The Variability of Velocity: An International Comparison
Author: Yung Chul Park

THERE HAS BEEN GROWING recognition of the importance of money in the determination of income, the level of employment, and prices in recent years. Much of this interest in the role of money seems to have been fostered by the experience that few countries have succeeded in suppressing inflation without controlling the supply of money during the postwar period and by the lack of success of fiscal restraints in curbing excessive spending in the United States in the late 1960’s.


THERE HAS BEEN GROWING recognition of the importance of money in the determination of income, the level of employment, and prices in recent years. Much of this interest in the role of money seems to have been fostered by the experience that few countries have succeeded in suppressing inflation without controlling the supply of money during the postwar period and by the lack of success of fiscal restraints in curbing excessive spending in the United States in the late 1960’s.

THERE HAS BEEN GROWING recognition of the importance of money in the determination of income, the level of employment, and prices in recent years. Much of this interest in the role of money seems to have been fostered by the experience that few countries have succeeded in suppressing inflation without controlling the supply of money during the postwar period and by the lack of success of fiscal restraints in curbing excessive spending in the United States in the late 1960’s.

Along with these developments has come “the revival of the quantity theory and the rise of the associated ‘monetarist’ approach to economic policy—an approach which stresses the explanatory and controlling power of changes in the quantity of money.”1 The essential aspect of the monetarist view appears to be the assumption that “velocity rather than the multiplier is the key relationship in the understanding of macro-economic developments in the economy.”2 It has long been suggested that the Quantity Theory holds in the long run, though it may not be an appropriate framework for short-run analysis.3 The Quantity Theory has also been suggested as the more applicable—or more feasible—hypothesis for analyzing the monetary problems in less developed economies.4 Practical considerations may also make it desirable for monetary authorities to base their policy decisions on a simple hypothesis, such as the constant velocity of money. In many countries, and particularly in the less developed countries, the construction of econometric models for policy and forecasting purposes is difficult in the absence of detailed knowledge of the structure of the economy and, most of all, of reliable and consistent data. Even in countries where elaborate econometric models are available, it may be questioned whether the analysis of monetary phenomena, based on such models, is more accurate and useful than the corresponding ones based on a simple hypothesis, such as the Quantity Theory. It is true that by adopting the constant velocity assumption one is not only ignoring some functional relationships that are important in understanding the workings of the economy but also forgoing the useful structural information that econometric models can yield. However, it may also be true that the theoretical and econometric problems associated with constructing economic models are so formidable that one can never judge whether the loss of the structural information is not outweighed by the advantages of simplicity inherent in the Quantity Theory.

In view of these considerations, it would be worthwhile to investigate, as a first step, how velocity has behaved during the postwar period in many countries. We shall begin our study in Section I with a brief discussion of reasons for the variability in velocity and a review of the relevant empirical work in this area. In Section II we examine the facts on the year-to-year variability for three different definitions of velocity, over the period 1953-68, in 30 countries, classified into three groups: (1) industrial, (2) other developed, (3) less developed. A 15-year period is chosen because of the availability of reasonably consistent data. In Section III we provide some explanations for the differences in the variability of velocity found between the less developed and the developed countries. Some concluding remarks will be found in Section IV.

I. Reasons for Variability and Some Evidence

The reasons for year-to-year variation in velocity are now well known. Nevertheless, it may be helpful to review these reasons and to outline briefly the evidence.

Although fluctuations in velocity are obviously inconsistent with a crude Quantity Theory, they are not inconsistent with more sophisticated versions of that theory. Consider, for example, the following distributed lag demand for money function


where money demand is a function of income in the current and all earlier periods, with declining weights (0 < β < 1) attaching to the earlier periods. This can be transformed into5


Assuming that Mtd=Mts=Mt (the demand for money is always equal to the supply of money), equation (2) can be written as6, 7


Divide through by Mt


It is clear from equation (4) that a sophisticated Quantity Theory described by equation (2) is consistent with fluctuations in velocity. These fluctuations are explained in equation (4) by fluctuations in the rate of change in money (Mt1Mt).8 This explanation is not unrelated to the explanation offered by Friedman for fluctuations in velocity. In his earlier work on the demand for money9 Friedman argued that the demand for money was a stable function of permanent income, so that in periods when measured income was above permanent income, velocity would tend to rise and when measured income was below permanent income, velocity would tend to fall.10

The variability in velocity may also be partly due to the variability in the lag in the adjustment of income to money. This variability may be due to the source of the change in money (e.g., the government’s borrowing from the central bank, the supply of bank loans, etc.). Again, shifts in confidence or expectations (largely nonquantifiable—psychological, sociological, and political) may account for observed variations in velocity. The Cambridge version of the Quantity Theory did place great stress on just this type of explanation, shifting the emphasis from the supply of money to the demand for money.11

The Keynesian, post-Keynesian, and recently the capital theoretic approaches (portfolio preference theory) suggest that the main determinants of the demand for money are (1) some interest rate(s) representing the opportunity cost of holding money; (2) a constraint variable: a measure of wealth and/or measured income. As the demand for money need not, of course, respond fully in the same period to these variables, there may be lags in the adjustment process.

