programs in that it provides a simplified link between monetary and national income accounts. For the velocity concept to be useful in the formulation of credit policies, velocity must be stable (not necessarily constant) in the short run (the long-run properties of velocity that are frequently discussed are not relevant to the usual policy periods) and predictable with a certain accuracy in terms of a few explanatory variables.

The requirements that velocity be stable and predictable, however, imply nothing about the method to be used in forecasting velocity. In particular, they do not imply that such forecasts can or should be made only by referring to a national income figure, as is always implied when recent trends in velocity are extrapolated. Rather, the requirement of a stable velocity should not be taken as an invitation to assume the existence of this stability in any simple correlation of income and the stock of money. Such a forecasting method is unable to project those marginal shifts in velocity that, in the end, produce the unwanted results discussed earlier. A linear function that includes only one independent variable (in this case, income) is incapable of explaining anything else but a linear trend. Thus, when the income elasticity of the demand for money is greater than 1, it can explain a declining trend in velocity but not any variation from this trend.

An extreme example of such a method is the assumption of constancy of velocity, regardless of the specific economic circumstances. Such an assumption implies the very restrictive notion that the elasticity of the demand for money balances with respect to current income, if that is the only independent variable considered, exactly equals 1. Alternatively, it implies that the elasticities of the demand for money with respect to whatever determinant variables are included exactly offset each other to keep velocity constant. Moreover, any projection in which the money/income ratio is used as a dependent variable implies the assumption that the demand for money is homogeneous in nominal income, i.e., the assumption of absence of money illusion. This empirical hypothesis is borne out in most studies of the long-run demand for money but it is not appropriate, a priori, for the projection of the demand for money in the short term, since it assumes instantaneous adjustment in the public’s money balances to purely nominal variations in independent variables.

More generally and preferably, the method used to project monetary holdings should not contain major restrictive assumptions. This can be avoided by using a demand for money function in which the desired (real) nominal money stock appears as the dependent variable and (real) nominal income appears among the independent variables on the right-hand side.

In the following, the theoretical considerations relevant in the projection of monetary holdings are discussed along with the experience gathered in some past financial programs.

The definition of money

The basic decision in each case concerns the appropriate definition of the monetary holdings. The criterion for deciding on a particular definition of money involves the resolution of a prior problem: Is the relevant definition of monetary holdings already implied in the concept of credit policies for financial programing purposes, or does the appropriate definition depend upon the type of credit ceiling adopted in each case?

The issue may be decided on the basis of the observation that a given payments deficit can continue at its initial level (assuming a large enough stock of foreign exchange) only if the reduction in the privately held money stock that results from the external deficit is offset by credit created by the banking system. If the banking system remains passive, the reduction in nominal assets held by the public would presumably initiate a self-correcting process leading to an elimination of the payments deficit. Financial programs, therefore, must be concerned with all aspects of the credit-creating mechanism that potentially allow an increase in aggregate credit that exceeds any desired increase to hold monetary assets. Since the credit-creating potential of the banking system is affected—aside from actions by the monetary authorities—by the public’s asset preferences, it follows that a projection is required of the level and distribution of all monetary liabilities of the banks; that is, monetary holdings are appropriately defined as currency in circulation plus demand deposits and time and savings deposits with banks.

This conclusion is in seeming contrast to the practical necessity to project only the demand for currency under a ceiling on the net domestic assets of the central bank that is defined as including reserve deposits of commercial banks. (Equivalently, this ceiling can be expressed in residual form in terms of the balance sheet items not covered by the ceiling, i.e., as currency issue minus net foreign assets.) There is no contradiction, however, when the demand for components of monetary holdings is derived so as to be consistent with the projection of overall demand for money. An inconsistency may develop when the projection focuses exclusively on the demand for currency on the assumption that the demand for currency is purely for transactions purposes; however, such an assumption is not supported by the evidence in many countries.

