The Secular Behavior of Income Velocity: An International Cross-Section Study

Several Hypotheses have been offered in the literature about the secular behavior of the income velocity of money. In general, these hypotheses relate the behavior of income velocity to the structural changes that accompany income growth. These hypotheses are, therefore, presented usually in terms of the relationship of income velocity to per capita income. It is, of course, recognized that many factors influence the behavior of income velocity.1 Some of these factors tend to increase relative money holdings as income increases and therefore to reduce income velocities. Other factors have the opposite effect. The hypotheses under discussion thus relate to the net effect of these countervailing forces. They differ because of differences in judgment about whether or when factors making for increasing or decreasing income velocities predominate.

Abstract

Several Hypotheses have been offered in the literature about the secular behavior of the income velocity of money. In general, these hypotheses relate the behavior of income velocity to the structural changes that accompany income growth. These hypotheses are, therefore, presented usually in terms of the relationship of income velocity to per capita income. It is, of course, recognized that many factors influence the behavior of income velocity.1 Some of these factors tend to increase relative money holdings as income increases and therefore to reduce income velocities. Other factors have the opposite effect. The hypotheses under discussion thus relate to the net effect of these countervailing forces. They differ because of differences in judgment about whether or when factors making for increasing or decreasing income velocities predominate.

I

Several Hypotheses have been offered in the literature about the secular behavior of the income velocity of money. In general, these hypotheses relate the behavior of income velocity to the structural changes that accompany income growth. These hypotheses are, therefore, presented usually in terms of the relationship of income velocity to per capita income. It is, of course, recognized that many factors influence the behavior of income velocity.1 Some of these factors tend to increase relative money holdings as income increases and therefore to reduce income velocities. Other factors have the opposite effect. The hypotheses under discussion thus relate to the net effect of these countervailing forces. They differ because of differences in judgment about whether or when factors making for increasing or decreasing income velocities predominate.

Fisher holds that there are economies of scale in the holding of money balances.2 He stresses the factors that make for decreasing relative money holdings. His formulation implies an income elasticity of the demand for money that is lower than unity or, in other words, a rising secular movement in income velocity. Baumol3 and Tobin4 support this view. On the other hand, Friedman believes that money is a luxury. He argues that “in countries experiencing a secular rise in real income per capita, the stock of money generally rises over long periods at a decidedly higher rate than does money income.”5 Thus, in his view the income velocity of money would tend to fall as income increases. Friedman defines money to include currency held by the public, demand deposits, and time deposits at commercial banks. Gurley and Shaw have suggested that “if consumers desire to hold a constant proportion of their financial assets in money balances during output growth, the ratio of money to national income rises during the earlier stages of growth and then eventually levels off.”6 In other words, income velocity would fall at first and then become constant. On the basis of a study of money income ratios in a number of industrial countries during the postwar period, Dorrance and Brehmer suggest that “as national per capita income rises, up to a certain point, money holdings rise relative to real income; after a certain point, the ratio of money to income falls with rising national income.”7 In other words, while income velocity would fall at first, as in the Gurley and Shaw hypothesis, it would after a certain point, according to these writers, tend to rise again.

Most of these propositions about the secular behavior of income velocity of money have been generalizations from its observed behavior in a few countries.8 However, there is very little empirical basis for assuming that the observed secular behavior of income velocity in a few countries can be generalized. Data for periods of sufficient length and for a large enough variety of countries are not available to make it possible to test whether such a generalization is justified. However, since these hypotheses about the secular behavior of income velocity imply that income velocity is related to levels of economic growth, a cross-section analysis of velocity levels in economies at different stages of economic growth may throw some light on the issue.

II

The only systematic attempt at an intercountry comparison of income velocity levels seems to have foundered in the sea of institutional differences. In his study, Doblin found that when the ratios were arranged according to the degree of economic advancement, an irregular pattern emerged.9 After eliminating about half of the 25 countries in the sample, he found some regularity in the relationship involving the income velocity of currency. The income velocity of money defined as currency plus demand deposits was reported to display “less regularity.”