There is at present a controversy over the appropriate constraint on the demand for money. The Quantity Theory and Keynesian monetary theory use nominal income as a constraint. The logic of this view is that money is a commodity used primarily to effect a given volume of transactions. The portfolio preference theory emphasizes the role of money as a productive asset and focuses attention on equilibrium in the balance sheet, the allocation of assets, and the services that money provides.

According to this approach, the relevant constraint on the demand for money would be a measure of nonhuman wealth or permanent income. A version of portfolio preference theory developed by Brainard and Tobin12 incorporates both income and nonhuman wealth simultaneously into the demand for money function; income represents the transactions requirement and nonhuman wealth is a constraint variable. There are, however, two difficulties with this approach. First, at least one asset in the portfolio must be treated as inferior (the demand for this particular asset falls as income rises), and it is not altogether clear what type of asset is likely to be inferior. Second, as Johnson points out, since income is the return on wealth and wealth the present value of income, the presence of the rate of interest and one of these variables in the function would make the other redundant.13

There are, in addition, a host of factors, some obviously relevant in the context of year-to-year variations, others more relevant to the secular behavior of velocity: changes in expected rates of inflation; changes in the structure of output, the distribution of income, the relative weights of small and large businesses, and the composition of population (rural-urban); financial/institutional innovations (availability of new money substitutes, new methods of making payments); variation in the ratio of nonmonetized income;14 errors in data.

Direct studies for the United States of the determinants of velocity by Chow,15 Latané,16 Meltzer,17 Brunner and Meltzer,18 Tobin,19 and Teigen20 have all found the rate of interest to be significant.21 This evidence is strongly supported by the many U.S. studies of the demand for money (single equations or part of econometric models). For the United Kingdom direct studies of velocity by Ball22 and by Kavanagh and Walters23 point to the same conclusion. Other studies by Fisher24 of the demand for money also find the rate of interest to be significant. Two empirical studies of velocity based on Canadian data (Macesich,25 Breton26) find the rate of interest to be an important variable. Anderson27 estimates a demand for money function with the rate of interest as a major variable for Denmark. From an examination of postwar data for nine countries, Adekunle28 shows that the interest rate coefficient meets the significance test in five out of six countries for the industrial and other developed groups. On the other hand, it should be mentioned that Kaufman and Latta29 find a significant interest elasticity for only four out of nine industrial countries.30

We can be very brief over the evidence bearing on the other influences on the demand for money. It has been shown that some form of wealth—either nonhuman or permanent income—performs decidedly better than measured income, while there does not seem to be room for both variables to operate simultaneously.31 In countries where the rate of inflation is both reasonably low and stable,32 it has been difficult to find a significant role for the rate of inflation. In conditions of hyperinflation, however, studies by Cagan,33 Harberger,34 Diz,35 and Hynes36 show that the demand for money and, hence, velocity can be significantly affected.

The effects of sectoral, distributional considerations on velocity are difficult to measure statistically. There is some evidence that velocity in the consumer sector is lower than velocity in the corporate sector and that the share of corporations in combined transactions tends to rise in years when business activity is high, and to fall during recessions.37 Other things being equal, this would tend to generate increases in velocity in booms and decreases in recessions.38 A study by Meltzer39 finds evidence that short-run changes in the mix of aggregate output can significantly affect the demand for money. While there are several empirical studies of the demand for money by different-sized businesses, there is no conclusive evidence on the question of whether economies of scale exist.40 A recent detailed study of velocity in the United States identifies in some detail the financial/institutional innovations that have influenced the demand for cash balances.41

In trying to explain the differences in the variability of velocity between the industrial and less developed countries, all the influences reviewed above—for example, interest rates, the expected rate of inflation, the structure of output, the distribution of income—could be treated as explanatory variables; however, lack of data makes it impossible to test a wide range of hypotheses. Also, it is difficult to evaluate on a priori grounds how a particular influence will affect the variability of velocity in the two groups of countries.