The formulation of a credit program is complicated if an economy has certain financial intermediaries, such as finance companies, whose sources of financing are not already controlled. These companies can extend credit to the private sector by taking in deposits (competing with commercial banks) or by borrowing on the capital market. Thus, for a given volume of liabilities of the banking system, finance companies are enabled to extend credit as a (usually small) multiple of the initial increase in deposits with them if there is a reflow of funds to them. It may therefore be necessary in some economies to extend credit controls to financial institutions other than banks.

Stocks and flows

The projection of the demand for monetary holdings, then, involves two theoretically separate problems. One problem is whether during the period of the program the public will continue to hold the stock of money that has been accumulated in the past or whether it will be induced by changes in certain variables, such as interest rates, prices, and the degree of credit restraint, to adjust this stock to a different desired level at the existing level of income. The other problem concerns the question of the rate at which the public during the period is likely to add to its equilibrium level of stocks in response to the growth in a scale variable such as income or wealth, i.e., the flow demand for money. Of course, any observed actual change in money holdings between periods is a net composite of these two effects. In order to identify these two effects separately and with some accuracy, one needs an estimated demand for money function. Although frequently the statistical information necessary to develop such a function is lacking, this does not mean that the stock adjustment demand can safely be neglected. Indeed, it is usually the stock adjustment effect that produces a significant shift in velocity.

The problem of simultaneity

However, even when the importance of considering both stock and flow adjustments is recognized, there remains a conceptual difficulty with demand for money projections for stabilization programs. This difficulty concerns the use of single-equation projections in a situation where simultaneous-equation projections are theoretically clearly superior. The deficiency of a single-equation projection is that, by itself, it does not allow for feedback effects on the demand for money that result from the influence of the credit and other policies finally adopted on income, prices, and interest rates during the period of the program. Stated differently, the variables determining the demand for money must be assumed to be known before it can be decided what specific monetary and economic policies will be pursued. Generally, however, the demand for money will not be independent of these policies. This deficiency of a single-equation approach can be partly overcome by using an iterative projection procedure. In any case, there is in practice usually no alternative to using a single relation in projecting the demand for money. However, when a single equation is used, it should be realized that an adjustment is necessary for the expected values of those explanatory variables that are influenced by the economic policies during the period of the program. These considerations underscore the importance of avoiding a procedure in financial programing that simply makes permissible credit expansion the residual necessary to satisfy a balance sheet identity.

It now remains to identify in detail the variables that enter the demand for money function and to survey the experience of financial programs in accounting for them in practice.

The demand for money function

A general demand for money function can be represented in the following form: 5



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and ǝMO*ǝYe>0,ǝMO*ǝrme>0,ǝMO*ǝre<0,ǝMO*ǝ(1Pdpdt)e0,ǝMO*ǝC<0,ǝMO*ǝW>0,ǝMO*ǝu0.

Frequently, this function is expressed in terms of desired real money balances, in which case the income variable is replaced by expected real income.6 In general, stock adjustment effects are thought to be the consequence of changes in the factors affecting the cost of holding money, represented in the function by the interest rate, price, and credit restraint variables and possibly by other factors included in the u term. The flow demand is associated with changes in the scale variables, income and/or wealth. The observable actual change in money holdings as the net result of these two effects is indicated by the entire demand for money function. This function is not likely to emerge unchanged from empirical testing in any one particular country. Rather, it lists in an exhaustive manner the principal determinants of money demand that are suggested by theory and have been found statistically significant in one country or another. In a specific country it may well prove important to specify in detail some other determinant of money demand that is now included in the catchall term u in the equation. For example, in an economy with no important restrictions on international capital movements, the possibility of substitution between holdings of domestic and foreign liquid assets may have to be recognized through the inclusion of domestic/foreign yield differentials in the demand for money function.

In addition to such specific determinants of the demand for money, the general function in actual application to short-term forecasting would also have to be expanded with respect to the existence of lags in the adjustment of actual to desired money balances, and/or in the formation of expectations. Allowance has to be made, in theory, for the first type of lag, since only actual (not desired) money balances can be observed directly. It is then postulated that actual money holdings approach desired money holdings with some kind of lag. In addition significant lags may exist in the process by which the public adjusts its expectations regarding, for example, price changes to actual price developments. That is, in theory, the variables entering the demand for money function are those that the public expects to hold over a period of time and not the actual observed values. For the time being, however, it is assumed that the public adjusts its expectations quickly to actual developments, so that observed values of variables can be used as good approximations to expected values.

