Why velocity of money changes

Such an unprecedented increase in money demand has slowed down the velocity of money, as the figure below shows. And why then would people suddenly decide to hoard money instead of spend it? A possible answer lies in the combination of two issues:. Indeed, during the prerecession period, for every 1 percentage point decrease in year Treasury note interest rates, the velocity of the monetary base decreased 0.

Since year interest rates declined by about 0. But the actual velocity has gone down by 5. This happened because the nominal interest rate on short-term bonds has declined essentially to zero, and, in this case, the best form of risk-free liquid asset is no longer the short-term government bonds, but money.

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Up next: Florida should close tax loopholes for corporations Column. Elon Musk tweets to ask if he should sell 10 percent of his Tesla stock Nov. Progress slow as Tampa Bay teachers, districts work out contracts Nov. The strategy has involved the announcement of target ranges for sterling M3 for several years ahead, with a stated goal of progressively slowing its rate of expansion.

The budget presented in the spring of emphasized the difficulties of relying too heavily on sterling M3 as an indicator of monetary policy. Accordingly, in and the target for sterling M3 was supplemented with targets for M1 and PSL2. PSL2 includes deposits at building societies, which are excluded from sterling M3; see the note to Table The practice of targeting M1 and PSL2, however, was abandoned after two years, in association with financial innovations that had altered the previous relationships of those aggregates with national income.

At the same time, the authorities in adopted a target for M0, the wide monetary base. Notwithstanding the fact that the targets were overrun for sterling M3 in , , and as well as for M1 in and and PSL2 in , the progressive lowering of monetary growth over the —84 period contributed to a substantial decline in British inflation Chart During , the authorities were confronted with conflicting signals from sterling M3, which had been expanding more rapidly than the upper bound of its target growth range, and M0, which was close to the lower bound of its target range.

The authorities continued to regard the aim of monetary policy as that of ensuring sustained and steady downward pressure on inflation. Moreover, the Chancellor of the Exchequer, in his October speech at the Mansion House, emphasized that:.

At the same time, the British authorities stated their assessment that the recent behavior of sterling M3 had been affected by structural changes and was not inconsistent with declining inflation, given that narrower measures of money had been growing relatively slowly, that the exchange rate was relatively firm, that real interest rates remained high, and that forecasts for business activity did not suggest inflationary pressures.

For those reasons, they decided to de-emphasize the sterling M3 target at that time. Subsequently, in announcing monetary objectives for the period from February through April , the authorities set a target range of 2—6 percent annualized growth for M0, compared with the 3—7 percent range they had set for M0 during the previous period, while raising the target range to 11—15 percent for sterling M3.

In the United States , monetary policy has pursued target growth rates for multiple monetary aggregates since However, a major shift in monetary strategy was announced in October , and another shift occurred around October The performance of the monetary aggregates and inflation during the period prior to October contributed, in the opinion of some close observers, to an erosion of the credibility of U.

In addition, during each of the latter three years the outcomes for M2 and M3 were either above or in the upper thirds of their target ranges. Moreover, through the beginning of , new one-year targets were adopted every quarter, with a regular practice of rebasing to the outcome for the most recent period, which typically overshot the level specified by the previous target. M1 growth also exceeded its initial targets in and Just as the Canadian experience during the late s indicated that adherence to monetary targets could not guarantee lower inflation, the U.

The period since October has been described as one in which the U. Downward shifts in the demand for goods and services seemed evident from the psychological impact associated with initiation of the credit control program in early and during the recession of when inflationary expectations began to wane; upward shifts appeared as the credit control program was lifted and more recently in the wake of the turn to a quite expansionary fiscal policy.

Those shifts led to extremely wide fluctuations in interest rates under the operating procedures that had been adopted in October Partly for that reason, in October the Federal Reserve again decided to change its operating procedures, this time toward a more judgmental approach based on targeting on borrowed reserves.

Since that time, U. It is noteworthy that the Federal Reserve has been criticized strongly over the past decade both for deviating from and for adhering to its targets. Just as associations have been drawn between the acceleration of inflation and the growth of monetary aggregates above their target ranges prior to October , associations have also been drawn between the depth of the U. By the end of , U. Such strength failed to materialize during the first two quarters of the year, however, and the velocities of the U.