Most of the studies on velocity or the demand for money tend to focus on the influence of interest rates as explanatory variables. As noted above, the empirical evidence in industrial countries overwhelmingly indicates that velocity is interest elastic, whereas it is not so clear in less developed countries. But this may simply reflect the different degrees of development in capital markets rather than the different behavioral patterns in the two groups of countries. This suggests that an examination of institutional and technological aspects of the economy may be crucial in understanding the differences in the variability of velocity in the two groups of countries. What follows will be an attempt to examine the facts on the variability of velocity and to identify what appear to be the major factors that are likely to generate differences in the variability between the industrial and the less developed countries.

II. The Results

The income velocity of money is a measure of the frequency with which money is received as, or paid out of, income. There are different measures of income velocity, depending on how money is defined and what concept of income is used. Our study will use three different measures:

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where Y = the monetary value of gross national product (GNP), hereafter referred to as money GNP, M1 = currency outside banks, M2 = demand deposits adjusted plus currency outside banks, M3 = M2 plus quasi-money. All the money figures are quarterly averages.

The variability of V1, V2, and V3 is computed in terms of the degree of dispersion of the observation of each velocity around its trend line (its average when there is no significant trend). To measure this concept of variability, we use the adjusted coefficient of variation, which is defined as the standard error of estimate as a percentage of the mean of the dependent variable. Since this statistic indicates the dispersion of velocity as a percentage of each average velocity, it implies that the higher the coefficient, the more variable is velocity.

The adjusted coefficients of variations of V1, V2, and V3 are given in Table 1. The most striking result is that all three definitions of income velocity are subject to greater year-to-year fluctuations in the less developed countries than in the industrial countries; the group averages for V1, V2, and V3 are almost twice as high as those in the industrial countries. If, however, four countries in the less developed group that show an exceptionally high variability (Argentina, Costa Rica, the Dominican Republic, and Paraguay) are excluded, the argument that velocity is relatively more variable in the less developed group is somewhat less convincing. Without these countries, the group averages of the coefficient of variation for V1, V2, and V3 are 4.6, 4.7, and 5.3, respectively. Although these averages are still considerably higher than those of the industrial group, they are not much different from those of the other developed group.

Table 1.

Thirty Countries: Coefficients of variation of Income Velocity, 1953-68

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Sources: International Monetary Fund, International Financial Statistics; for the United Kingdom’s currency and narrow money, Central Statistical Office, Monthly Digest of Statistics and Financial Statistics.

The result on the relative variability of V1, V2, and V3 in each group is a mixed one; it is not possible to say which definition of velocity is relatively more stable over the period.

III. An Interpretation of the Results

Instability in the economy

Variations in velocity may reflect the inherent instability in the economic structure and social and political system. Social and political instability influences decisions and preferences with respect to the holding of money.42 Substantial variability in the rate of inflation may also be responsible for sharp fluctuations in velocity. In general, it would be reasonable to assume that less developed countries are subject to relatively greater instability of this type.43 Indeed, one characteristic of less developed countries is the relatively high social and political instability. In addition, most less developed countries depend basically upon the export of a few crops and the import of capital. As a result, they are more exposed to abnormal seasonal conditions and externally generated fluctuations in income, against which they have only limited and inadequate stabilization weapons.44 Thus, the relatively high variability in velocity in less developed countries might be explained by the higher instability inherent in those countries.

The degree of monetization

In our definition of V1 V2, and V3, we used money GNP as the numerator, but the appropriate income for our purpose is not total GNP but only the portion of it that requires the use of money, namely, monetized income. The extent to which changes in the degree of monetization and fluctuations in nonmonetary income contribute to variations in velocity in advanced economies is likely to be small. However, in many less developed economies the nonmonetized sector forms a significant part of the national income, and the most important component in this sector is agriculture. Being dependent primarily upon weather conditions, the agricultural component of nonmonetary income is subject to erratic fluctuations. Variations in velocity in less developed countries may then be caused primarily by wide fluctuations in nonmonetary income. It is quite possible that had we used monetized income as the common numerator, V1 V2, and V3 might have displayed much smaller variation in less developed countries. Empirical studies on the demand for money have not been very successful in capturing the significance of this variable simply because of the absence of accurate data and a reasonable proxy variable for the degree of monetization.45

Errors in data

Some fluctuations are inevitable owing to errors in data, and this problem could be more serious in less developed countries. There is unfortunately no way of knowing the extent to which errors in the data are responsible for the variation in velocity. It may be that the absolute errors in both GNP and money supply cancel each other out so that the ratio itself is rather free from such a random factor as erroneous data.