Income and wealth

The general demand for money function has always included a scale variable. Wealth or permanent income has been employed as such a variable only in research confined to a few developed economies. Most money projections for financial programs have used either expected real income or expected nominal income. When the latter was employed, the projections have sometimes neglected the possible effects on the demand for money from price expectations. The problem of properly accounting for the simultaneous determination of real and financial variables in an economy arises, in particular, when a nominal (real) income value must be chosen for a projection of the demand for liquid assets using a demand for money function.

It is usually assumed that the change in real output is known. To a large extent the change can be regarded as supply determined in the short run in many economies when no significant dislocations—policy-induced or otherwise—occur over the period. This is not to deny, however, that levels of aggregate demand (influenced by credit policies) in conjunction with degrees of capacity utilization in the economy may influence real output, even in developing economies. One can also argue that even the availability of credit enters an assumed aggregate production function as an independent variable. These considerations undoubtedly point to the desirability—and also the difficulty—of always working with a model that explicitly integrates the real and financial sectors of an economy. In the absence of such models, one has to ensure in the best possible way that the real output assumed to be known in the financial projections is not inconsistent with the financial values (credit) necessary to validate the real output assumption. When expected nominal income enters the demand for money function, an assumption must be made regarding the development of the price level over the period of the program. The behavior of the general price level over the period is partly predetermined by previous policy decisions and behavior patterns and is partly dependent upon the policies adopted over the period. It is assumed here that financial policies are aimed at containing the rise in the price level to the amount regarded inevitable on the basis of certain behavioral characteristics of the economy. Thus, financial policies in a program could aim either at stability in the rate of price level change or at a reduction in that rate.

Annual projections of the demand for money forecast the desired money stock for the end of the period but, in the absence of quarterly national income data, have little to say about the seasonal pattern of money demand and its components. This pattern, therefore, is inferred indirectly from past actual monthly (quarterly) data on currency and deposits and is superimposed on the annual projection of the stock of money. At times, varying harvest and crop conditions make it necessary to alter these seasonality patterns.

On a strict interpretation, the demand for money is viewed as a flow demand when money is related exclusively to income. Frequently, however, this assumption has proved to be empirically untenable, even though money was correlated only with income and velocity shifts were introduced ad hoc, often justified on grounds of changes in confidence. While such changes have important influences on the demand for money, the introduction of a shift in velocity more generally represents a recognition of the influence of variables other than income or wealth on the demand for money. These variables are the interest rates, the expected change in the rate of change of prices, and the degree of credit restraint—factors that represent the rate of return on money and the cost of holding money rather than other assets. It is changes in these variables that induce stock adjustment effects in the demand for money, either reinforcing or counteracting the flow demand.

Interest rates and degree of credit restraint

The effects on the demand for money of interest rates on alternative financial assets have been systematically observed in developed economies. However, in financial programs in many economies there is evidence that sharp changes in the availability of credit have an influence on the demand for money in the sense that during tight credit policies velocity tends to increase, and vice versa. This agrees with the observations made in most developed economies where the effect of tight credit policies on the demand for money is thought to be transmitted largely via the increase in interest rates on other financial assets, such as bonds, resulting from an increased supply of these securities. However, in economies where there are imperfections in financial markets, where there is no broad market for other financial assets, or where interest rate data on these assets are unreliable, the degree of credit restraint itself may be used as an approximate measure of the increased opportunity cost of holding money balances. During periods of tight credit policy the public will attempt to maintain planned expenditures by economizing on available liquid balances and by extending intersectoral nonbanking credit. Thus, the public would succeed to a limited extent in counteracting a restrictive credit policy by way of increasing velocity. In general, therefore, stabilization programs that introduce marked changes in the degree of credit restraint would have to base their demand for money projections on some short-run variation in velocity. This represents, in fact, the argument that the degree of credit restraint (measured, perhaps, by the ratio of the expansion of net bank credit to the change in current income, by the change in the rate of credit expansion, or by changes in the rediscount rate of the central bank) may enter into the demand for money function as a proxy variable for the effective opportunity cost of holding money. It also illustrates the afore-mentioned case against the wholly residual treatment of credit policies in financial programing. Another direct influence of credit policies on the demand for money results from the requirement of many commercial banks that their loan customers hold compensating balances.