This paper examines the relation between income velocity levels and the level of economic development in the context of a cross-section analysis. Using the data for the postwar period in 37 countries,10 an attempt is made to see which of the alternative hypotheses, if any, best describes the behavior of income velocity. The countries in the study are regarded as representing, more or less, different levels of economic growth. The average velocity ratio for each country is matched with the corresponding measure of the country’s level of development. The behavior of three alternative definitions of income velocity are investigated. These are (1) the income velocity of currency (V1), (2) the income velocity of narrow money (V2)—currency plus demand deposits, and (3) the income velocity of broader money (V3)—currency, demand deposits, and quasi-money. In order to ensure, as far as possible, that the velocity behavior observed is free from cyclical and other short-term influences, averages of the velocity ratios for at least ten years within the period 1950–64 are used. Currency, demand deposits, and quasi-money are as defined in the International Monetary Fund’s publication, International Financial Statistics (IFS), and data for these are taken from IFS.

Following conventional practice, per capita income is used as a proxy for the level of development. The income data used are 1958 per capita gross domestic product converted into U.S. dollars by means of 1958 exchange rates, as presented in the United Nations’ Yearbook of National Accounts Statistics, 1964.11

It should be recognized that there are many difficulties in carrying out such a cross-section study. Conceptual and other differences in measurement are likely to make intercountry comparisons dangerous. The variables themselves are clearly subject to substantial errors of measurement. The average velocities calculated for these countries for the period cannot be assumed to represent strictly the “normal” velocities that are required for a cross-section study. It is in the nature of this study that differences in per capita income levels are assumed to reflect differences in the structural characteristics that affect the secular behavior of velocity. To the extent that the latter are not fully reflected in the former, the results obtained may be less useful than they appear at first sight. An attempt has been made in Section IV to take into account separately some structural differences between countries that do not reflect differences in per capita incomes. One serious difficulty arises from the need to express per capita income data in a common unit of account in order to relate income velocities to per capita income levels in different countries. This raises the additional problem of the validity for this purpose of any exchange rate that might be used for conversion of data expressed in national currencies. It is not known to what extent the use of 1958 exchange rates for this purpose is really justified. The levels of per capita income prevalent in 1958 may not in any case be representative of the average per capita incomes of these countries during this period. It is, of course, clear that the results of a cross-section study, particularly for a relatively small group of countries, may not provide an adequate reflection of the nature of secular behavior.

III

Table 1 presents the average income velocities, starting with the country with the highest per capita income. To obtain some indications of general tendencies, the countries studied are first divided (Table 2) into a small number of income groups.

Table 1.

Average Income Velocities1

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V1 = income velocity of currency; V2 = income velocity of “money” (currency plus demand deposits); V3 = income velocity of “money plus quasi-money.”

Per capita gross domestic product converted into U.S. dollars at 1958 exchange rates as presented in the UN Yearbook of National Accounts Statistics, 1964.

Table 2.

Income Velocities by Per Capita Income Groups1

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The grouping used follows the classification used by Graeme S. Dorrance in his “Inflation and Growth: The Statistical Evidence,” Staff Papers, Vol. XIII (1966), pp. 82–102, where the classes are referred to, respectively, as Very Wealthy, Wealthy, Average, Poor, and Very Poor.

It will be observed that the levels of both V1 and V2 seem to fall, the higher the income group, until, at the highest income group, they rise. The V3 level, on the other hand, falls regularly as one moves from a lower to a higher income group. When the two highest groups are combined into one ($1,000 and above; V1 = 11.71, V2 = 3.72, V3 = 1.89), the velocity levels decline, the higher the per capita income level. It is, of course, clear from Table 1 that the tendencies indicated by the groupings can only be considered suggestive, since each group average is made up of widely dispersed velocity levels.

Rank correlations provide further indications of the nature of the relationships between the different velocities and per capita incomes. A rank correlation of —0.0702 was estimated for V1, –0.5005 for V2, and –0.6306 for V3. The rank correlations for V2 and V3 are significantly different from zero at the 1 per cent level. Thus there seem to be inverse relationships between V2 and V2, respectively, and per capita income levels. However, the result for V1 does not suggest the existence of any linear relationship.

