Abstract
This paper is a slightly modified version of the author’s doctoral dissertation, presented to the University of Wisconsin in August 1967.
This paper is a slightly modified version of the author’s doctoral dissertation, presented to the University of Wisconsin in August 1967.
Evidence is continually being accumulated which suggests that relationships in the monetary sector are not only stable and predictable but are also indispensable for an understanding of behavior in other sectors of an economy, for instance, in explaining consumption expenditures. Most of this evidence, however, has been based on the analysis of the experience of a relatively small number of countries representing a particular type of economic environment.
There has been little systematic analysis of the behavior of private desired money balances in those types of economies commonly referred to as less developed. Yet, there is considerable discussion in general of what is called the “economics of the less developed countries.” What differences in behavior in the monetary sector does the dichotomy, developed and less developed economies, imply? Does the form of the demand for money in the less developed economies differ from that existing in the developed economies? Is it that theoretical relationships developed to explain monetary behavior, and conclusions and opinions based on the interpretation of monetary experience, in the developed economies are applicable to the other type of economic environment as well? This is the problem to which this study is addressed. One must add that the general applicability, over space and time, of a theoretical formulation does not rule out appropriate modifications.
The available theoretical formulations as well as empirical findings do not provide common views about underlying monetary relationships, even when they refer to the same economy. There is much controversy about particular aspects of the behavior of the demand for money. This paper will attempt to clarify some of these issues. Of particular interest, however, is the investigation into the degree of uniformity of behavior in the different economic environments prevailing in developed and less developed countries. Adopting a general demand-for-money hypothesis, this paper attempts to verify whether, and to what extent, the structural characteristics generally associated with the terms “developed” and “less developed” economies influence the type and behavior of the variables that enter into the demand relationship.
I. The Demand for Money
This study of the behavior of the demand for money is based on the hypothesis of a general demand relationship which permits alternative specifications about the behavior of certain variables. In particular, it specifies a relationship which permits the direct observation of the role of expectations in the monetary sector. While theoretical hypotheses about behavior in the monetary sector often relate desired real balances to the expected values of the explanatory variables, in empirical verifications it is often assumed that the current or measured values of the variables are equal to their desired and expected values. Recent work in monetary analysis suggests that these assumptions may not be safely made about all the variables in the relationship. Specifically, it suggests that expectations play an important role in explaining behavior in the monetary sector.1
In contemporary theorizing about expectations, the expected value of a variable is related to past observed values of the variable. That is, the expectation function takes some form of a distributed lag model.2 Such expectation functions have been used extensively in empirical investigations of consumption and investment demand. The particular expectation form used in this paper will be discussed in detail below. In any event, the manner of the adaptation to the past values of a variable depends, inter alia, on institutional and structural characteristics. Hence, in comparing behavior in the monetary sectors of different economic environments, apart from the possible differences in the types (or influence) of the explanatory variables that enter into the relationship, one important source of difference is likely to relate to the manner in which expectations with respect to these variables are formed.
Feige has developed a functional relationship that permits direct investigation of the manner in which expectations are formed in the monetary sector.3 The demand-for-money relationship that is specified and estimated in this paper is based on his adaptive expectation model. Desired real balances are related to expected real income, expected rates of change in prices, and current rates of interest. Thus, and with the variables, except the rate of change in prices, in logarithms,
where M*t= desired real balances
Ye= expected real income
r= interest rate
u= disturbance term.
Equation (1.1) is a relationship involving desired real balances. Since the analysis has time dimensions, t, it is possible that equilibrium conditions in the relationship may not be achieved during a discrete period of time, or, more generally, in the short term. There may be inertia, as well as technical reasons why, given the values of the underlying determinants of desired balances, it may not be possible during a particular week, quarter, year, or any other period of measurement for holders to adjust their actual to their desired holdings. The costs to the holder of maintaining a disequilibrium between desired and actual balances as well as the costs of eliminating the disequilibrium are likely to vary from one economic environment to another.4 Therefore, in comparing behavior in different economic environments, one aspect of the difference in the demand for money that one may consider is the difference in the speeds of adjustment of actual to desired balances. However, for the purposes of this analysis, the assumption is made that desired real balances adjust to current effective demand during the period of analysis (which in this instance is the calendar year), i.e.,
where Mdt is the current demand for real balances.
Also in equation (1.1) there are other variables that are not directly observable—the expected values of real income and of the rate of change in prices. In order to relate these variables to observables, Nerlove’s expectation function is used.5 Specifically, the expected value of a variable, N, is formed as follows:
The equation states that in each period people revise their notion as to the expected value of N in proportion to the difference between its measured or observed value and what was previously considered as expected. In the formulation, λ is simply the elasticity or coefficient of expectation (with respect to N). It is expected to lie between zero and unity. If λ is equal to unity, Net = Nt, and expectation about the value of N is based entirely on its current value. In such cases expectations are said to be static. On the other hand, when λ is less than unity, the expected value depends also on past values of N, and it fluctuates less than the current measured value. Expectations then are said to be non-static. Equation (1.3) can be solved in terms of all past values of N:
Expressed in this form, the expectation function is a distributed lag with geometrically declining weights.
In estimating the demand relationship, the expected values of real income and of the rate of change in prices are specified as being generated in a manner similar to that in equations (1.3) and (1.4). However, the elasticities of expectation with respect to real income and to the rate of change in prices are assumed to be different. In comparing behavior in two different economic environments, it is likely that one will find the sizes of all the elasticities of expectation in one environment to be consistently larger or smaller than the corresponding ones in the other; on the other hand, it is less likely that the elasticities of expectation with respect to all variables in one environment will take the same value. The ability to forecast the values of different variables is not uniform—for this ability is not independent of the variability of the variables. Therefore there is little reason to assume, a priori, that the elasticities of expectation are equal. Following equation (1.4), the expected values of real income and of the rate of change in prices (or, more simply, inflation) are generated as follows:
The relationship specified in equation (1.1) assumes that expectations with respect to interest rates are static. That is, ret = rt. This assumption may not be correct. However, (1) an explicit test of this assumption for the United States suggests that it is correct, 6 and (2) on a priori grounds one would expect that the influence of the substitution effects emanating from financial assets would be less important in less developed than in developed economic environments. Thus, in comparing behavior in these two environments, rather than completely developing the substitution effects of financial assets, attention is focused on those of real assets, as represented by the expected depreciation in the value of money. Contrary to theoretical specifications, expected rates of change in prices have not been found to play a significant role in the money-demand relationships estimated for the United States. For other developed countries, price movements have been found to play significant roles only in situations characterized by violent upward movements in prices.7 On the other hand, behavior in the less developed countries is generally considered to be significantly influenced by expectations of inflation.8 Thus, contrary to the implied suggestion about the role of expected rates of change in prices in the money-demand function of the industrial countries, one would expect this variable to be important in the money-demand relationship in less developed countries.
Expected (as opposed to current) income has been found to be the appropriate variable in empirical money-demand functions estimated for some developed countries. Earlier it had been found to be the appropriate constraint in the consumption function. Are expectations with respect to income equally nonstatic in less developed countries? So far there is no empirical basis for answering this question. Presently, it will be argued that there are reasons to believe that the manner in which expectations with respect to income and rates of change in prices are generated is likely to be different in less developed and developed countries.