The rate of interest on deposits often shows little variation in developing economies, and its effect on the demand for money therefore has generally not been observed in these countries. However, when changes in the rate of interest paid on deposits have occurred during a financial program, a significant effect on money demand has usually been observed. At times, the increase in deposit balances was very comsiderable in circumstances where “more realistic” deposit rates induced reflows of funds to the banks from unorganized credit markets. Yet, this effect was sometimes neglected in the relevant monetary projections. This is another specific case of the general problem of simultaneity in projecting the demand for money: the effects on the demand for money of the policies proposed for the period of the program cannot safely be neglected. While a reliable quantification of the effects of these types of interest rate changes on the demand for money often may be very difficult owing to the noted absence of sufficient empirical observations, the grounds for a qualitative approximation, making use of the experience in similar economies, are strong.

Changes in price levels

In general, observations on the effects of changes in the expected rate of inflation on the demand for money (other than the influence from nominal or real income) over annual periods have shown that such changes are an important explanatory factor when inflation is pronounced. Aside from the instances of habitually strong inflation, the effects of changes in the rate of price changes on the demand for money have been observed in financial programs following a currency devaluation. In this situation, if no allowance is made for the effect of the expected increase in the price level on the demand for money the result may be an overprojection of the demand for money. This has happened at times when the country in question had previously experienced a steady rate of inflation, and no influences on the demand for money could be observed from significant changes in that rate. Once again, while reliable quantification may not be possible, the case for a qualitative approximation is strong.

Time lags and repressed inflation

So far the problem of time lags has been ignored. The two principal types of lag were noted earlier. One concerns the lag involved in the adjustment of actual to desired money balances. The other lag may arise in the adjustment of expectations concerning income, prices, and interest rates to actual changes in these variables. There is disagreement on the length of the lag in adjustment of actual to desired money balances in developed economies. Most evidence for developing economies, however, indicates that actual money balances are adjusted to desired balances within a year—the period of most programs supported by the Fund. This does not mean, however, that this type of lag therefore can be ignored in practice. In many programs the incremental demand for money is projected on the assumption that actual money balances observed at the beginning of the period in fact represent desired holdings. However, many financial programs are adopted precisely because domestic credit expansion had been excessive but the excess had not yet been fully absorbed by a loss in net foreign assets—leaving a part of actual money holdings at the beginning of the program as undesired holdings still to be liquidated. Usually this occurs in times of repressed inflation (price freezes, introduction of exchange and trade restrictions); the liquidation of excess money holdings then happens when—as a result of the financial program—price controls are (partially) lifted and an import and exchange liberalization is effected. It is therefore necessary to come to a judgment in each particular case as to the extent that actual money balances at the beginning of the program can be considered desired holdings over the period, on the basis of which any incremental demand for money can be projected.

Lags in the formation of expectations are evidenced in country studies, with the general result that these lags are longer in developed economies than in developing economies, particularly concerning income expectations.7 Current income may therefore be a suitable approximation to expected income in most developing economies. In other countries permanent income or wealth may be more appropriate scale variables in the demand for money function. Expectations of changes in the rate of inflation appear to differ widely among countries. Such changes have been anticipated without appreciable lag in countries with a prolonged inflationary experience, owing in good part, it appears, to the signals provided by the annual adjustments in wage settlements in the public and private sectors. In countries with recent steady changes in prices, a sudden increase in one year often seems to be only partly expected but strongly influences price expectations and, accordingly, the demand for money in the next year. As noted before, this sometimes follows a currency devaluation.