Lagged adjustment and the transmission mechanism

There may be reasons to believe that the lag in the monetary sector is shorter in less developed countries than in industrial countries. First, it is often argued that the representative economic horizon is shorter in less developed countries than in advanced countries.46 The relatively high risks and uncertainties attributable to economic and sociopolitical instability, lack of knowledge, and various market imperfections inherent in less developed economies have been pointed out as the reasons behind such a time preference pattern. Indeed, in a risky and uncertain environment the rational time pattern is likely to be a short one, with more emphasis on current rather than future events. For instance, owners of wealth would prefer a financial portfolio that is subject to relatively little risk and quickly convertible. To avoid unpredictable dangers, entrepreneurs would favor the pattern of operation that can be adapted to new situations quickly and easily. Given these characteristics of less developed economies, one could perhaps argue that the outside lag is shorter in those countries than in advanced countries for the reason that entrepreneurs as well as households are able to react more quickly to any changes in government policies.

Second, monetarists contend that monetary impulses work their effects on GNP through a chain of portfolio substitution relations. Suppose that the government conducts an open market purchase of government securities. The immediate consequence of this operation is to disturb the initial portfolio balance. Relative interest rates must change to attain a new portfolio equilibrium. Thus, further substitutions among assets are made; money is exchanged for other government and private securities, and subsequently the rates on these assets must be bid down. Ultimately, owners of wealth will be induced to substitute into physical assets, such as producer goods and consumer durable goods. It is at this stage that income begins to be affected. The crucial aspect of this transmission process is that the final substitution into physical goods does take place as a result of changes in relative interest rates that are set in motion by the monetary process. The portfolio adjustment theory implies that the lag involved in the transmission process depends, inter alia, on the length of the chain of transactions between the initial change in the quantity of money and the first transaction involving nonfinancial assets. The length of the chain will in turn depend upon the range of available financial assets in which wealth may be held. The broader the range of alternative financial assets, the longer will be the length of the chain of transactions and, hence, the longer the time lag in the transmission process. The variety of available financial assets in less developed countries is extremely limited, and the proportion of these assets in private wealth is relatively low. There is money, on the one hand; there are real physical assets, on the other. “There is little in between. Treasury bills, government bonds, prime industrial bonds, readily marketable shares—all these assets that form the transition between money and real assets in countries with fully developed financial systems play a minor role in the asset structure of most of the less developed countries.”47 In these conditions the impact of changes in the quantity of money will not be diffused among the various money substitutes but will be transmitted directly to the markets for real assets. In other words, changes in the supply of money would be more likely to impinge directly on expenditures in the less developed countries than in the industrial countries. This follows from the fact that capital markets, and hence alternative sources of finance, are more sophisticated in the latter group of countries. Hence, the effects of monetary changes in less developed countries could possibly be swifter and stronger than in industrial countries.

While our data cannot throw too much light on this argument, we have explored two approaches to evaluate the hypothesis that there is a difference in the lag structure between the two groups of countries. First, we measure the adjusted coefficients of variation for lagged velocity, again around their trend line.


Second, we estimate the following three equations.48


The coefficients of variation of V1*, V2* and V3* are given in Table 2. An interesting result (consistent with the hypothesis) is that the coefficients of variation of V1* and V2* are now higher than those of V1. and V2 in 9 and 10 of the 14 less developed countries, respectively. Although the coefficient of variation of V3* is lower in most (10) countries, this may be ignored on the ground that V3 is not a relevant velocity for policy considerations in less developed countries. On the other hand, in the industrial group the reverse seems to be true; the coefficients of V1*, V2* and V3* become lower than those of V1, V2, and V3 in 4, 8, and 8 of the 11 countries, respectively.

Table 2.

Thirty Countries: Coefficients of Variation of Lagged Income Velocity, 1954-68

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Sources: International Monetary Fund, International Financial Statistics; for the United Kingdom’s currency and narrow money, Central Statistical Office, Monthly Digest of Statistics and Financial Statistics.

This finding is reinforced by the results of regressions of equations (5), (6), and (7). The lagged term ΔM1, t-1 in equation (5) is significant in only 3 countries in each of the less developed and industrial groups. But there is a substantial contrast between the two groups in the result of equation (5). The lagged term ΔM2, t-1 is significant in only 2 of the 14 less developed countries, whereas it is significant in 8 of the 11 industrial countries. In none of the less developed countries is the term ΔM3, t-1 in equation (7) significant, but it is in 5 of the industrial countries (see Table 3).

Table 3.