To investigate the underlying tendencies more thoroughly, least-squares relationships were estimated for the average individual country data presented in Table 1. In equations (1), (2), and (3), the 37 velocity levels have been related linearly to the per capita income levels, using logarithmic values of the variables.

logV1=1.16-0.03logY¯+U1,R¯2=0(1)tvalue0.39
logV2=1.30-0.22logY¯+U2,R¯2=0.16(2)tvalue2.75
logV3=1.55-0.40logY¯+U3,R¯2=0.34(3)tvalue4.44

Equation (1) gives the cross-section estimates between the log of the velocity of currency and the log of per capita income. The estimated linear relationship is very weak. Neither the correlation nor the regression coefficients meet the usual statistical standards.12 A linear relation, however, seems to describe the relationship between the logarithms of the V2 and V3 levels and of per capita incomes. Although the proportions of the variances in V2 and V3 explained by per capita income are not high, they differ significantly from zero. The signs of the regression coefficients in (2) and (3) suggest that the relationship between the levels of both V2 and V3 and the levels of per capita income is inverse. These estimates indicate that, on the average, as per capita income increases, the levels of both V2 and V3 decline. From this cross-section analysis, it seems that, on the average, an increase of 1 per cent in per capita income leads to a decrease of 0.22 per cent in the velocity of “money” (currency plus demand deposits). The estimated elasticity in equation (3) is larger. An increase of 1 per cent in per capita income leads to a fall of 0.4 per cent in the level of the velocity of “money plus quasi-money.”

However, as Table 2 suggests, the relationship between the logarithms of the velocity levels and those of the levels of per capita income might be curvilinear. This possibility is investigated by fitting least-squares relationships separately to the countries in the first two income classes ($1,000 and above) and to those in the last three ($999 and below).13 If the indications given by Table 1 are correct, one would expect that the coefficient of log Y¯ for the $l,000-and-above group would be positive and significantly different from zero. For the $999-and-below group, one would expect that the coefficient of log Y¯ would be negative and significantly different from zero, and that the proportions of the variances in the velocities explained would be higher than those reported in the earlier three equations. On the whole, the results do not bear out those expectations.14 For the $1,000-and-above group, the signs of the regression coefficients of log Y¯ for the velocity of currency (V1) and the velocity of “money plus quasi-money” (V3) are positive, while that of V2 is still negative. However, none of the regression coefficients differ significantly from zero. For the $999-and-below group, the signs of the coefficients of log Y¯ are still negative. The coefficients of log Y¯ for V2 and V3 are significantly different from zero, but that of V1 is still not significant. The R¯2 for log V1 is still zero, while the R¯2 obtained for each of the other two velocities is lower than that reported in (2) and (3).

IV

Turning back to the estimates involving all the 37 countries, it will be recalled that, unlike this study, Doblin was not able to report any regularities until he eliminated 12 of his 25 observations. These eliminations were based on two criteria. He eliminated those countries (1) where checks were used for wage payments and at the retail level15 and (2) where time and savings deposits formed unusually high proportions of “money plus quasi-money.”16 It was between the velocity of currency of the remaining 13 countries17 and the level of development that he reported finding regularity.

It is possible that the underlying relationships between velocity levels and levels of per capita income are clouded by institutional differences mirrored in the proportions of currency, demand deposits, and time and savings deposits in the total of “money plus quasi-money.” Countries can be classified into three groups according to which of these proportions is the highest for them. It would be generally agreed that currency holdings consist almost entirely of active balances, that a relatively large proportion of demand deposits consists of active balances, and that quasi-money is largely inactive. For V3 one could, therefore, expect that countries for which the currency proportion is the highest are likely to have higher velocities at the same income levels than those for which the demand deposit proportion is highest, and even higher than those for which the quasi-money ratio is highest. This could not be expected to be true for V1 and would be rather unlikely for V2. To obtain useful generalizations it is not necessary to eliminate some of these countries, as Doblin did. The differences between countries in this respect are easily taken care of by suitable modifications in the equations.