Critics have argued that the Federal Reserve should have responded sooner than it did to counter the decline in velocity with an increase in monetary growth, particularly with short-term real interest rates in the range of 10 percent per annum. But a substantial reduction in taxes was scheduled to become effective at mid-year, and it was difficult to predict what impact the fiscal stimulus would have on economic activity. By contrast, in the second half of , the Federal Reserve changed its policy stance, allowing U.

During , the Federal Reserve faced the choice of how to react to M1 growth considerably in excess of its target range. Although the economy was not in a recession, as it had been in the first half of , signs of economic activity growth and inflationary pressures did not appear to be strong, and velocity levels had dropped significantly.

Accordingly, in July the Federal Reserve rebased its M1 target at a higher level and also widened the target range.

By the fourth quarter, M1 velocity had dropped even more, and the members of the Federal Reserve policy committee agreed at their November meeting that: Under prevailing circumstances, and unless the dollar declined sharply further, the strength of M1 thus far did not appear to suggest strong inflationary consequences. Accordingly, it was decided that growth of M1 above its revised target range would be acceptable for the second half of the year. There is disagreement over the policy lessons that should be drawn from the observed behavior of velocity and the central bank experience with monetary targeting over the past decade.

There are advocates of three different schools of thought. Advocates of passive rules have not been dissuaded by the past decade of experience, but argue that discretion is inherently inflationary and destabilizing, and contend that the difficult choices that central banks have confronted can partly be attributed to the fact that they did not adhere sufficiently closely to the targets they announced.

Advocates of activist rules suggest that some of the difficulties confronted by central banks could be alleviated by shifting from the types of fixed monetary targets that have been announced over the past decade to rules that provide an explicit prescription for countercyclical behavior. Advocates of discretion argue that no mechanical rule can respond adequately to all contingencies that may arise. The sources of these disagreements, and the strengths and weaknesses of the three schools of thought, may be illuminated by a review of the different types of models that have been developed for analyzing the behavior of velocity and for drawing inferences about the appropriate conduct of monetary policy.

This part of the paper provides a streamlined presentation and comparison of the different types of models that have been used to analyze the interrelationships between prices, output, and money and the behavior of velocity. Its purpose is to shed light on important conceptual issues in the debate over the appropriate conduct of monetary policy, which to a considerable extent has been confused by an inadequate recognition of the strengths and limitations of alternative analytic frameworks, and by misperceptions of the types of theoretical models and assumptions that support different conclusions.

Three different approaches have been developed for analyzing the behavior of velocity and for addressing questions about the appropriate conduct of monetary policy. The first approach has concentrated narrowly on the demand for money; however, the lack of a complete framework of analysis recognizing the endogenous nature of the arguments in the money demand function limits the usefulness of such models for economies in which income, prices, and money interact simultaneously.

The third approach, which has gained increasing attention in recent years, also employs a complete macroeconomic framework, but under the assumption that expectations about inflation rates and other endogenous variables are rational and take account of relevant information about the structure of the macroeconomic system and expectations about the future values of exogenous variables, including the setting of monetary policy. These three approaches are each reviewed separately below. The subscript t denotes time.

The logarithm of velocity v t is simply obtained by subtracting the logarithm of income from both sides of equation 1. These features are in accordance with one extreme case of the simple Keynes-Hicks IS-LM model, in which prices are assumed to be fixed in the short run and the interest rate provides the transmission mechanism through which the money supply affects the level of output. The extreme case is that in which the demand for money is insensitive to the interest rate so the LM curve is vertical but saving and investment are not, and in which the demand for money has a unitary income elasticity.

In that case, an increase in the money supply would require income to change proportionately in order to restore equilibrium in both the goods and money markets. While equation 1 has been widely adopted as a description of the long-run demand for money, much of the empirical literature has hypothesized that adjustment costs can result in short-run deviations of actual from desired real money balances.

Typically, adjustment costs have been represented simply by adding a lagged dependent variable to equation 1. Thus, a representative short-run money demand function is: Throughout the past decade of monetary targeting, central banks relied heavily on relationships like equation 2 in analyzing the behavior of their monetary aggregates.