In order to complete the specification of the monetary sector, the supply of real balances is specified in such a way that it depends on a predetermined nominal supply of cash balances and the price level:
where Mst = supply of real balances
Zt = the predetermined nominal money supply
Pt = the price level.
The nominal supply of money is assumed to depend on important factors that do not affect the demand for real balances. These factors include variables such as commercial bank reserve ratio, central bank credit, and the country’s gold and foreign exchange reserves.9 Finally, the equilibrium condition in the monetary sector is
where Mt is the observed stock of money. In estimating the demand-for-money relationship, the functional form is
In equation (1.9), equations (1.5) and (1.6) will be substituted for the respective expectation variables, and, as will be explained in detail in Section II, the resulting equation is reduced by applying the Koyck transformation. The reduced equation, which is overidentified, is given an identity by imposing nonlinear constraints on the relationship and estimating by a nonlinear technique. The five coefficients obtained are as follows:
λ1 = income expectation elasticity
λ2 = inflation expectation elasticity
b1 = income elasticity of the demand for money
b2 = interest elasticity of the demand for money
b3 = the coefficient of the rate of change in prices.
The expectation elasticities are expected to be between zero and unity. The income elasticity is expected to be positive, while the signs of b2 and b3 are expected to be negative.
Estimates obtained from equation (1.9) will clarify the manner in which expectations of income and of rates of change in prices are formed. The more common empirical relationship estimated, which is a special case of equation (1.9), involves the specification that λ1 = λ2 = 1, or that expectations with respect to income and inflation are static. An estimate of this special case will also be provided. In addition, estimates of an intermediate form are also made. Here expectation with respect to the rates of change in prices is assumed to be nonstatic, while that with respect to income is assumed to be static.
Differences in the form of the demand function
The question of differences in the applicability of the demand relationship to different economic environments may now be raised. In particular, interest is centered on differences in the demand-for-money relationship in two broad groups of countries: the developed and the less developed countries. It is clear that this dichotomy is broad and may be useful only as a first approximation. However, as Bauer and Yamey point out, “The discernment of uniformities underlying diversity of circumstances is the primary task of scientific enquiry and, indeed, of all systematic enquiry into phenomena.”10
The literature on the economics of less developed countries points to certain characteristics that these countries have in common, especially when they are compared with the standards existing in the United States, Canada, and Western Europe.11 Do any of these differences in characteristics imply differences in the behavior of desired real balances in the less developed and developed groups of countries? In the following sections the implications of these differences for the form of the demand-for-money function are explored.
The elasticities of expectation
Expected variables generated by functions such as equation (1.4) have been interpreted in two ways in empirical investigations of the monetary sector. First is the Friedman approach, in which expected income enters into the relationship as a proxy for the expected yield on wealth. Friedman denies the validity of formulations of the demand-for-money relationship in which the transaction motive for holding money is important and, consequently, current income is the appropriate scale effect. He contends that the asset motive predominates and, thus, only that part of income which is considered as permanent influences the demand for money.
More explicitly, he argues that “Much of the theoretical literature on ‘motives’ for holding money suggests interpreting money holdings as one of the balance-sheet items that act as shock absorbers for transitory components of income; as an asset item that is increased temporarily when the transitory component is positive and that is drawn down, if necessary, to finance consumption when the transitory component is negative.” 12 Viewed this way, the appropriate constraint in the money-demand relationship would be current income. As an alternative, he argues for and interprets his results as suggesting the treatment of money as a “durable consumer good held for the services it renders and yielding a flow of services proportional to the stock…” The shock absorber role is then filled by other items in the balance sheet (e.g., “stock of durable goods, consumer credit outstanding, personal debt, and perhaps securities held”). This way of viewing money holdings implies that the appropriate constraint is the expected yield on wealth or permanent income.
The second approach is to interpret the expected variable generated by equation (1.4) simply as an optimal forecast of the variable. This approach follows from Muth’s demonstration13 “that if the process generating measured income is such that the change in measured income is a first order moving average of random deviates, then the expectation generating function … provides an optimal forecast of measured income.” 14 The primary interpretation given to expected income and the expected rate of change in prices in this study is thus a more direct one: They are interpreted, respectively, as the optimal forecasts of income and of the rate of change in prices.
It will be recalled that in the expectation function in equation (1.4), when λ = 1, expectations are static and the expected value of the variable depends solely on its current measured value. One may ask if there are any a priori reasons to expect that the elasticities of expectation in the money-demand function will differ consistently between less developed and developed economies. That is, that only one of the following conditions will hold:
or
To reach some tentative conclusions on this aspect of the comparative behavior of the demand relation, one would have to look into the characteristics that differentiate these two economic environments. One factor that will account for a difference in the relative sizes of the elasticities of expectation is differing lengths of the representative economic horizon.15 The shorter the length of the representative economic horizon, the bigger the λ, i.e., the more static the expectations.
Would one expect the representative economic horizon to be shorter in a less developed economic environment than in a developed one? The literature on the economics of the less developed countries leaves little doubt on the question of the relative lengths of economic horizon in less developed and developed economies. Representative time horizons in (the private sector of) the less developed economies are shorter than those in developed economies. Discussions under titles such as “Investment Decisions in Underdeveloped Countries” and “Some Social Obstacles to ‘Capital Formation’ in ‘Underdeveloped Areas’ “usually include considerations of factors that account for this time preference pattern.16 The factors considered include the economic and the sociological, the political and the psychological, the subjective and the objective. Whether one approaches the issue from the sociopolitical point of view (where societal values and attitudes are important) or whether one emphasizes the objective conditions (e.g., the lower per capita income, the greater income instability, the greater imperfections of knowledge and of markets, etc., in the less developed countries), the conclusion about the time preference pattern seems to be the same. In fact, of course, there appears to be an interdependence among these economic, political, social, and cultural variables.17 Although the treatment from a sociological point of view may be less convincing, it seems that, by definition, the time horizon in the less developed economic environment is shorter than in the developed economic environment.18
Consider the low level of per capita income. Given existence that is near the subsistence level and the devotion of almost all output to the maintenance or improvement of an exceedingly low standard of living, it is clear that more concern will be devoted to current than to future welfare. In fact, fortified by, or partly because of, the social and economic instability, the lack of knowledge, and the other imperfections that combine to make for relatively high risks and uncertainties, no other pattern of time preference may be rational. The rates of discount on the present value of future income are such that economic horizons are shorter. These factors affect not only the proportion of income that is saved but also the forms in which savings are held, as well as what investment decisions are made.19 It means that available savings are held in forms that have relatively little risk, that are quickly convertible, and that are directly under the owners’ control. It means that the demand for assets is such that it reduces the scope—apart from the supply limitations—for promoting risk-spreading assets and thus perpetuates the high risks present in this economic environment.
To these, add another characteristic of the less developed countries —the relatively high social and political instability. This instability also limits the economic horizon and biases investments in favor of short-term projects, such as inventory accumulation and commercial transactions, and against long-term projects, such as industrial and agricultural investments. In this environment where political changes often imply changes in other spheres, including official, economic, and commercial policies, “A short-term rhythm of operations makes it easier to adapt to new situations …, to avoid unforeseeable dangers. An industrial enterprise cannot be adapted so easily or quickly. It lacks the security that lies in liquidity and flexibility.”20
The economic structure itself is characterized by relatively greater instability.21 Most less developed countries, because of their greater dependence on the export of a few crops and the import of capital, are susceptible to externally generated fluctuations in income levels and in the levels of economic activity. Apart from this external source of fluctuations there is another, more autonomous, source of instability. Because of the structure of economic activity, abnormal seasonal patterns constitute a major source of fluctuations in incomes. Further, these fluctuations occur in environments where the available techniques of stabilization are limited, or inefficient, or both.