Confidence, changes in exchange and trade practices, and monetization

Still other factors have a bearing on annual variations in velocity. Important among these from the point of financial programs are changes in the trade and exchange system where significant liberalizations are likely to produce initially a downward stock adjustment effect on the demand for liquid assets, which possibly is counteracted by a shift by the public from foreign exchange holdings into domestic liquid assets. This has been observed most often after a period of serious inflationary pressures. A factor often invoked—and like some others difficult to quantify with any precision—is the effect on the demand for money of changes in the public’s confidence in the political stability of the country. This factor also has often been found important in inducing the shifts between foreign exchange and domestic liquid assets just mentioned. A lack of public confidence in an overvalued currency equally can lead to such a shift in anticipation of a devaluation.

Allowance also may have to be made for the effects of monetization as well as for the effects of changes in the income distribution, if any, on the demand for money. In this latter area, changes in fiscal policy may be important. The advance of monetization in any one year is likely to depend heavily on expected variation in the activity of the nonmonetized sector. Consideration of the monetization factor is particularly important in the specification of a demand for currency function.

The projection of components of liquid assets

Until now the problem of forecasting has been discussed only for the stock of total liquid assets. However, the formulation of credit ceilings on the domestic assets of the monetary authorities, as well as the actual expansion of aggregate bank credit possible under these ceilings, depends upon the distribution of total liquid assets between currency, demand deposits, and quasi-monetary deposits. It is necessary therefore to arrive at a projection of the components of total liquid assets.

Two approaches—used in a complementary way whenever possible—are available for this purpose. Most commonly, a projection of liquidity components is obtained by applying a money/quasi-money ratio and a currency/deposit ratio to the initial projection of demand for money plus quasi-money. In this case, the projection of liquidity components is dependent upon the behavioral assumptions (forecasts) made for the money/quasi-money and the currency/deposit ratios. These ratios are a function of the asset preferences of the public and would, theoretically, have to be “explained” in terms of the same general set of variables that “explains” the demand for broad money. As a practical approximation, these ratios are usually extrapolated along their trend value, which implies, however, the assumption that no shift in velocity will occur.

The validity of this procedure frequently can be checked through the formulation and estimation of a separate demand function for currency, in addition to the one already obtained for total liquid assets. Once a separate estimate for currency is available, the demand for total deposits can be derived as a residual. If it is necessary to obtain more detail, another separate function, e.g., for demand deposits, has to be estimated. The explanatory variables for the currency demand function are drawn from the set of independent variables of the general demand for money function; these variables, of course, have a different importance and weight in currency demand functions. Care has to be taken, moreover, to account properly for the substitution possibilities between currency and deposits by including in the function the yield on substitute money components. The separate projection of currency (or other money components) can then be used to check the overall money forecast as well as the distribution implied in the trend extrapolation of money/ quasi-money and currency/deposit ratios.

Some technical problems

The foregoing discussion has listed a number of considerations that are relevant in attempts to project the demand for money in the context of financial programs. In what follows, some technical problems in forecasting are reviewed.

The use of end-of-period values or of average-period values for the money stock has no influence on the estimate of the demand for money when there are no seasonal or other variations in the demand for money over the yearly program period, as the taking of averages is an attempt to correct for such variations. If it could be assumed that only seasonal variations were present in the data, the choice of end-of-period or average-period figures for the money stock would influence only the base to which the seasonal adjustment has to be applied. The seasonality pattern, as noted earlier, is inferred indirectly from the actual monthly (quarterly) money stock data and is superimposed on the annual projection of the end-of-period or average-period stock of money. However, the averaging of figures for the money stock is distinctly preferable in all cases, since the use of end-of-period figures may strongly bias the estimates of the demand for money owing to the possible spurious variation in the money stock data on the end-of-period dates, which may have no resemblance to the regularly observed seasonal patterns.