In equations (4), (5), and (6), the earlier equations (1), (2), and (3) have been modified to allow for these institutional differences and thus for the expected differences in velocity levels. Two dummy variables, D1 and D2, have been introduced, representing countries in which currency and demand deposits, respectively, form the highest proportion of “money plus quasi-money.”18 The introduction of the dummy variable does not necessitate any basic changes in the conclusions reached on the basis of equations (1), (2), and (3).

logV1=1.30-0.08logY¯-0.07D1-0.004D2+U4,R¯2=0(4)tvalues0.790.810.06
logV2=1.27-0.21logY¯+0.01D1-0.05D2+U5,R¯2=0.12(5)tvalues2.10.150.61
logV3=1.13-0.28logY¯+0.22D1+0.18D2+U6,R¯2=0.43(6)tvalues2.82.22.2

As anticipated, the dummy variables do not enter significantly into the relationship involving log V1 and log V2, and the correlation and regression coefficients do not appear to be different from those obtained in equations (1) and (2). However, in the log V3 relation, both D1 and D2 seem to enter significantly. This implies that the intercepts of the log V3 function differ between the three types of countries, though the slope is necessarily the same.

For countries in which the proportion of currency to “money plus quasi-money” is higher than the other two proportions, the intercept is highest (1.35). For those in which the proportion of demand deposits is higher, the intercept is second highest (1.31). This indicates that in a scatter diagram relating V3 levels to per capita income levels, the V3 levels of countries in which currency forms the highest proportion of money plus quasi-money will tend to be higher than those of countries in which demand deposits form the highest proportion and even higher than those of countries in which quasi-money forms the highest proportion. The results are, therefore, in accordance with expectations. Allowing for these differences between countries is seen to improve the fit. However, the elasticities in equations (3) and (6) are within two standard errors of each other.

V

The observations made so far relate to the levels of income velocities. The findings suggest an inverse secular relationship between income velocity (V2 or V3) and the stage of economic growth. However, Table 3, which gives the 37 average annual rates of growth of income velocities, shows that there were only 7 declines in V1, 13 declines in V2, and 23 declines in V3. The fact that velocity showed increases in so many individual countries over the period concerned, while the cross-section analysis (especially with respect to V2 and V3) showed decreases, could be explained by arguing that the increases probably represent relatively short-run variations caused mainly by short-run influences. If these short-run influences could be abstracted from, the direction of change in income velocity might conform more closely to its expected behavior as reflected in the findings about the relationship between levels of income velocity and the stage of economic growth.

Table 3.

Average Rate of Change of Velocity

(In per cent per annum)

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At this stage, it is possible to ask whether rates of change of income velocity should themselves be expected to show any particular patterns in relation to the growth of income. In particular, it could be asked whether any inference about the relative rates of change in income velocity could be drawn from any of the hypotheses about income velocity levels already considered.

The Friedman hypothesis does not lend itself easily to such inferences. The proposition that velocity falls as per capita income increases secularly does not make explicit the relative rapidity with which one should expect the fall to occur with changes in the level of income. From the Gurley-Shaw hypothesis, however, it can be argued that as per capita income increases the rate of fall decreases until at a sufficiently high per capita income level the change is zero or negligible. From the Dorrance-Brehmer hypothesis, it is possible to suggest that as per capita income increases the rate of fall of velocity decreases, but that, unlike the Gurley-Shaw hypothesis, the rate of change of velocity may, at sufficiently high per capita income levels, actually become positive. These two hypotheses (Gurley-Shaw and Dorrance-Brehmer) imply a certain behavior with respect to the comparative rates of change of velocity in an international cross-section analysis; other things being equal, the higher the level of development, the smaller the rate of fall in velocity.

Stated in this way a testable hypothesis emerges. It is clear, of course, that this proposition cannot explain all the observed disparities in the rate of change of velocity among countries. It is likely that the period covered in each country is not long enough for the secular determinants to predominate over the short-run influences. Bearing in mind that the explanatory variable with which this analysis is primarily concerned is the level of development, it would be desirable to get rid of the influence of factors not related to that level. One such factor that might affect the relative rates of change of velocity is the rate of change of prices.19 Analysis of the demand for money emphasizes the effects of price movements on money holdings. Expectations of rapid price increases result in the shifting of wealth from money to other forms of wealth. In cross-section analysis, one would expect that part of the differences in relative rates of change of velocity would be explained by differences in expectations as to price movements. The complete relation takes the following form:

VY=a+blogY¯+cP+U7,(7)

where V’ is the average annual rate of change of velocity, Y′ is the average annual rate of change in real per capita income in the same period. Y¯ is the 1958 per capita income expressed in U.S. dollars and represents the level of development. P’ is the average annual rate of change in consumer prices during the period and is used as a proxy for price expectations. The sign of the coefficient of log Y¯ is positive, because it is expected that for a given rate of growth in real per capita income, the higher the level of development, the higher V′. Similarly, the coefficient of P′ is expected to be positive, since the expectations of rapid price increases tend to reduce the relative money holdings and therefore to increase VY and vice versa.