This puzzle has been well documented for the United States, although it is by no means unique to that country. Some economists have argued that the modification of simple velocity functions to recognize institutional developments can improve the explanation of both long-run and short-run movements in velocity. The velocities of monetary aggregates that include the new financial instruments will similarly decrease.

As has already been discussed, several of the major industrial countries have experienced significant shifts in velocity associated with financial innovations; indeed, such shifts contributed importantly to the Canadian decision to abandon the practice of monetary targeting in , and to the U.

Note, however, that while sustained changes in the level or trend of velocity might, at least partially, be explained by financial innovations, it is difficult to attribute reversible fluctuations in velocity to financial innovations, since there generally is no reason for the demand for the monetary aggregate ever to shift back to its preinnovation level.

A second argument for modifying equation 2 is the fact that the nominal money supply for the economy as a whole is controlled by the monetary authorities.

Thus, if the public wishes to adjust its real money balances, given the amount of money supplied by the authorities, such adjustment must take place through variations in the price level. The only difference between equations 2 and 3 is that the lagged dependent variable of equation 2 has been replaced in equation 3 by a current money supply aggregate deflated by the price level for the previous period, reflecting the hypothesis that the public slowly adjusts its holdings of real money balances through variations in the price level.

Moreover, it is possible to obtain the same type of reduced form equation from a large number of models that use equation 1 as one of their structural components. Thus, unstable estimates of equation 3 would not necessarily imply that the demand for money was misspecified, but might reflect instability in other sectors of the economy. Nevertheless, this approach correctly identifies the endogeneity of the price level and thereby makes a valuable contribution to understanding the behavior of velocity.

Indeed, equation 3 implies that velocity depends negatively on the contemporaneous level of the money supply; an increase in the money stock in one period does not lead immediately but only after a lag to equiproportionate increases in the levels of prices and nominal GNP:.

This dependency of velocity on the contemporaneous money stock distinguishes equation 4 from the description of velocity corresponding to equation 2. In equation 4 , the money supply is an exogenous variable; so too are the levels of output and the interest rate. A third reason for modifying equation 2 is to relate the behavior of money demand to exchange rate expectations.

It can be argued that, in deciding on their holdings of money denominated in a given currency, individuals take into account not only expected rates of return on domestic-currency-denominated substitutes for domestic money, but also expected rates of return on assets denominated in foreign currencies.

The expected rate of change in the exchange rate is then introduced into the model in the form of a relationship between domestic and foreign interest rates. The development of this line of argument in the literature, however, has not been entirely satisfactory, as is shown in Appendix VIII. This Appendix extends the analysis to show that an increase in the expected rate of depreciation of the domestic currency will raise velocity by making it attractive to hold less domestic currency at given levels of domestic income and interest rates.

In particular, the expression for velocity is:. As in equation 4 , velocity depends negatively on the contemporaneous supply of the domestic currency. But, again, the behavior of velocity is described by a reduced form of a system of equations rather than by a structural money demand function alone. While equation 4 is based on the assumption that the price level is endogenous, equation 5 is derived from a model that takes the behavior of the contemporaneous exchange rate as endogenous.

Hence, the short-run interaction between money, income, and the interest rate is not completely explained, even though the nature of that interaction may be quite important for understanding the behavior of velocity. In general, however, the foregoing criticisms of the technique of analyzing the behavior of velocity with models that focus narrowly on extended money demand functions rather than on complete macroeconomic models raises an important caveat about their relevance for policy analysis.

It is often argued, following Poole , that central banks should adopt a monetary aggregate rather than an interest rate as an intermediate target only if the financial sector of the economy is subject to less variability than the real sector of the economy.

The caveat, however, is that the argument is not based on a complete macroeconomic model. The disequilibrium models under consideration here incorporate a long-run money demand function of the kind described in equation 1.

This framework explains the interrelations between money, output, and prices and hence the behavior of velocity in the following way. After an exogenous change in the money supply, individuals find themselves holding a different level of real money balances than they desire; thus, they revise their expenditure plans and, in doing so, induce a deviation in output from its full employment level.