While the foregoing discussion has not been exhaustive, it seems clear that the representative economic horizon is shorter in the less developed economic environment than in the developed one. Thus, one would expect that the elasticities of expectations for the less developed countries would be larger than the corresponding ones for the developed countries. One would expect this to be true not only of monetary sector behavior but also of behavior in other sectors. Specifically, in forecasting income and rates of change in prices, one would expect greater weight to be given to recent experiences in less developed than in developed economies. The greater variability of income and of rates of change in prices 22 in the less developed countries implies that their elasticities of expectation as generated by the adaptive mechanism, which essentially reflects the “proportionate errors associated with previous levels of expectations,” will be larger than the corresponding ones in the developed economies.
The role of income
In order to develop similar a priori notions about the relationship of the income elasticities, one has to look at least conceptually into the motives for holding money. One can broadly divide the motives for holding money balances into the medium of exchange and the store of value or into the transactions and the asset motives. Although it is clear that it may not be necessary or possible to separate money holdings into the parts held for transactions and for assets or any other purposes, it is nonetheless clear that the services provided by monetary balances include those of medium of exchange and store of value. To say that some part of money balances is held for transactions purposes is not to say that a rigid mechanical relationship exists between that part and transactions. In any event, whatever one’s views about the motives for holding money, the asset and transactions motives are parts of the reasons for the demand for money. Differences in views are based upon which of the transactions or asset motives should be given pride of place.
How will the aggregate demand for the services provided by money vary between a less developed and a developed economy? While there is general agreement that the demand for the services provided by money grows with increases in income, it is not clear whether a given percentage increase in real income would lead to the same proportionate increase in desired money balances in both types of economies.
Since money is an asset—one form of holding wealth—increases in income may lead to increases in the demand for money associated with the asset motive. With respect to this motive, Cagan argues that “If … current real income increases, an individual will want to substitute cash balances for part of his illiquid assets, for now he can more readily afford to forego the premium received for holding his assets in an illiquid form ….”23 If increases in real income lead to diversification of asset portfolios in the direction of more liquid assets, the resulting proportionate increases in desired money balances may depend on the relative proliferation of near-monies or liquid assets generally. Most of the available evidence suggests that the more advanced the economy, the greater the availability and holding of financial assets.24 The U.S. experience has been interpreted as showing that
As agriculture, and perhaps also independent nonfarm business, have declined in importance relative to industry and trade and corporate enterprise, so also has the direct ownership of real assets by individuals relative to their total wealth. Wealth holders have consequently come to hold a larger part of their wealth in the form of claims of great variety.25
More general evidence has been presented by Goldsmith to show that the ratio of the value of total financial assets to the value of national wealth is uniformly higher for developed than for less developed economies.26 Thus, there are more assets in the developed economies that can satisfy the liquid asset motive associated with increases in real income or wealth. One may therefore infer that since there is a greater degree of proliferation of liquid assets in the developed than in the less developed countries, part of this liquidity service may be satisfied by the holding of relatively more of the other liquid assets. Or, more simply, a given percentage increase in real income will lead to a higher proportionate increase in desired money balances, associated with the liquid asset motive, in an economy where there are K liquid assets than in one where there are N liquid assets (where N>K).
Even if the alternative liquid forms of holding wealth available in developed and less developed economies are the same, it is not clear that the income elasticities ascribable to this motive will be the same for both types of economies. One reason for holding money that is subsumed under the asset motive is the precautionary or emergency motive. Friedman and Schwartz have pointed out that “… the major virtue of cash as an asset is its versatility. It involves a minimum of commitment and provides a maximum of flexibility to meet emergencies and to take advantage of opportunities. The more uncertain the future, the greater the value of such flexibility and hence the greater the demand for money is likely to be.” 27 Earlier in this study attention has been drawn to the greater degrees of instability, uncertainty, and market imperfections that exist in the less developed economies. Therefore, one might expect higher income elasticity ascribable to the precautionary motive in the lower income countries.28 However, existence near the subsistence level may be such as not to permit the forgoing of the premium received from holding assets in illiquid form. In fact, money may lose a substantial part of the flexibility and versatility which makes it a superior asset (to hold for precautionary purposes) in this environment, which is more susceptible to inflationary pressures, or where expectations of inflation play important roles in determining economic behavior.
With respect to the transactions demand, there seems to be agreement that, other factors remaining constant, there is proportionality between increases in transactions and money holding for transactions purposes. However, there is no agreement about whether this proportionality is a constant one or whether it varies with the size of transactions and in what direction. For example, Fisher argues that there are economies of scale with respect to the holding of transactions balances. “… the man who spends much, though he needs to carry more money than the man who spends little, does not need to carry as much in proportion to his expenditure…. We may therefore infer that, if a nation grows richer per capita, the velocity of circulation of money will increase.” 29 In a similar vein Garvy, in trying to explain the postwar rise in income velocity in the United States, points to increasing efficiency in the use of money balances by both businesses and individuals as a causal factor.30 On the other hand, Warburton has argued that “there is probably a general tendency for people to hold larger cash balances, as time goes by and their average income increases, relative to their expenditures for goods and services.”31
As pointed out earlier, this discussion of the motives for holding money is meant to be conceptual. The observed income elasticity is the result of the combined influences of these motives—influences which may not operate in the same direction. Thus, any conclusion that may be reached about the relative aggregate or net impact of increases in real income on desired real balances can only be conditional. Unless, as Warburton argues, people hold proportionally larger transactions balances as their income increases, one would expect the income elasticity to be larger in the less developed countries.
The substitution effects
As should be readily conceded, there are many alternatives to holding money. They comprise the broad range of assets in which wealth can be held. They include different types and forms of financial and real assets. For instance, Friedman has listed four forms, other than money, in which wealth can be held: bonds, equities, physical nonhuman goods, and human capital.32 Cagan lists the alternatives as fixed-return assets (bonds); variable-return assets (equities and titles to producer goods); and nonperishable consumer goods.33 Each of these alternative forms can be further divided into smaller groups, depending, for example, on differences in time duration or the sector of the economy on which the claim is drawn. For present purposes, however, these alternative forms can be consolidated into two categories: financial and physical. One can then inquire if there is likely to be any difference between the two groups of countries with respect to the influence of these alternative substitutes on the demand for money.
There is general agreement that substitution effects stemming from financial assets would be relatively small in less developed countries. While in some developed countries the proliferation of financial assets has led to arguments about the uniqueness of money, the situation in less developed countries is described as one where there are few organized dealings in bills or commercial paper and where markets in government short-term and long-term securities and corporate stocks are often lacking.34 This follows from a characteristic of these economies which has been mentioned earlier, the lower proportion of wealth that is held in the form of financial assets in these countries. To be effective, monetary policy tends to rely more on quantitative and selective instruments (e.g., ceilings on credit expansion to specific sectors and on reserve and liquidity ratio requirements) than on more general and indirect instruments, such as open market operations.