Countries in Whicht-Ratios of Lagged Terms in Equations 5, 6, and 7 Are Significant at the 5 Per Cent Level

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In interpreting the results, we reached these conclusions. We have identified three reasons why the observed variability in velocity might be greater in the less developed than in the developed countries. These were greater general instability, year-to-year changes in the degree of monetization, and greater errors in the data. On the other hand, the lag in adjustment that is possibly smaller in the less developed countries would, if anything, make for less variability in this group. It may be, then, that the first three sets of considerations tend to overwhelm the last one.

IV. Concluding Remarks

The main purpose of this paper has been to compare the variability of velocity on an international scale. The results indicate that prediction and economic policy based on a crude Quantity Theory or on the time trend analysis of velocity is subject to substantial error, this being larger for the less developed countries. An important question would be, then, whether velocity can be treated as a stable function of a fairly small number of variables and whether this function can be specified with reasonable accuracy. Owing to the lack of necessary data, we were not able to do this; however, studies for some developed countries (e.g., the United States, the United Kingdom, and Canada) have shown that a stable demand function for money can be isolated, but the evidence leaves much to be desired. In contrast to the findings of a fair number of studies bearing on the stability issue for the industrial countries, little evidence is available that a reasonably stable velocity—or money demand function—can also be obtained from the data of the less developed countries. Needless to say, even if such a stable money demand function is estimated, it does not necessarily imply that the quantity of money is an important determinant of money income. As Ando points out, in order to show that money is important, one has to show that some real expenditures are sensitive to interest rates in addition to the existence of a stable money demand function.49 To ascertain the impact of changes in the quantity of money, therefore, we may have to rely on an elaborate econometric model of the entire economy. However, insofar as one believes in velocity as the key causal macroeconomic relationship, it is imperative that stability of the velocity function be defined and measured with some precision to be useful for policy purposes. To this end, further econometric studies on the demand for money are needed for the industrial as well as for the less developed countries.

La variabilité de la vitesse de circulation de la monnaie: comparaison à l’échelle internationale


L’auteur de cet article s’est proposé d’examiner la variabilité d’une année à l’autre de la vitesse de circulation de la monnaie considérée sous trois aspects différents; l’étude couvre la période 1953-68 et porte sur 30 pays répartis en trois groupes: 1) pays industriels, 2) autres pays développés, 3) pays moins développés. La variabilité de la vitesse de circulation est exprimée par le coefficient ajusté de dispersion autour de la courbe de tendance de la vitesse de circulation. Les résultats montrent que la prévision et la politique économiques fondées sur la seule Théorie quantitative ou sur l’analyse de la tendance chronologique sont sujettes à une marge d’erreur appréciable, plus large encore pour les pays moins développés.

L’auteur examine les quatre facteurs d’ordre structurel susceptibles de provoquer des différences entre la variabilité des pays industriels et celle des pays moins développés. Il s’agit 1) du degré d’instabilité de l’ensemble de l’économie, 2) du caractère défectueux des données, 3) des variations du niveau de monétisation, et 4) du retard de l’ajustement du secteur monétaire. Les trois premiers facteurs auront vraisemblablement pour effet de conférer une variabilité relativement plus élevée aux pays moins développés. En revanche, le retard de l’ajustement étant probablement plus faible dans les pays moins développés, la variabilité s’en trouvera réduite dans ce groupe de pays. Dans les limites de cette analyse, les résultats montrent que les trois premières séries de facteur ont tendance à prévaloir sur la quatrième.

El grado de variación de la velocidad: comparación internacional


La finalidad de este trabajo es examinar el grado de variación de la velocidad de un año para otro, según tres definiciones distintas de la velocidad, para el período 1953-68, y para 30 países clasificados en tres grupos: 1) industriales, 2) otros desarrollados, 3) menos desarrollados. El grado de variación de la velocidad se mide mediante el coeficiente ajustado de las variaciones en torno a la línea de tendencia de la velocidad. Los resultados indican que la predicción y la política económica basadas en una sencilla Teoría Cuantitativa, o en el análisis cronológico de tendencia de la velocidad, están sujetas a error sustancial, siendo éste mayor para los países menos desarrollados.

Se examinan en este trabajo los cuatro factores institucionales que pueden crear diferencias entre los países industriales y los menos desarrollados, por lo que se refiere al grado de variación. Son los siguientes: 1) inestabilidad general en la economía, 2) errores en los datos, 3) variaciones en el grado de monetización, y 4) el desfase de ajuste en el sector monetario. Lo probable es que los tres primeros sean los que causen un grado de variación relativamente mayor en los países menos desarrollados. Por otro lado, el desfase de ajuste, que posiblemente sea menor en los países menos desarrollados, hará que sea menor el grado de variación en este último grupo. Dentro de los límites de este método, los resultados dan a entender que el peso de las tres primeras consideraciones es muchísimo mayor que el de la última.