The choice of the transformation to be applied to the variables of the demand for money function involves a problem in either statistical estimation techniques or economic theory, depending on what transformation is applied. When the transformation is applied equally to all variables in the equation—e.g., left-hand and right-hand side variables are expressed in difference or logarithmic form—the theory underlying the specification of the money demand function remains unchanged. The transformation of variables in this case is an attempt to overcome statistical problems arising from serial correlation, or it is an attempt to directly estimate elasticity coefficients. However, when a mixed transformation is used in a money demand function to be estimated—e.g., the dependent variable is expressed in difference form, whereas the independent variables remain in level form—the underlying theory of the demand for money is changed. When this change is the intended result, it may be entirely proper. In practice, the issue involved arises frequently when the change in the stock of money and quasi-money is made a function of the level of nominal GNP on the theory that changes in monetary holdings are a proxy for savings. However, recent empirical tests cast some doubt on the validity of this hypothesis. Tests applied to a sample of 21 countries show that changes in narrow money (currency plus demand deposits) are better explained by changes in income than by the level of income; they also show that changes in quasi-money are better explained by the level of income than by changes in income. This preliminary evidence does not support the hypothesis presented above, since holdings of quasi-money are frequently only a small fraction of total money holdings. Pragmatic arguments for the hypothesis on the grounds of goodness of statistical fit are not very satisfactory; statistical fit can almost always be improved by including in the regression theoretically irrelevant variables, as long as they have some accidental correlation with the dependent variable. However, in periods of stabilization policies when it is usually as important to predict variations in trend as to predict the trend itself, estimated demand for money functions are useful only when they include variables that are causally or functionally related to money demand.

The relevance of incorporating lags into the demand for money function has been mentioned earlier. When annual data are used, lags in the adjustment of actual to desired money balances probably cannot be observed, except in developed economies, since this adjustment is completed largely within one year in other economies. As noted before, a consideration of this lag may still be important when projecting the incremental demand for money after a period of excessive credit expansion. With the use of quarterly data, however, explicit lag patterns must be introduced into the function and tested. Lags in the formation of expectations within a country usually can be expected to change only slowly over time and, therefore, can be assumed constant in the estimation of the demand for money function.8

APPENDIX: Symbols and Sources Used in Charts

(Annual data in current national currency units)

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Les variations de la vitesse de circulation de la monnaie et les plafonds de crédit


Pour que les politiques de crédit adoptées dans le cadre de programmes financiers puissent donner de bons résultats, il faut que l’on puisse disposer, entre autres, d’une projection, établie avec un degré de précision raisonnable, du comportement de la vitesse de circulationrevenu de la monnaie ou, ce qui revient au même, de la demande d’encaisse au cours de la période couverte par le programme. L’auteur expose en détail le concept du financement par la liquidité qui représente pour lui l’élément de financement correspondant sur le plan monétaire aux variations imprévues du rapport monnaie/revenu au cours de la période. Lorsqu’il y a financement par la liquidité – ce qui ne se produira que si les prévisions concernant la demande d’avoirs liquides n’ont pas été établies avec suffisamment de précision – le plafond de crédit fixé dans le cadre du programme devient incompatible avec l’objectif initial de balance des paiements. Examinant un groupe de pays ayant appliqué dans le passé des programmes financiers à la suite d’un accord avec le Fonds, l’auteur montre que le financement par la liquidité a été à certains moments important quantitativement en ce sens qu’il a constitué une proportion notable de la variation réelle du crédit du système bancaire pendant la durée d’application du programme. Lorsqu’il est important, le financement par la liquidité occasionne des variations imprévues dans les avoirs extérieurs nets du système bancaire et dans le revenu nominal.

La majeure partie du document est consacrée à une étude des facteurs théoriques qui se rapportent à la projection de la demande d’avoirs liquides et à un examen des résultats obtenus par certains programmes financiers. L’auteur détermine une fonction générale de la demande de monnaie et souligne la nécessité de tenir compte à la fois de l’ajustement du stock monétaire et du flux de la demande de monnaie. L’auteur accorde aussi une attention toute particulière au problème de la simultanéité, problème qui exige que l’on tienne compte des répercussions qu’auront sur la demande de monnaie les mesures qu’on se propose d’appliquer pendant le programme. Un certain nombre de suggestions sont ensuite offertes et notamment celle de faire figurer le degré de resserrement du crédit dans la fonction de la demande de monnaie en en faisant une variable de remplacement du coût d’opportunité effectif de la détention d’encaisse dans certaines économies. Les influences des autres variables explicatives sur la demande de monnaie sont analysées en mettant surtout l’accent sur les conditions souvent réunies dans les pays qui envisagent l’adoption d’un programme financier. En conclusion, l’auteur examine certains aspects techniques des projections de la demande de monnaie.