V1Y=-5.51+2.13logY¯+0.07P+U8,R¯2=0.40(8)tvalue4.792.76
V2Y=-4.29+1.65logY¯+0.06P+U9,R¯2=0.32(9)tvalue4.072.29
V3Y=-5.71+1.91logY¯+0.08P+U10,R¯2=0.42(10)tvalue4.523.59

Equations (8), (9), and (10) present the estimates for the three alternative velocity definitions. In all three equations, the coefficients of the explanatory variables not only have the expected signs but also are significantly different from zero. In each equation, both variables seem to contribute significantly to the explanation of V′/Y′; the income variable, however, explains a greater proportion of the variance. (See Table 4.)

Table 4.

PartialR¯2 BetweenVYand Indicated Variables

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It is possible to conclude from these estimates that the higher the level of development, the slower the rate of decrease in income velocity (V1, V2 and V3) associated with a given rate of rise in per capita income. In Sections III and IV, the results had suggested that an inverse linear fit best describes the logarithmic relationship between the level of V2 or V3 and the level of development. If the rate of decrease in V2 and V3 becomes slower at higher levels of development, as the present results indicate, then at sufficiently high per capita income levels, the rate of change of velocity could perhaps become zero. This would be consistent with the Gurley-Shaw hypothesis that velocity becomes constant at very high per capita income levels. Since there is no evidence of exactly what will happen when such high levels of income are reached, the present findings are of course consistent also with the Dorrance-Brehmer hypothesis that velocity would start rising again when very high levels of per capita income are reached. The conclusion with respect to the relative rates of change could then be interpreted as implying that the relationship between the levels represents perhaps one segment of a potentially curvilinear relationship. For the velocity of currency (V1), no relationship was discernible between the level of development and the level of velocity. It is difficult, therefore, to draw any conclusion about the behavior of the velocity of currency from the fact that the results in equation (8) are significant.

VI

This paper presents the results obtained from a cross-section study of income velocities in countries at different levels of per capita income. When countries are grouped according to the level of income, an inverse relationship is observed at first between income velocity and income for all three money totals, except that the velocity of currency is found to rise again for the highest group. For the logarithmic values of the individual country data, it is found that the relationships between per capita incomes and the velocities of “money” and “money plus quasi-money” are inverse and linear. When curves are separately fitted to data for countries with incomes of $1,000 and above, and those below $1,000, the results obtained are not significant.

To allow for some institutional differences between countries, dummy variables were introduced to represent countries in which the proportion of currency and of demand deposits, respectively, to “money plus quasi-money” are the highest. The basic conclusions obtained earlier were found to remain unchanged. However, the dummy variables enter significantly only into the relationship for the velocity of “money plus quasi-money.” As could be anticipated, the intercept for countries for which the currency proportion is highest is greater than that for countries for which the demand deposit proportion is highest and even greater than that for countries for which the quasi-money proportion is highest.

The relationship between (a) the rate of change of velocity per unit change of per capita income and (b) the level of per capita income was also studied for all three money totals, allowing in this instance for the influence of the rate of change of prices. It was found that the higher the level of per capita income, the smaller the rate of decrease in income velocity that was associated with a given rise in per capita income. This indicates that at very high levels of per capita income the rate of decrease of velocity might become zero or possibly negative.

Since no significant relationship had been found earlier between levels of the income velocity of currency and levels of income, no conclusion was drawn for the velocity of currency from the results obtained for the rate of change of velocity. For the totals of “money” and “money plus quasi-money,” however, a significant inverse relationship between levels of velocity and levels of income had been found. Therefore, the results of the study of the rate of change of velocity per unit increase in income were taken to indicate that at very high levels of per capita income, the level of velocity for these money totals might, with further increase in per capita income, tend to remain constant in accordance with the Gurley-Shaw hypothesis or even to start rising again in accordance with the Dorrance-Brehmer hypothesis.