Another characteristic of the less developed economies is the ability to identify two types of money markets: the organized and the unorganized. While both the organized and the unorganized markets are less integrated and narrower than the money markets in the developed economies, the unorganized markets are even more so. These unorganized markets have been described as follows:
They are much less homogeneous than the organized markets and are generally scattered over the rural sector. There is very little contact between the lenders and borrowers in different localities…. the relationship between borrower and lender is not only that of a debtor and creditor but is also an integral part of a much wider socioeconomic pattern of village life and rural conditions.
In unorganized money markets, moreover, loans are often contracted and paid for not only in money but in commodities …35
The substitution effects of that part of the transactions on these markets that is conducted in terms of commodities—bushels of commodities or products harvested from specified areas of farms—should properly be allowed for in the category of real assets.
Information on financial yields in this sector is scanty and thus is not available in forms that are needed for systematic analysis. It is known that the levels of these yields, which reflect high monopoly and risk elements, are much higher than those in the organized sector. However, to the extent that there is some linkage between the unorganized and organized markets, movements in the yields on loans in the organized markets may also reflect movements in the yields on the unorganized markets. This linkage may occur: 36 (1) through marketing boards, large landowners, exporters and traders who borrow from commercial banks and make advances to agriculturists, either directly or through smaller merchants; (2) through importers extending credit to village retailers; and (3) through cooperative credit societies, land mortgage banks, private agricultural banks, and government-financed agricultural credit institutions, who operate mainly in the unorganized money market but get a substantial portion of their working capital (subscribed capital, deposits, and borrowings) from the organized market.
Although subject to exceptions, the money markets in the developed economies are broader, more integrated, and less dichotomous than those in the less developed countries. In the developed as in the less developed group, the degree of broadness of the markets varies from country to country. However, as Goldsmith has noted, financial instruments and institutions are more important in developed than in less developed countries. Indeed, the proliferation of financial substitutes in some developed countries has led to controversy about the stability of the demand for money.37 This controversy stems “from recognition of the substitutability between money (conventionally defined as medium of exchange) and the wide range of alternative financial assets provided by government debt and the obligations of financial institutions, and between money and the access to credit provided by an elaborate credit system, in a financially advanced economy.” 38 This study can cast very little light on this particular controversy, except to the extent that the relative stability and predictability of the estimated demand relationship for the developed countries (or the more financially advanced ones in this group), compared with those estimated for the less developed countries, can be interpreted as relating to the issue.39 Reference to it, however, highlights a process whereby, as an economy develops, these money substitutes become more and more important in the demand-for-money relationship and, some will argue, ultimately render the relationship useless in tracing the effects of changes in the stock of money.
Theoretically, when attention is turned to real or physical assets, the substitution effects of these assets should be important in both types of economies. However, since financial assets cannot be easily substituted for money in the less developed countries, real assets take on added importance. The importance of real asset substitutes to the holding of money is further accentuated in these countries in view of their low levels of per capita income, as existence is near the subsistence level and relatively high proportions of income are spent on food and necessities. This means that money holdings will be particularly sensitive to the yield on real assets.
Following conventional practice, the yield on real assets is approximated by the rate of change in prices. Cagan, for instance, argues tha “Variations in the cost of holding cash balances when the alternative is to hold consumers’ goods can be determined solely by the change in the real value of a given nominal cash balance—the rate of depreciation in the real value of money. The variation in the real value of good because of their physical depreciation is fairly constant and can be ignored.”40 That is, this opportunity cost can be represented by the rate of change in prices.41 Even when the role of price changes or inflation is not discussed explicitly in these terms, there is general theoretical agreement that it influences the holding of money balances. Thus,
The willingness of individuals and businesses to hold an expanded quantity of money, or financial claims denominated in money terms, is influenced by their expectations regarding the future price levels. If prices are expected to rise markedly, holders of money will try to limit any increase in the money value of their holdings, or may even attempt to dispose of them.42
Since one important reason for holding money is that it has a store of value characteristic, when prices are expected to increase, money loses some of this attribute. Holders will tend to adjust their holdings in order to minimize losses that may result from the expected decline in the purchasing power of money. Some of this adjustment will involve the replacement of money by physical assets. As holdings of financial assets (not denominated in money terms) are negligible in the less developed countries, the substitution effects of physical asset alternatives to holding money may be expected to be more important in this group of countries.
Attempts to isolate the effect of price expectations on the demand for money have been successful mostly in countries experiencing rapid price increases.43 Several attempts at isolating the effects of price changes on the demand for money in the United States, for example, have not been successful.44 Several reasons have been offered as explanations for this finding. It is said to be due to the fact that, except during war periods, price changes in the United States have been small. It may simply mean that over any substantial period of time the yields on financial and real assets move together. Most of the empirical investigations of the behavior of the demand for money use the yields of financial assets denominated in money terms—i.e., interest rates. These rates, which are invariably market rates, may already incorporate expectations as to the movements in prices. For not only money balances but also, as has been noted above, holdings of these types of financial assets are influenced by expectations about price movements. Thus, in a situation where prices are expected to change, the real interest rate is adjusted by the expected rate of inflation to give expected market interest rates.45 In such a situation it will be difficult to isolate the influence of expected price changes in a multiple relationship which also includes the market interest rate.
These factors may have implications for differences in the role of price expectations in the demand-for-money relationship in developed and less developed countries. In the developed countries with more nearly perfect markets and integrated economies, the expected rates of change in prices are more likely to be reflected in the market rate of interest. In the less developed countries not only are the sectors less integrated but also the capital markets are more imperfect, and the stated rates may diverge substantially from actual market rates. Thus, the rate of change in prices is perhaps the best indicator of the cost of holding assets in the form of money or of any other asset with a fixed nominal value. Price changes will also play a greater role in less developed countries because of the greater proportion of real assets in total wealth and, given existence near the subsistence level, of the great costs involved in inattentiveness to price movements.
II. The Empirical Approach
The differences in the economic environments of the developed and less developed groups of countries may thus imply certain differences in the form of the demand function. In the following sections, an attempt will be made to see if the evidence suggests that these types of differences exist. At the same time, however, evidence will be sought to support the view that at another level of simplification, the demand hypothesis has general applicability. The empirical hypotheses to be tested include the following:
(1) In developed and less developed economies, the demand for money is a predictable function of a limited number of variables.
(2) The form of the demand-for-money function differs for broadly defined groups of countries.
(a) The expected variables are more appropriate in the sense that expectations are less static in the demand relationship of the developed than in that of the less developed group of countries.
(b) The income elasticity of the demand for money is positive; a stronger (liquid) asset motive makes for higher income elasticities in less developed than in developed economies.
(c) Opportunity costs of holding money involving real assets are more important in the less developed group of countries.
(d) In the developed group of countries all substitution effects can be subsumed under those of financial assets.
Three money-demand functions implying different specifications about the formation of expectations are estimated. The most general of these relationships has been developed in Section I.
where, again, M is the private demand for real balances; Ye and
where λ1 and λ2 are, respectively, the income and inflation expectation elasticities. In the estimation,
The coefficients (the B’s) in equation (2.4) are combinations of the b’s and the λ’s in equations (2.1), (2.2), and (2.3). Expressed in terms of these original structural parameters, the coefficients of equation (2.4) are as follows:
B0 = (1–λ1) (1–λ2)a
B1 = (1–λ1) + (1–λ2)
B2 = (1–λ1) (1–λ2)
B3 = b1λ1
B4 = –b1λ1 (1–λ2)
B5 = b2
B6 = –b2 [(1–λ1) + (1–λ2)]
B7 = b2 [(1–λ1) (1–λ2)]
B8 = b3λ2
B9 = –b3 [(1–λ1) λ2.