In statistical matter (except in the résumés and resúmenes) throughout this issue,

Dots (…) indicate that data are not available;

A dash (—) indicates that the figure is zero or less than half the final digit shown, or that the item does not exist;

A single dot (.) indicates decimals ;

A comma (,) separates thousands and millions;

“Billion” means a thousand million;

A short dash (-) is used between years or months (e.g., 1955-58 or January-October) to indicate a total of the years or months inclusive of the beginning and ending years or months ;

A stroke (/) is used between years (e.g., 1962/63) to indicate a fiscal year or a crop year;

Components of tables may not add to totals shown because of rounding.


Volume 3: Dahomey, Ivory Coast, Mauritania, Niger, Senegal, Togo, and Upper Volta

Pp. xxxviii+786

Maps, Index, Statistical Tables

This volume, covering the seven members of the West African Monetary Union, is the third in the series of books describing the economies of selected African countries. Following the format established in Volumes 1 and 2, the opening chapters in this latest volume describe arrangements for regional cooperation among the seven countries and compare the monetary systems, trade and payments relations, and exchange control systems. The remaining chapters cover each individual country’s production, economic development plans and progress, treatment of foreign investments, national budgets and fiscal policies, money and banking arrangements, and foreign trade, aid, and payments.

The text and tables concentrate on data for 1962-68 but include some figures for 1969. These data are drawn from published sources and from material gathered by the Fund in its regular consultations with member countries. Maps of the region and each country, together with a comprehensive index, complete the volume.

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Mr. Park, economist in the Financial Studies Division of the Research Department, is a graduate of Seoul National University and of the University of Minnesota.


Harry G. Johnson, “Recent Developments in Monetary Theory—A Commentary,” in Money in Britain, 1959-1969, ed. by David R. Croome and Harry G. Johnson (Oxford University Press, 1970), p. 84.


Ibid., p. 89.


See Karl Brunner and Allan H. Meltzer, “Predicting Velocity: Implications for Theory and Policy,” The Journal of Finance, Vol. XVIII (1963), p. 319. See also Milton Friedman, “A Theoretical Framework for Monetary Analysis,” The Journal of Political Economy, Vol. LXXVIII (1970), p. 222.


See R. J. Ball’s review of George Horwich’s Money, Capital, and Prices in The Economic Journal, Vol. LXXV (1965), p. 146. See also J. J. Polak, “Monetary Analysis of Income Formation and Payments Problems,” Staff Papers, Vol. VI (1957), p. 39, and V. C. Shah, “Monetary Analysis in India, 1948-49–1958-59,” The Indian Economic Journal, Vol. IX (1962), p. 306.


Write equation (1) for Mt1d, multiply through by β, and then subtract the equation for M,-i from equation (1).


The distributed lag hypothesis is consistent both with the permanent income hypothesis and with the partial adjustment process in the money market. Suppose that the demand for money is a function of permanent income Yp, Md = mYp where Ypt = bYt + b(1—b)Yt-1 + b(1—b)2Yt-2 + …. Permanent income is a weighted average of current and past incomes. The sum of the coefficient is equal to 1. Friedman gives b a weight of 0.33. See Milton Friedman, A Theory of Consumption Function (National Bureau of Economic Research, 1957), p. 147.

Suppose, on the other hand, that the public are slow to adjust their money balances to desired levels as specified in the following equation,


where c is an adjustment coefficient (0 < c < 1) and Mtd=kY (i.e., desired money balances are a function of income). Rearranging the terms, the above adjustment equation can be written as


which is completely equivalent to equation (3) in the text. It is difficult to discriminate empirically between the two entirely different hypotheses.


Note that the coefficient for Mt-i is negative. Thus, the distributed lag form of the demand function with geometrically declining weights implies that an exogenous increase in M has a positive effect in the current period, and this is followed by a depressing effect in the next period. If we do not assume geometrically declining weights, the distributed lag hypothesis implies an oscillating monetary multiplier. For a verbal rationalization of this process, see Alan A. Walters, “Professor Friedman on the Demand for Money,” The Journal of Political Economy, Vol. LXXIII (1965), pp. 545-51.

One might normally expect that an increase in M would generate an expansionary effect that would taper off gradually in subsequent periods. Indeed, this appears to be the basic assumption of most of the studies on the lags in monetary policy.