Le comportement séculaire de la vitesse des revenus: Etude transversale sur le plan international

Résumé

Ce document présente les résultats obtenus à partir d’une étude comparative de la vitesse des revenus dans divers pays à différents niveaux de revenu par tête. En ce qui concerne les valeurs logarithmiques des données se rapportant à chaque pays, on a constaté que le rapport entre le revenu par tête et la vitesse de circulation de la “monnaie” et de la “monnaie plus la quasi-monnaie” était inverse et linéaire. Aucun rapport significatif n’a été constaté pour la vitesse de circulation-revenu de la monnaie fiduciaire. Ces résultats restent inchangés lorsqu’on fait intervenir des variables fictives pour représenter les pays dans lesquels la monnaie et les dépôts à vue constituent, respectivement, la majeure partie de la “monnaie plus la quasi-monnaie”. Cependant, les variables fictives n’affectent que le rapport relatif à la vitesse de circulation de la “monnaie plus la quasi-monnaie”.

Le rapport entre 1) le taux de variation de la vitesse par unité de variation du revenu par tête et 2) le niveau du revenu par tête, a été également étudié pour les trois totaux monétaires en tenant compte de l’influence du taux de variation des prix. Il a été constaté que plus le niveau du revenu par tête est élevé, plus le taux de diminution de la vitesse des revenus, lié à une augmentation donnée du revenu par tête, s’affaiblit; ce qui conduit à penser qu’à des niveaux très élevés de revenu par tête le taux de diminution de la vitesse pourrait devenir égal à zéro ou même être négatif. En ce qui concerne les totaux “monnaie” et “monnaie plus quasi-monnaie”, pour lesquels on a constaté un rapport inverse significatif entre les niveaux de la vitesse et les niveaux de revenu, ces résultats ont été interprétés comme indiquant qu’à des niveaux très élevés de revenu par tête, le niveau de vitesse pourrait, si le revenu par tête augmentait encore, avoir tendance à rester constant, selon l’hypothèse de Gurley-Shaw, ou même à commencer à remonter, selon l’hypothèse de Dorrance-Brehmer.

El comportamiento secular de la velocidad-ingreso del dinero: un estudio transversal internacional

Resumen

En este trabajo se presentan los resultados obtenidos en un estudio transversal sobre la velocidad-ingreso en países con distintos niveles de ingreso per capita. Para los valores logarítmicos de los datos de los distintos países, las relaciones entre el ingreso per capita y la velocidad del “dinero” y del “dinero más cuasi-dinero” resultaron ser inversas y lineales. No se halló ninguna relación representativa para la velocidad-ingreso de billetes y monedas. Esos resultados siguieron siendo iguales cuando se introdujeron dos variables imaginarias para representar países en los que la moneda y los depósitos a la vista formaban, respectivamente, la proporción más elevada del “dinero más cuasi-dinero”. Sin embargo, esas variables imaginarias sólo entraron significativamente en la relación que incluye la velocidad del “dinero más cuasi-dinero”.

Se estudió también, con respecto a los tres totales monetarios, la relación entre 1) la tasa de variación de la velocidad por cada variación unitaria del ingreso per cápita y 2) el nivel del ingreso per capita, habida cuenta de la influencia de la tasa de variación de los precios. Se halló que cuanto más elevado era el nivel de ingreso per capita, menor era la tasa de merma en la velocidad del ingreso que va asociada con una determinada subida en el ingreso per capita, lo que indica que a niveles muy altos de ingreso per capita, podría hacerse nula o incluso negativa la tasa de merma de velocidad. En cuanto a los totales de “dinero” y “dinero más cuasi-dinero”, para los que se había hallado una significativa relación inversa entre niveles de velocidad y niveles de ingreso, se consideró que esos resultados eran indicativos de que a muy altos niveles de ingreso per capita, al producirse un nuevo aumento del mismo, el nivel de velocidad podría tender a permanecer constante de acuerdo con la hipótesis de Gurley y Shaw, o incluso a empezar a subir de nuevo de acuerdo con la hipótesis de Dorrance y Brehmer.