Variabilidad de la velocidad y topes al crédito


El éxito de la política crediticia en los programas financieros depende, entre otras cosas, de que haya una proyección bastante precisa del comportamiento de la velocidad del dinero como ingreso o, de forma equivalente, de la demanda de saldos de activos líquidos durante el período del programa. En este trabajo se elabora el concepto de la financiación de liquidez, que representa la partida de financiación que constituye el equivalente monetario de las variaciones no previstas de la razón dinero/ingreso durante el período. Cuando hay financiación de liquidez—lo cual ocurre solamente cuando las previsiones de la demanda de activos líquidos no son bastante precisas—el tope al crédito establecido en el programa ya no concuerda con la meta original de balanza de pagos. Se demuestra que, en el caso de un grupo seleccionado de países con los cuales se han concertado programas financieros en el pasado, la financiación de liquidez ha tenido a veces importancia cuantitativa, en el sentido de que ha ascendido a una proporción significativa de la variación efectiva del crédito del sistema bancario durante el período del programa. Los efectos de una financiación significativa de liquidez serán variaciones imprevistas en los activos netos del sistema bancario frente al exterior y en el ingreso nominal.

La mayor parte del estudio se dedica a un examen de las consideraciones teóricas pertinentes a la proyección de la demanda de activos líquidos, y a un examen de la experiencia obtenida con varios programas financieros. Se presenta una función general de demanda de dinero, y se subraya la importancia de considerar tanto los ajustes en el volumen de dinero guardado como en la demanda flujo. Se dedica también atención especial al problema de la simultaneidad, que hace necesario considerar los efectos que la política propuesta para el período del programa pueda tener sobre la demanda de dinero. Como resultado se sugiere, entre otras cosas, que el grado de contención del crédito puede de por sí entrar en la función de demanda de dinero como variable de aproximación del costo efectivo de oportunidad que represente el guardar dinero en ciertas economías. Se examina también la influencia de las otras variables explicativas sobre la demanda de dinero, destacando las condiciones que suelen existir cuando se preparan los programas financieros. El artículo termina con un examen de ciertos aspectos técnicos de las proyecciones de la demanda de dinero.


Mr. Brau, economist in the Stabilization Policies Division of the Exchange and Trade Relations Department of the Fund, has studied at the Georg August University of Göttingen and the Free University of Berlin in Germany and is a graduate of Duke University.


For a more detailed discussion, see Section IV, page 487.


An increase in the money/income ratio represents a decrease in velocity, and vice versa.


For a similar concept, see Robert Triffin, “A Statistical Framework for Monetary and Income Analysis,” Chapter 17 in Maintaining and Restoring Balance in International Payments, ed. by William Fellner, Fritz Machlup, Robert Triffin, and others (Princeton University Press, 1966), pp. 213-21.


For a discussion of the definition of credit ceilings, see Graeme S. Dorrance and William H. White, “Alternative Forms of Monetary Ceilings for Stabilization Purposes,” Staff Papers, Vol. IX (1962), pp. 317-42.


For a partial listing of the literature and evidence on velocity variability, see Yung Chul Park, “The Variability of Velocity: An International Comparison,” Staff Papers, Vol. XVII (1970), pp. 620-37.


For a discussion of the rationale of money demand functions, see Milton Friedman, “A Theoretical Framework for Monetary Analysis,” Journal of Political Economy, Vol. 78 (March/April 1970), pp. 202-206.


See Joseph O. Adekunle, “The Demand for Money: Evidence from Developed and Less Developed Economies,” Staff Papers, Vol. XV (1968), pp. 220-66.


On the estimation of expectation formation, see Kenneth F. Wallis, “Some Recent Developments in Applied Econometrics: Dynamic Models and Simultaneous Equation Systems,” Journal of Economic Literature, Vol. VII (1969), pp. 781-82. See also Adekunle, op cit.

IMF Staff papers: Volume 18 No. 3
Author: International Monetary Fund. Research Dept.