The error term of the reduced equation can also be expressed in terms of the original disturbance term in equation (2.1)
Vt = Ut+d1Ut-1+d2Ut-2
where the constants are functions of the structural parameters, and the original disturbance term is assumed to be distributed as follows:
Ut = –d1Ut-1–d2Ut-2+et
and where et is independently distributed. The reduced equation (2.4) with ten variables and six structural parameters is over identified with respect to the structural parameters. Its estimation by a constrained nonlinear estimation technique, however, results in unique estimates of the parameters being obtained simultaneously. Thus, equation (2.4) was estimated by a constrained nonlinear estimated procedure. The nonlinear constraints implied by that equation are
In addition to equations (2.1) or (2.4), which will be referred to as Model III, two other demand relationships based on alternative specifications about the formation of expectations are also estimated. In Model I the specification is made that λ 1=λ2=1. Income and price expectation elasticities are assumed to be static. The demand relationship thus becomes one in which all explanatory variables are current. This is the form of the demand relationship that is most commonly estimated. In that case, equation (2.1) becomes simply
Here there is no need for reduction, and estimation is by the classical least-squares method. For this model only, individual country estimates are also given. For the other models, estimates for groups of countries and for all countries together are given. The Model I results for individual countries are only interpreted as suggestive. The degrees of freedom involved are such that the estimates can be interpreted with very little confidence.
In Model II, the specification is made that in equation (2.1) λ1=1. Thus, it is assumed that desired balances are related to current and not to expected real income. On combining the price expectation relationship with equation (2.1) and reducing,
Expressed in terms of the structural parameters of the model, the coefficients of the reduced equation (2.6) are
C0 = (1–λ2) a
C1 = (1–λ2)
C2 = b1
C3 = –b1 (1–λ2)
C4 = b2
C5 = –b2 (1–λ2)
C6 = b3λ2
and the error term of the reduced equation, V1t = U1t + d1U1t-1. The original disturbance term is assumed to be distributed as follows:
U1i = –d1U1t-1+e1t,
where e1t is independently distributed and has a mean equal to zero. Again, with seven variables in the relationship, the five structural parameters of equation (2.6) are overidentified. With the appropriate nonlinear constraints imposed on its coefficients, it is estimated by the nonlinear estimation technique. The nonlinear constraints implied are
C5 = –C1C4
C3 = –C1C2.
In this study, money is defined conventionally or as so-called narrow money. The International Monetary Fund’s monthly publication, International Financial Statistics (IFS), presents monetary data for most of its member countries based on this conventional conceptualization. As defined in IFS,” ‘Money’ … comprises Currency and Deposit Money held by the domestic non-Government Sector. ‘Currency’ consists of domestic notes and coins in current use. ‘Deposit Money’ means deposits unrestrictedly exchangeable on demand into currency at par and without penalty …”47 For details of the specific items included in the money totals for each country, see Appendix I. The rates of change in prices are, specifically, the rate of change of the cost of living index. The yields on all financial assets are represented by the interest rates on financial claims denominated in money terms; see Appendix II.
The money and price data in this paper are taken from IFS, and income data are from issues of the United Nations’ Yearbooks of National Accounts Statistics. The income data, especially those of the less developed countries, are likely to be subject to wide margins of error. However, it is not too easy to decide whether these errors are systematic and if so in what direction. This is especially so when one considers the additional problem of the conversion of the money and income data for all the countries to a common currency. In this paper, the income and money totals of the different countries have been converted to U.S. dollars, using exchange rates calculated by the United Nations to reflect purchasing power parities in 1958.
Systematic empirical verifications of the generality, over space, of economic propositions have been handicapped by lack of data, but data are gradually becoming available and this handicap is slowly disappearing. However, as has been pointed out, “A single time series of 10 observations is barely worth analyzing….”48 And, except for a relatively small number of countries, available data are of this nature. Thus, the next best approach, especially given sound theoretical support, is to pool the time series of countries which share the characteristics that are relevant for the analysis. The discussions in Section I lay such a foundation. And, as has been argued there, while diversity of circumstances do exist, they may not obscure the observation of basic uniformities. Further, it may be mentioned that the problems that may be involved in combining the time series of different countries also exist in other types of data. In fact, “there is no reason to postulate that differences among countries are of a more fundamental type than differences among aggregates for the same country in different years, or differences among households in the same country. The latter differences are not usually regarded as insuperable obstacles in time series or cross-section analysis. Consequently, we should not hesitate to attempt combining time series from several countries, if only to see what difficulties arise.”49
The classification of countries adopted in this study follows that used by IFS in its international tables, where countries are divided into industrial, other developed, and less developed. Hitherto, discussions have proceeded in terms of developed and less developed countries. The division into three groups is in part a concession to arguments for a more detailed classification. At the same time, however, it provides an intermediate group whose demand-function behavior in relation to that of the other groups should be consistent with expectations. By this classification, the countries in the study are divided as follows: (1) Industrial (Canada, Denmark, France, Germany, the Netherlands, Norway, Sweden, Switzerland, and the United States); (2) Other developed (Australia, New Zealand, South Africa, and Turkey); and (3) Less developed (Ceylon, the Republic of China, Costa Rica, India, and Mexico). In order to estimate the demand relationships, the time series, which run generally from 1950–61, are pooled for the countries in each group. The period covered for each country is presented in Appendix III. Estimates are also made for all countries combined. The choice of countries is based mainly on the availability of consistent data. Further, since data on economically meaningful interest rates are required, the proportional representation of the less developed countries is limited. Those of this group that are included may, in a sense, be considered as representative of the more structurally sophisticated less developed countries.
III. Measurements and Forms of the Functions
Before presenting the results, certain preliminary comments should be made about the interpretation to be given them. First, the results refer directly to the countries and period covered. Thus, comments made about behavior in the different economic environments refer explicitly to these environments as they are represented by the countries listed in Section II and for the historical period concerned. Second, the tentative, and indeed the exploratory, nature of the insights into money-demand behavior that may be gained from the estimates needs to be emphasized. Even when free of statistical biases, no results of a single study can be considered as other than tentative. These estimates are not likely to be free of biases. For instance, since the money-demand and supply relations are only the monetary sector of a “simultaneous equation” econometric model, the estimates are probably subject to the so-called least-squares bias in simultaneous equation models. The fact that the forms of the demand relationship reported do not contradict experience (interpreted to include prior findings) may be taken as lending some credibility to the presumption that they have some measure of validity.
Model I
This particular formulation which involves only synchronous variables was estimated for the individual countries, the different groups of countries, and for all countries combined. It is the most restrictive of the three alternative models estimated: it imposes the restrictions that λ1 = λ2 = 1 and as such becomes a model in which the desire for real balances is related, on the Friedman interpretation, to the transactions motive. One would expect that, in terms of comparative group behavior, this model would perform best in explaining the behavior of that group where the role of expected prices and income is least important or where current observations play important roles in the formation of expectations.