This deviation, however, is temporary; prices will react, although sluggishly, and will in turn influence expectations, generating a dynamic pattern of price and output adjustment that continues until prices have moved to the same extent as money and the disequilibrium in the money and output markets has vanished. The disequilibrium model that is presented in Appendix II leads to the following reduced form equation for velocity: Notice that equation 6 describes the behavior of velocity completely in terms of exogenous variables the money supply and the long-run level of output or predetermined variables the past values of the price level.

Notice also that equation 6 , like equations 4 and 5 , shows that a contemporaneous change in the money supply has a negative effect on velocity. Hence, all these equations imply that the variability of velocity is not independent of the behavior of the monetary authorities.

One important feature of this disequilibrium model is that changes in the money supply, even when they are entirely expected, can influence real variables such as the level of output. In recent years, economic theory has moved increasingly away from analysis based on the assumption of adaptive expectations toward analysis based on the assumption that expectations are formed rationally, in the sense that agents take account of whatever relevant information is available about the structure of the economy and the values of exogenous or predetermined variables.

Several different types of complete macroeconomic models have been used to address questions about the appropriate conduct of monetary policy under the assumption that expectations are formed rationally.

It is now appreciated that the answers to these questions depend critically on the effectiveness of monetary policy, within the different types of models, at generating changes in the short run in the relative prices and other variables that influence the supply decisions of firms and factors of production, which in turn combine to influence the aggregate level of output for the economy as a whole.

The classical model is then used to discuss both the case for a money supply target and the choice of instruments for controlling the money supply. It should be emphasized at the outset that the theoretical conclusions about alternative types of central bank rules, and especially the theoretical case against central bank discretion, have been challenged by arguments that the analytic models oversimplify the stability and predictability of macroeconomic relationships.

These arguments will be reviewed later. It should also be emphasized, however, that the models discussed in this paper do not assume that economic agents have complete information about the structure of the economy, but only that private economic agents have as much information as central banks.

In this regard, it should be noted that the results derived from these models are based on the assumption that agents have incomplete information on the current values of economic variables, in particular the general price level. The section ends with a focus on the implications of incomplete information for the distinction between activist rules and discretion. In addition to assuming 1 that economic agents are optimizing units that use whatever relevant information is available when forming their expectations about future variables, the classical models hypothesize 2 that the supply of output depends positively on the gap between the current price level and prior expectations of the current price level, and 3 that prices adjust rapidly to allow for continuous clearing in all markets.

The second assumption, which has been labeled the Lucas aggregate supply relation, is based on the theory that optimizing firms will increase production as the observed prices of their own output rise relative to their expectations about the general price level, on which information becomes available with a lag. The lack of full current information prevents firms from distinguishing between relative and absolute movements of the price level.

This is the source of the inverse correlation between inflation and unemployment, as depicted by the Phillips curve, in the classical model. An alternative model, discussed later, relies on a certain type of stickiness in the price-adjustment process, rather than on a current misperception of relative price changes, for influencing the supply decisions of microeconomic agents.

In models based on rational expectations, a forecast for one particular variable takes into account whatever relevant information is available about other variables that are known to affect the behavior of the forecast variable. In a model in which prices adjust rapidly to clear all markets continuously, rational individuals know that changes in the money supply will quickly affect the general price level.

Thus, their expectations about the price level depend on their expectations about the money supply. Accordingly, an unexpected increase in the money supply will lead to an unexpected increase in the general price level, which will result in an increase in output. The important implications for monetary policy in this kind of model are derived from the fact that only the unexpected component of the money stock affects the supply of output, and even then only for the short time that it takes firms and other economic agents to perceive that their expectations were incorrect.

By contrast, both the expected and the unexpected components of the money supply affect the price level. Note also that even if the rate of growth of the money supply is anticipated and, therefore, does not affect output, it will nevertheless affect the nominal interest rate through its impact on inflation.

This relation follows from the Fisher condition, whereby the nominal rate of interest is equal to the real rate plus the expected rate of inflation.

The example of a classical model that is presented in Appendix III follows the literature in focusing on the case of a closed economy. In the example, the derived solution for velocity takes the following form:.