Whether the distributed lag hypothesis is a good approximation to behavior or not is essentially an empirical question. Walters finds no conclusive evidence on the oscillating monetary multiplier from U.K. data (ibid., pp. 550-51). The results of the Friedman and Meiselman study also hardly support the hypothesis. See Milton Friedman and David Meiselman, “The Relative Stability of Monetary Velocity and the Investment Multiplier in the United States, 1897-1958,” in Stabilization Policies (Commission on Money and Credit, Englewood Cliffs, N.J., 1963), pp. 165-268. We have estimated the first difference version of equation (3) with data for the 30 countries under consideration. Our results do not provide convincing evidence on the distributed lag form of money demand.


We have estimated equation (4) in the text for all three definitions of money. In most countries the fit was not satisfactory, and there was evidence of significant serial correlation in the error term.


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


This point may be clarified as follows: Assuming that Md = Ms, the demand for money function in footnote 6, Md = mYp, which is shown to be equivalent to equation (1), can be transformed as YM=γYYp. This equation implies that variations in velocity reflect a divergence between current and permanent money income.


For a lucid account of this, see Alvin H. Hansen, Monetary Theory and Fiscal Policy (New York, 1949), pp. 49-53.


William C. Brainard and James Tobin, “Pitfalls in Financial Model Building,” The American Economic Review, Papers and Proceedings of the Eightieth Annual Meeting, Vol. LVIII (1968), p. 103.


Harry G. Johnson, “Monetary Theory and Policy,” The American Economic Review, Vol. LII (June 1962), pp. 335-84.


See the discussion of this in Section III.


Gregory C. Chow, “On the Long-Run and Short-Run Demand for Money,” The Journal of Political Economy, Vol. LXXIV (1966), pp. 111-31.


Harry Allen Latané, “Cash Balances and the Interest Rate—A Pragmatic Approach,” The Review of Economics and Statistics, Vol. XXXVI (1954), pp. 456-60.


Allan H. Meltzer, “The Demand for Money: The Evidence from the Time Series,” The Journal of Political Economy, Vol. LXXI (1963), pp. 219-46.


Brunner and Meltzer, op. cit., pp. 319-54.


James Tobin, “The Monetary Interpretation of History” (A Review Article), The American Economic Review, Vol. LV (June 1965), pp. 464-85.


Ronald L. Teigen, “Demand and Supply Functions for Money in the United States: Some Structural Estimates,” Econometrica, Vol. 32 (1964), pp. 476-509.


The only conflicting study for the United States is the one by Friedman, “The Demand for Money: Some Theoretical and Empirical Results” (cited in footnote 9); his methodological approach, however, was faulty. He introduces the rate of interest only to account for the residuals from an equation explaining real money balances by real permanent income.


Robert J. Ball, “Some Econometric Analysis of the Long-Term Rate of Interest in the United Kingdom, 1921-61,” The Manchester School of Economic and Social Studies, Vol. XXXIII (1965), pp. 45-96; only a very small selection from a large number of estimated equations.


N. J. Kavanagh and A. A. Walters, “Demand for Money in the United Kingdom, 1877-1961: Some Preliminary Findings,” Bulletin of the Oxford University Institute of Economics and Statistics, Vol. 28 (1966), pp. 93-116.


Douglas Fisher, “The Demand for Money in Britain: Quarterly Results, 1951 to 1967,” The Manchester School of Economic and Social Studies, Vol. XXXVI (1968), pp. 329-44.


George Macesich, “Determinants of Monetary Velocity in Canada, 1926-1958,” The Canadian journal of Economics and Political Science, Vol. 28 (1962), pp. 245-54.


Albert Breton, “A Stable Velocity Function for Canada?” Económica, New Series, Vol. XXXV (1968), pp. 451-53.


B. N. Anderson, “The Demand for Money in Denmark, 1921-62,” Nationaløkons. Tids., Vol. 104 (1966), pp. 223-43 (in Danish). (The abstract of the article appears in The Journal of Economic Abstracts, Vol. V (1967), p. 841.)


Joseph O. Adekunle, “The Demand for Money: An International Comparison,” The Indian Economic Journal, Vol. XVI (July-September 1968), pp. 22-43.


G. C. Kaufman and C. M. Latta, “The Demand for Money: Preliminary Evidence from Industrial Countries,” Journal of Financial and Quantitative Analysis, Vol. 1 (September 1966), pp. 75-89.