Before getting to the group estimates, however, the individual country estimates may be discussed briefly. These estimates cannot be interpreted with much confidence because of the limited degrees of freedom involved. They are presented in Appendix IV, Table 5. For all the countries in the industrial group, the signs of the income and interest rate elasticities are the correct ones. Except for Canada, Denmark, and Sweden, the sign of the price variable is also the correct one. Despite the limited degrees of freedom, real income meets the significance test50 in almost all the countries, with most of the income elasticities near unity. Of the substitution variables, the interest rate seems to play a significant role in the money-demand function of more than half of the industrial countries. The price variable, on the other hand, seems to play a minor role in explaining the variances in the desired balances.
The over-all results for the individual other developed countries are relatively less satisfactory. The signs of the income elasticities are the appropriate ones in three of the four countries. However, in only one of these, Turkey, is the elasticity significantly different from zero. The direction of the influence of the interest rate is the correct one in each country, and in New Zealand and South Africa the interest elasticities are significantly different from zero. In all but one of the countries, the sign of the price variable is the correct one; however, the influence of price movements on money balances seems to be significant only in South Africa.
With respect to the less developed countries, real income is positively related to real balances and its coefficient significantly different from zero in all instances. In three (the Republic of China, Costa Rica, and Ceylon) of the five countries, the sign of the interest rate is the correct one. In only one of these (Costa Rica), however, is the elasticity significantly different from zero. In all countries, except the Republic of China, the direction of the influence of price changes is the correct one. However, the coefficient of the price variable is significantly different from zero only in Mexico.
Shaky though these individual country estimates are as a basis for any firm conclusions, they nonetheless suggest that the explanatory variables affect desired balances in the expected directions. On the whole, the results suggest that pooling data from different countries is not too artificial. Attention may now be turned to the group and aggregate estimates. These are presented in Table 1.
1. Model I: Regression Coefficients and Other Statistics of Equation (2.5)
Degrees of Freedom.
1. Model I: Regression Coefficients and Other Statistics of Equation (2.5)
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| b1 | 0.9829 | 1.0183 | 0.9695 | 1.0252 |
| (0.0267) | (0.1071) | (0.0085) | (0.0173) | |
| b2 | –0.0118 | –1.6991 | –0.33186 | –0.3856 |
| (0.1133) | (0.2782) | (0.02295) | (0.0556) | |
| b3 | –0.0333 | –4.1455 | –0.4612 | –0.8435 |
| (1.2188) | (1.0714) | (0.3302) | (0.6188) | |
| a | –1.3664 | 1.2279 | –1.4032 | –0.8985 |
| (0.1441) | (0.4607) | (0.0425) | (0.0751) | |
| R2 | 0.9388 | 0.8084 | 0.9969 | 0.9638 |
| DF1 | 95 | 40 | 51 | 194 |
Degrees of Freedom.
1. Model I: Regression Coefficients and Other Statistics of Equation (2.5)
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| b1 | 0.9829 | 1.0183 | 0.9695 | 1.0252 |
| (0.0267) | (0.1071) | (0.0085) | (0.0173) | |
| b2 | –0.0118 | –1.6991 | –0.33186 | –0.3856 |
| (0.1133) | (0.2782) | (0.02295) | (0.0556) | |
| b3 | –0.0333 | –4.1455 | –0.4612 | –0.8435 |
| (1.2188) | (1.0714) | (0.3302) | (0.6188) | |
| a | –1.3664 | 1.2279 | –1.4032 | –0.8985 |
| (0.1441) | (0.4607) | (0.0425) | (0.0751) | |
| R2 | 0.9388 | 0.8084 | 0.9969 | 0.9638 |
| DF1 | 95 | 40 | 51 | 194 |
Degrees of Freedom.
For the industrial group, the signs of all the coefficients are the correct ones; however, only the coefficient of real income is significantly different from zero. The results for the other developed group suggest that the model explains the variance in real balances (in this group of countries) satisfactorily. Real income, interest rate, and rate of change in prices all influence real balances in the expected directions, and all the coefficients are significantly different from zero. As for the less developed group, both real income and interest rates seem to influence desired balances significantly. Although the sign of the price variable is the correct one, the coefficient is not significantly different from zero. The estimates for all countries combined show that both real income and interest rates influence desired balances significantly and in the expected directions. While price changes seem to influence the over-all behavior in the expected direction, their influence does not seem to be significant. Even though the estimated goodness-of-fit measures have to be adjusted downward because of the apparent autocorrelation, this simple model seems to explain desired balances rather satisfactorily in spite of the diversity of circumstances that exist within the different groups and over all.
Comparing the group estimates, one will notice that in all the demand-for-money relationships, the role of real income is as expected; not only that, the income elasticities for the three groups as well as for all countries combined are not significantly different from unity. Thus, measured income, or the related transactions motive, does explain part of the variance in money holdings. Whether expected income performs better, subsequent estimates will indicate. However, these results suggest that the assumption that income expectations are static may not be too far from reality in most of the countries. At least, the estimates suggest that λ is nearer unity than zero. Interest rates play a significant role in each of the group and over-all demand relationships, except that of the industrial countries. The fact that, for this group of countries, the price variable, also, does not seem to influence desired balances suggests that inability to isolate both substitution effects may be due to estimation problems relating to the fact that, in this group, the yields on financial and on real assets are related or move together. In the estimates for the other developed group, both interest rates and price changes seem to have substantial influences on desired balances. In the results for the less developed countries, the interest rate is the only substitution effect that appears to play an important role in explaining money holdings. These results should be interpreted, bearing in mind the restrictions placed on the demand relationship. If one interprets the results as reflecting the relative appropriateness of the restriction, λ1 = λ2 = 1, to the group behavior and then interprets the results as reflecting in part the specification errors, one can say that they are least appropriate for the industrial group of countries.
Model II
This model, it will be recalled, is the special case of equation (2.1) in which the specification is made thatλt = 1. In terms of that equation, this model is less restrictive than Model I, for although it relates real balances to current real income and interest rates, it allows for possible nonstatic price expectations. As has been indicated above, the reduced equation (2.6) is an overidentified equation which, on the introduction of the appropriate nonlinear constraints, is estimated by a nonlinear estimation technique. Before discussing the estimates obtained when the estimation method is nonlinear, it is interesting for one to see what the estimates are like when the coefficients are estimated without constraints. It is possible that the nonlinear estimation technique is too sensitive to apply to a set of data such as is analyzed here. It is therefore instructive to get an indication from the less demanding linear technique as to the appropriateness of the model. The reduced equation (2.6) is
where the nonlinear constraints are
C3 = — C1C2
C5 = — C1C4.
The estimates obtained when the coefficients are left free to vary are presented in Table 2. From the table it will be seen that the model fits the observations reasonably well. In all instances, the signs of the estimated coefficients are the correct ones. The signs of the coefficients of Mt-1 Yt, and rt-1 are positive, while those of the coefficients of Yt-1, rt, and
Model II: Regression Coefficients and Other Statistics of Equation (2.6) Estimated Without Constraints
Degrees of Freedom.