Unless the contrary is stated, the analysis will assume that the disturbance terms are independent of their previous values. Equation 7 reflects the fact that an unexpected change in the money stock affects the behavior of velocity through its effects on both the nominal interest rate and the level of output.

However, although an unexpected increase in the money supply always increases the level of output, its effect on the nominal rate of interest may be positive or negative, and thus its overall effect on velocity is ambiguous.

The model also implies that unexpected changes in money cause velocity and the nominal interest rate to increase or decrease together, but lead to an ambiguous correlation between changes in output and changes in velocity see Appendix III. The implications of this classical model differ in several important ways from the implications of the demand for money and disequilibrium approaches. In general, the ambiguous correlation between changes in output and changes in velocity within the classical macroeconomic framework emphasizes again that inferences drawn from the money demand approach may be misleading.

In addition, equation 7 differs very significantly from the solutions for velocity presented in equations 4 , 5 , and 6 in that a distinction is made between the expected and unexpected components of the money supply.

This distinction will give rise to important differences in the conclusions that are drawn about the appropriate role of monetary policy as a tool for stabilizing output and employment. Models with rapid price adjustment and rational expectations provide theoretical support for a money stock target.

The support is based on two propositions: first, that the exercise of discretion by central banks can surprise the public temporarily and can thereby have short-lived effects on output, but can do no more to output than create variability around its expected time path; and second, that once discretion has been ruled out, a money stock target appears superior to a nominal interest rate target.

By contrast, in both the disequilibrium models and the demand for money framework, the choice between a money stock or an interest rate target depends on the relative variability of real and monetary disturbances and on the estimated values of the coefficients in the model. These propositions are demonstrated below. The analysis does not address the question of whether a money stock target is superior to a target for some other nominal magnitude, such as nominal GNP; that issue is discussed in the next major part of the paper.

Two distinctions should be kept clear throughout the analysis: that between discretion and rules; and that between active and passive rules. As defined earlier, discretion should be understood to refer to monetary policy that does not follow a prespecified and preannounced rule. However, the fact that central bankers choose to follow a rule does not imply that they must try to achieve a fixed target for the monetary aggregate a passive rule.

Activist rules will be considered later. The analysis of macroeconomic models under the rational expectations assumption leads to a number of strong conclusions, labeled theoretical to indicate that they have been challenged for reasons that will be elaborated later.

In addition to presenting the theoretical case based on these models against central bank discretion and to suggesting that a monetary target is preferable to an interest rate target, it will now be demonstrated that the assumptions of rapid price adjustment and rational expectations together provide a theoretical case in favor of passive rules and against active countercyclical rules. It will then be shown that this case is not necessarily undermined when prices adjust slowly, but that if prices in some markets are sticky for long enough to allow anticipated monetary policy to influence relative prices in the short run, rational expectations models provide a case for an activist countercyclical monetary rule.

An underlying premise of the theoretical case against central bank discretion is the inference that unexpected fluctuations in money growth around its expected path lead to unexpected fluctuations in prices and output. In the classical rational expectations model, monetary policy cannot improve welfare by changing the expected path of output over time, since as soon as the behavior of the money stock becomes anticipated it no longer affects output.

By contrast, and to anticipate the discussion of a different model, to the extent that monetary policy is capable of affecting output in the short-run through channels other than surprise, the rational expectations hypothesis provides a case for monetary policy to react in a systematic way to dampen the impacts of any disturbances to the economy, but it also provides a case for avoiding any discretion or additional surprise in its own response to disturbances.

This line of argument leads to the conclusion that central banks should minimize the unpredictable elements of their behavior and constitutes the theoretical case in favor of a central bank rule. One of the issues that has received attention in the literature is whether a money supply rule is preferable to a nominal interest rate rule. It is now widely recognized that a nominal interest rate target may have the undesirable feature of leading to an indeterminate price level in the long run.

Now, assume a passive interest rate rule, such that the authorities always allow the money supply to adjust to the level consistent with some fixed nominal interest rate target, i.