It is not surprising to find that studies for the less developed countries are far more ambiguous. Adekunle (loc. cit., p. 28) finds that the interest rate is not a significant variable in the demand for money function in studies for three less developed countries (Ceylon, India, and Pakistan). For India there are conflicting studies on the significance of the interest rate in the demand for money. See, for example, Damodar Gujarati, “The Demand for Money in India,” The Journal of Development Studies, Vol. Five (October 1968), pp. 59-64; D. Biswas, “The Indian Money Market: An Analysis of Money Demand,” The Indian Economic Journal, Vol. IX (January 1962), pp. 308-23; V. K. Sastry, “Demand for and Supply of Money in India,” The Indian Economic Journal, Vol. X (July 1962), pp. 29-38. Gujarati and Biswas show that both the short-term and long-term interest rates are statistically insignificant, whereas Sastry finds that interest rates play a significant role in velocity.


David E. W. Laidler, The Demand for Money: Theories and Evidence (Scranton, Pennsylvania, 1969), p. 91.


E.g., the United States and the United Kingdom. This, however, may not be true for the last two years or so in the United States.


Phillip Cagan, “The Monetary Dynamics of Hyperinflation,” in Studies in the Quantity Theory of Money, ed. by Milton Friedman (University of Chicago Press, 1956).


Arnold C. Harberger, “The Dynamics of Inflation in Chile,” in Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld, by Carl F. Christ and others (Stanford University Press, 1963), pp. 219-50.


Adolfo César Diz, “Money and Prices in Argentina, 1935-62” (unpublished doctoral thesis, University of Chicago, 1966).


Allan Hynes, “The Demand for Money and Monetary Adjustments in Chile,” The Review of Economic Studies, Vol. XXXIV (1967), pp. 285-93.


Paul F. McGouldrick, “A Sectoral Analysis of Velocity,” Federal Reserve Bulletin, Vol. 48 (1962), pp. 1557-70.


This behavior of velocity during the cycle is consistent with at least three other hypotheses: first, the procyclical movement in interest rates; second, the Friedman explanation in terms of measured and permanent income; third, the notion that precautionary demand for money falls in the boom and rises in the recession.


Allan H. Meltzer, “The Demand for Money—A Cross-Section Study of Business Firms,” The Quarterly Journal of Economics, Vol. LXXVII (1963), pp. 405-22.


Ibid., and Edward L. Whalen, “A Cross-Section Study of Business Demand for Cash,” The Journal of Finance, Vol. XX (1965), pp. 423-43.


George Garvy and Martin R. Blyn, The Velocity of Money (Federal Reserve Bank of New York, 1969), Chapter 6, pp. 67-77. The four major influences discussed are, in the author’s words, “compensating arrangements to settle payments which tend to reduce the demand for cash balances as well as the volume of debits; second, important and rapidly developing policies and arrangements designed to decrease the amount of balances required to meet a given flow of business payments; third, the related efforts of corporations to invest temporarily redundant cash; and, finally, recent developments that tend to lessen the demand for cash balances on the part of consumers.” These influences are mainly on the secular behavior of velocity.


In Section I it was pointed out that shifts in confidence or expectations may account for observed variations in velocity. To the extent that this is true, the impact of these factors on velocity would be relatively greater in less developed countries.


For some evidence of higher variability in their rate of inflation, see Joseph O. Adekunle, “Rates of Inflation in Industrial, Other Developed, and Less Developed Countries, 1949-65,” Staff Papers, Vol. XV (1968), pp. 531-57.


In terms of Friedman’s permanent income explanation (see footnotes 9 and 10), this implies that less developed countries are subject to greater discrepancies between current and permanent income, and hence to greater variability in velocity than industrial countries.


In a recent cross-section study of velocity, Melitz and Correa use Goldsmith’s classification of countries as a proxy for the rate of monetization and find it a significant variable (Jacques Melitz and Héctor Correa, “International Differences in Income Velocity,” The Review of Economics and Statistics, Vol. LII (1970), pp. 12-17).


Joseph O. Adekunle, “The Demand for Money: Evidence from Developed and Less Developed Economies,” Staff Papers, Vol. XV (1968), p. 230.


Polak, op. cit., p. 39.


Regression of money income on current and past levels of the stocks of money has been a standard method of measuring the monetary multiplier and lags of monetary policy. Although the technique has been used extensively, it is not altogether clear whether this specification is consistent with theories on macroeconomics. For instance, it is not obvious what equation (5) implies about the nature of the demand for money. Within the Quantity Theory framework, we have shown that either the permanent income hypothesis or the partial adjustment hypothesis gives rise to a lagged relationship between income and money. (See footnotes 6 and 7.) However, both hypotheses imply that the sign of the coefficient for M,t-1 is negative.


Albert Ando, “Money and Banking: Discussion,” The Journal of Finance, Vol. XVIII (1963), pp. 355-56.