Model II: Regression Coefficients and Other Statistics of Equation (2.6) Estimated Without Constraints
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| C1 | 0.9929 | 0.9051 | 0.7837 | 0.9629 |
| (0.0113) | (0.0194) | (0.0594) | (0.0090) | |
| C2 | 0.7503 | 0.3557 | 0.2931 | 0.4220 |
| (0.1311) | (0.1151) | (0.0932) | (0.0635) | |
| C3 | –0.7425 | –0.2902 | –0.0775 | –0.3836 |
| (0.1321) | (0.1205) | (0.0993) | (0.0648) | |
| c4 | –0.1343 | –0.2147 | –0.1769 | –0.1081 |
| (0.0246) | (0.0839) | (0.0540) | (0.0221) | |
| C5 | 0.1318 | 0.0515 | 0.1498 | 0.1203 |
| (0.0215) | (0.0810) | (0.0461) | (0.0199) | |
| C6 | –0.3818 | –0.6830 | –0.9033 | –0.5360 |
| (0.1482) | (0.1505) | (0.1568) | (0.0822) | |
| C0 | 0.0090 | 0.0523 | –0.2924 | –0.0338 |
| (0.0238) | (0.0574) | (0.0845) | (0.0128) | |
| R2 | 0.9993 | 0.9979 | 0.9994 | 0.9994 |
| DF1 | 92 | 37 | 48 | 191 |
| C3 = —C1C2 | –0.7450 | –0.3219 | –0.2297 | –0.4063 |
| C5 = —C1C4 | 0.1333 | 0.1943 | 0.1386 | 0.1041 |
Degrees of Freedom.
Model II: Regression Coefficients and Other Statistics of Equation (2.6) Estimated Without Constraints
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| C1 | 0.9929 | 0.9051 | 0.7837 | 0.9629 |
| (0.0113) | (0.0194) | (0.0594) | (0.0090) | |
| C2 | 0.7503 | 0.3557 | 0.2931 | 0.4220 |
| (0.1311) | (0.1151) | (0.0932) | (0.0635) | |
| C3 | –0.7425 | –0.2902 | –0.0775 | –0.3836 |
| (0.1321) | (0.1205) | (0.0993) | (0.0648) | |
| c4 | –0.1343 | –0.2147 | –0.1769 | –0.1081 |
| (0.0246) | (0.0839) | (0.0540) | (0.0221) | |
| C5 | 0.1318 | 0.0515 | 0.1498 | 0.1203 |
| (0.0215) | (0.0810) | (0.0461) | (0.0199) | |
| C6 | –0.3818 | –0.6830 | –0.9033 | –0.5360 |
| (0.1482) | (0.1505) | (0.1568) | (0.0822) | |
| C0 | 0.0090 | 0.0523 | –0.2924 | –0.0338 |
| (0.0238) | (0.0574) | (0.0845) | (0.0128) | |
| R2 | 0.9993 | 0.9979 | 0.9994 | 0.9994 |
| DF1 | 92 | 37 | 48 | 191 |
| C3 = —C1C2 | –0.7450 | –0.3219 | –0.2297 | –0.4063 |
| C5 = —C1C4 | 0.1333 | 0.1943 | 0.1386 | 0.1041 |
Degrees of Freedom.
For the other developed and the less developed groups of countries, although all the coefficients have the expected signs, the coefficients of one variable in each case is not significantly different from zero: that of rt-1 in the other developed and of Yt-1 in the less developed group of countries. Again, given the large standard errors involved, –C1C2 and – C1C4 are close in both demand relationships to the corresponding C3 and C5. The λ2 obtained from these estimates for the other developed and the less developed groups are 0.10 and 0.22, respectively. Thus, the relationship of the λ2 of each group to that of each of the others is what one would expect on a priori grounds.
For all countries combined, the result also suggests that the specification is appropriate. For the group as well as the over-all results, this model seems to be capable of explaining behavior better than Model I. Armed with these preliminary notions about the appropriateness of Model II, one can now turn to the estimates obtained when estimation is performed such that the overidentification in the structural parameters of equation (2.6) is eliminated. The structural estimates obtained when the reduced equation is estimated by the nonlinear least-squares technique are presented in Table 3.
Model II: Estimates of the Parameters of Equation (2.6) with Nonlinear Constraints
Model II: Estimates of the Parameters of Equation (2.6) with Nonlinear Constraints
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| 1 —λ2 | 0.9975 | 0.8252 | 0.5372 | 0.9889 |
| (0.0087) | (0.0742) | (0.0849) | (0.0034) | |
| b1 | 0.7672 | 0.9771 | 0.9704 | 0.4891 |
| (0.1276) | (0.0406) | (0.0114) | (0.0649) | |
| b2 | –0.1337 | –0.6362 | –0.3183 | –0.1304 |
| (0.0213) | (0.1359) | (0.0260) | (0.0210) | |
| b3 | –151.86 | –9.5725 | –0.6524 | –40.606 |
| (526.46) | (4.4233) | (0.1271) | (14.155) | |
| a | 0.00981 | –0.0334 | –0.6457 | 0.0040 |
| (0.01606) | (0.0718) | (0.1248) | (0.0102) | |
| λ2 | 0.0025 | 0.1748 | 0.4628 | 0.0111 |
Model II: Estimates of the Parameters of Equation (2.6) with Nonlinear Constraints
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| 1 —λ2 | 0.9975 | 0.8252 | 0.5372 | 0.9889 |
| (0.0087) | (0.0742) | (0.0849) | (0.0034) | |
| b1 | 0.7672 | 0.9771 | 0.9704 | 0.4891 |
| (0.1276) | (0.0406) | (0.0114) | (0.0649) | |
| b2 | –0.1337 | –0.6362 | –0.3183 | –0.1304 |
| (0.0213) | (0.1359) | (0.0260) | (0.0210) | |
| b3 | –151.86 | –9.5725 | –0.6524 | –40.606 |
| (526.46) | (4.4233) | (0.1271) | (14.155) | |
| a | 0.00981 | –0.0334 | –0.6457 | 0.0040 |
| (0.01606) | (0.0718) | (0.1248) | (0.0102) | |
| λ2 | 0.0025 | 0.1748 | 0.4628 | 0.0111 |
One thing is immediately apparent in Table 3, and that is that in all instances, the signs of all the structural parameters are the correct ones. For the industrial group, real income enters the relationship significantly with an elasticity of about 0.77. Interest rate is also significant in the relationship, with the direction of its influence negative as expected. Although the sign of the price variable is the expected one, the standard error is several times larger than the coefficient. The λ2 estimated for this group is 0.0025, which suggests that the price expectation elasticity is close to zero and that current rates of change in prices have little influence on price expectation formation.
For the other developed group of countries, the signs of all coefficients are again the expected ones. Rates of price change, however, seem to have little influence on desired real balances. Both the real income and interest rate elasticities are more than three times their respective standard errors. The λ2 for this group of countries is about 0.17, a price expectation elasticity that is close to zero but that is larger than the one obtained for the industrial group.
For the less developed countries, not only are all the signs of the coefficients the correct ones but also each of the coefficients is at least five times as large as its standard error. The price expectation elasticity estimated for the less developed countries is 0.46 and is significantly different from zero. Compared with the findings for the industrial and other developed groups, current price movements have a greater impact on price expectation formation.