Thus, monetary policy does not provide a nominal anchor to hold down the price level. This indeterminacy result can be viewed as a price instability problem. The instability problem does not arise when the authorities choose a money stock target. Then, fluctuations in the levels of prices, output, and velocity will depend only on the random disturbances that are not under the control of the authorities.

By setting a passive money supply rule, central banks cannot totally eliminate output and employment fluctuations, but they can minimize them. Whether a passive money supply rule is preferable to an activist rule for adjusting the money supply in reaction to disturbances to the economy is a separate issue.

The answer depends not only on whether expectations are formed rationally, but also on whether institutional constraints prevent or delay some prices from responding to anticipated changes in the money supply. For rational expectations models with rapid price adjustment, an activist rule cannot stabilize output following disturbances to the economy, and accordingly is no better than a passive rule, since a rational public would take the rule into account in forming its expectations and adjusting rapidly to the disturbances.

Consideration is given later to a model in which a different price adjustment process provides a theoretical case for an active rule. The theoretical case for adopting a money supply rule leaves an important policy issue outstanding: which policy instrument should the monetary authority use in attempting to adhere to a money supply rule when it can only control the money supply indirectly? This issue was widely discussed in the United States, for example, during the years before and after the shift in the operating procedures of the Federal Reserve in October Although that discussion focused in part on political considerations, the issue can be addressed in economic terms by comparing two alternative techniques of monetary control.

The first technique attempts to achieve a money stock target by manipulating interest rates; the second operating technique is to control some monetary base. Although the theoretical analysis assumes that the economy is closed, there is a presumption that the qualitative nature of the conclusions would extend to an open economy to the extent that countries can pursue independent monetary policies in an environment of flexible exchange rates.

The analysis depends on a description of the relationship between the money supply, the monetary base, and the level of interest rates.

A simple but appealing form of that relationship is: The implications for the levels of prices and output that can be derived from these alternative instruments are presented in Appendix V.

Under an interest rate regime:. How do equations 9 and 10 compare? That does not necessarily imply, however, that the choice of a monetary base instrument is inferior to the choice of an interest rate instrument for controlling the money supply.

In general, therefore, such considerations suggest that the appropriate instrument is an empirical choice that depends on both the values of the structural parameters in the economy and the relative variances of the random disturbances affecting the system. Likewise, purchases of stock can also lower market interest rates, because companies that obtain funding by issuing stock will have a lower demand to borrow money.

Therefore, any factors that cause people to hold money will decrease the velocity of money, while factors that increase spending or investment will increase the velocity of money. Therefore, the demand for money is inversely related to the velocity of money.

To understand how the velocity of money changes, one must understand what changes the demand for money. Under most economic models, over the long-term, inflation depends on how much the growth of the money stock exceeds real GDP. The supply of money is the only factor that politicians can control, at least directly. Real GDP and the velocity of money cannot be controlled legally or politically. So to control inflation by targeting the money growth rate, a central bank must know what influences the demand for money and how changes in monetary policy rules will influence that demand.

The increase in aggregate demand with lower interest rates will depend on the debt load of consumers and firms and on economic conditions. While lower interest rates do stimulate aggregate demand, with all else being equal, the magnitude of this effect will depend on debt loads and economic conditions.

High debt loads will decrease the stimulatory effect of lower interest rates, because debtors will be reluctant or unable to increase their debt load. Furthermore, they must decrease spending and investments to pay their debt. Likewise, when economic conditions are poor, consumers and firms will be reluctant to increase spending or to increase investments, because of the increased risk.

This is best illustrated by the prolonged period for the economy to emerge from the Great Recession of to , despite record low interest rates. Consumers and firms were deeply in debt, so their creditworthiness had declined dramatically. Additionally, because banks wanted to avoid more losses, their lending requirements became stricter.

Thus, few people could take out loans, even if they wanted to. Furthermore, because people didn't have money to spend, firms were also unwilling to borrow, since they already had excess capacity due to their depressed economy. So, at the start of the Great Recession, lower interest rates had a much lesser effect in stimulating the economy, which is why the after effects of the recession lasted so long.

Inflation may increase or decrease the velocity of money, depending on which factors are more prominent. Low inflation increases demand for money because higher prices requires more money for a given amount of goods and services. But higher inflation also increases the holding costs of money.