*

Mr. Ezekiel, Chief of the Financial Studies Division of the Research Department, is a graduate of the University of Bombay. He taught economics at St. Xavier’s College, Bombay, and at the University of Bombay, and was Financial Editor of The Economic Times. He has contributed a number of articles to economic journals and is the author of The Pattern of Investment and Economic Development (Bombay, 1967).

Mr. Adekunle, a graduate of Ohio Wesleyan University and of the University of Wisconsin, was an economist in the Fund’s Research Department when this paper was prepared. He is now employed by the Central Bank of Nigeria.

1

For detailed discussions of these factors, see, for example, Clark Warburton, “The Secular Trend in Monetary Velocity,” The Quarterly Journal of Economics, Vol. LXIII (1949), pp. 86–90; Irving Fisher, The Purchasing Power of Money (New York, 1911); Albert Gailord Hart and Peter B. Kenen, Money, Debt, and Economic Activity (Englewood Cliffs, N.J., 1961), pp. 174–81; Richard T. Selden, “Monetary Velocity in the United States,” in Studies in the Quantity Theory of Money, ed. by Milton Friedman (University of Chicago Press, 1956), pp. 179-257.

2

Fisher, op. cit., pp. 79–89.

3

William J. Baumol, “The Transactions Demand for Cash: An Inventory Theoretic Approach,” The Quarterly Journal of Economics, Vol. LXVI (1952), pp. 545–56.

4

James Tobin, “The Interest-Elasticity of Transactions Demand for Cash,” The Review of Economics and Statistics, Vol. XXXVIII (1956), pp. 241–47.

5

Milton Friedman, “The Demand for Money: Some Theoretical and Empirical Results,” The Journal of Political Economy, Vol. LXVII (1959), p. 1.

6

John G. Gurley and Edward S. Shaw, Money in a Theory of Finance (The Brookings Institution, Washington, 1960), p. 130. Money conventionally defined.

7

Graeme S. Dorrance and Eckhard Brehmer, “The Growth of Liquidity in Selected Industrial Countries” (mimeographed paper, May 31, 1962), p. 2.

8

Thus, Friedman’s finding is based exclusively on U.S. data.

9

Ernest M. Doblin, “The Ratio of Income to Money Supply: An International Survey,” The Review of Economics and Statistics, Vol. XXXIII (1951), especially pp. 206–209. He used alternatively per capita income and per capita energy consumption as measures of economic advancement.

10

The countries are those for which the required data are available.

11

Pages 383–87.

12

The significance of the regression coefficients is tested at the 95 per cent level of confidence. The t value should be at least 2.04. In Section V, where a one-tailed test is performed, the t ratios should be at least 1.70.

13

The alternative of fitting a curvilinear relation directly is handicapped by the fact that log Y¯ and log Y¯2 are perfectly correlated.

14
$l,000-and-above group
logV1=-0.51+0.51logY¯+U,R¯2=0tvalue0.88
logV2=-1.52-0.30logY¯+U,R¯2=0tvalue0.58
logV3=-1.09+0.12logY¯+U,R¯2=0tvalue0.56
$999-and-below group
logV1=-1.22-0.05logY¯+U,R¯2=0tvalue0.50
logV2=-1.27-0.21logY¯+U,R¯2=0.09tvalue1.9
logV3=1.44-0.36logY¯+U,R¯2=0.20tvalue2.8
15

These were United States, Australia, Canada, Ireland, New Zealand, South Africa, and United Kingdom.

16

Comprising Switzerland, Sweden, Denmark, Finland, and Norway.

17

Republic of China, Bulgaria, Mexico, Poland, Japan, Argentina, Greece, Italy, Austria, Netherlands, Czechoslovakia, France, and Belgium.

18
Defining C = currency, DD = demand deposits, QM = quasi-money, and M2 = “money plus quasi-money,”
D1=1,whereCM2>DDM2,QMM2,andD1=0,forothers;
D2=1,whereDDM2>CM2,QMM2,andD2=0,forothers;
Since there are three categories, allowance for two of them is sufficient. Therefore,
D1=D2=0,whereQMM2>CM2,DDM2.
19

The influence of another variable—the yield on financial assets—could be allowed for. However, information about this variable is not available for a large proportion of the countries concerned; it is lacking especially in the developing countries.