For all countries combined, the direction of the influences of the explanatory variables are the expected ones. Probably reflecting the greater weight of the industrial countries in the over-all estimates, the price variable’s coefficient is less than three times its standard error and, given the estimate of λ2, current price movements have little effect on price expectation formation. On the whole, Model II performs better than Model I. The best improvement in the explanatory power of Model II over Model I occurs in the industrial group. While in Model I none of the substitution effects seems to have been significant in explaining the behavior of desired balances, in Model II the substitution possibilities related to financial assets now play a significant role.
Model III
Having looked at the special cases of equation (2.1), attention is now turned to the equation itself. Here, it will be recalled that the demand relationship is specified such that 1 ≠; λ1 ≠ λ2 ≠ 1. In this model, the most general of those examined in this study, desired balances are related to expected income, to expected rates of change in prices, and to current rates of interest. Again, the reduced equation (2.4) is an over-identified one which has been made just identified by imposing nonlinear constraints on the coefficients and is estimated by a nonlinear estimation technique.
The estimated parameters are presented in Table 4. Estimates from the unrestricted version of equation (2.1) are presented in Appendix IV, Table 6. One thing that would be noticed on comparing the estimates in Tables 3 and 4 is that the alternative estimate of common parameters do not vary widely because of changes in specifications. This suggests that there may be some underlying stability in the relationship. Turning first to the Model III results for the industrial group, the conclusions as to the respective roles of the explanatory variables are the same as those drawn from Model II. Both real income and interest rates are significantly related to desired money holdings. And the elasticities are, respectively, positive and negative, as expected. Current price movements do not seem to play a significant role in explaining the behavior of real balances; although the estimated coefficient is negative, it is less than one third of its standard error.
Model III: Estimates of the Parameters of Equation (2.1) with Nonlinear Constraints
Model III: Estimates of the Parameters of Equation (2.1) with Nonlinear Constraints
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| 1–λ1 | 0.2404 | 0.0999 | 0.0115 | 0.6386 |
| (0.0994) | (0.0479) | (0.0151) | (0.0475) | |
| 1 —λ2 | 0.9968 | 0.7635 | 0.4177 | 0.9258 |
| (0.0119) | (0.0799) | (0.1085) | (0.0230) | |
| b1 | 0.7605 | 1.1311 | 0.9777 | 0.9988 |
| (0.1868) | (0.0864) | (0.0113) | (0.0689) | |
| b2 | –0.1098 | –0.6543 | –0.3306 | –0.0777 |
| (0.0221) | (0.1263) | (0.0253) | (0.0163) | |
| ba | –209.56 | –7.0630 | –0.5173 | –13.177 |
| (796.68) | (2.8085) | (0.1047) | (4.194) | |
| a | 0.0116 | 0.0297 | –0.7789 | –0.0304 |
| (0.0173) | (0.0662) | (0.1542) | (0.0109) | |
| λ1 | 0.7596 | 0.9001 | 0.9885 | 0.3614 |
| λ2 | 0.0032 | 0.2365 | 0.5823 | 0.0742 |
Model III: Estimates of the Parameters of Equation (2.1) with Nonlinear Constraints
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| 1–λ1 | 0.2404 | 0.0999 | 0.0115 | 0.6386 |
| (0.0994) | (0.0479) | (0.0151) | (0.0475) | |
| 1 —λ2 | 0.9968 | 0.7635 | 0.4177 | 0.9258 |
| (0.0119) | (0.0799) | (0.1085) | (0.0230) | |
| b1 | 0.7605 | 1.1311 | 0.9777 | 0.9988 |
| (0.1868) | (0.0864) | (0.0113) | (0.0689) | |
| b2 | –0.1098 | –0.6543 | –0.3306 | –0.0777 |
| (0.0221) | (0.1263) | (0.0253) | (0.0163) | |
| ba | –209.56 | –7.0630 | –0.5173 | –13.177 |
| (796.68) | (2.8085) | (0.1047) | (4.194) | |
| a | 0.0116 | 0.0297 | –0.7789 | –0.0304 |
| (0.0173) | (0.0662) | (0.1542) | (0.0109) | |
| λ1 | 0.7596 | 0.9001 | 0.9885 | 0.3614 |
| λ2 | 0.0032 | 0.2365 | 0.5823 | 0.0742 |
Again, as for the λ2 estimated in Model II, the price expectation elasticity for the industrial group is close to zero, suggesting that the lag in price expectations formation is very long. The income expectation elasticity is larger, 0.76. Thus, for the industrial group of countries, expected income is more appropriate than current income in the money-demand function. This supports the findings from U.S. data that expected income is the appropriate income variable in the demand-for-money function. However, the size of the elasticity obtained here is much larger than the one that has been obtained for the United States alone, 0.40.51 There is, of course, no reason to expect the elasticity estimated for the United States to be the same as an elasticity that represents average behavior in nine industrial countries (including the United States). On the contrary, given the relative level of development in the United States compared with the other industrial countries, the estimated income expectation elasticity deviates from that of the United States in the expected direction.
For the other developed group, the income, interest rate, and price coefficients have the expected signs. Both the income and interest rate elasticities are more that five times their standard errors. With respect to the expectation elasticities, both the income and the price expectation elasticities for the other developed countries are larger than those estimated for the industrial group of countries. Thus, greater proportions of current income and of the current rate of inflation are considered as permanent in the other developed than in the industrial countries.
In the Model III results for the less developed countries, real income, interest rates, and rates of price change are all significantly related to desired balances, and all three coefficients have the expected signs. At the same time, the coefficients are at least five times their respective standard errors. The λ1 estimated for the less developed group is not significantly different from unity. Thus, income expectations are static in this group of countries. Current income, rather than expected or permanent income, is the appropriate argument in the demand-for-money function. On the other hand, the estimate of λ2, similar to that obtained in Model II, suggests that expected prices, not current prices, is the appropriate variable in the demand function. “Holders of money presumably judge the ‘real’ amount of cash balances in terms of the quantity of goods and services to which the balances are equivalent, not at any given moment of time, but over a sizable and indefinite period …”52 In the less developed countries, compared with the two other groups of countries, current movements in prices have great impact on price expectations.
The results for all the countries combined, as expected, are a sort of average representation of behavior in all the types of economies included in the study. All the explanatory variables have the expected signs, with the real income and the interest rate coefficients meeting the statistical tests of significance with considerable ease. The estimated income expectation elasticity, about 0.36, is lower than any of the ones obtained for the groups. The price expectation elasticity is very close to the one estimated for the industrial group of countries.
From the results of the models presented above, some conclusions can be reached as to the specifications of the demand-for-money function that may be appropriate in each of the different economic environments considered. With respect to the industrial countries, although the sign of
For the other developed group of countries, the results suggest that, in addition to interest rates, real income and expected rates of change in prices are the appropriate arguments in the demand-for-money relationship. However, of the three groups of countries, the results for this group are the least conclusive. For instance, although there is some indication that expected income may be the appropriate income variable, the income expectation elasticity is not significantly different from unity. At the same time, the coefficient of the price variable just barely passes the significance test.
The most interesting results are those for the so-called less developed group. They are most interesting because it is for this type of economy that the least amount of information is available about the form of the demand-for-money function. At the same time, however, for reasons mentioned in Section II, this type of economic environment is the least appropriately represented in this paper. In any event, Model II, of the alternative models examined here, seems to be the best representation of desired balances behavior in the less developed group. That is, interest rates, current real income, and expected rates of change in prices seem to be the appropriate variables in the money-demand function of these countries. For the structurally less sophisticated countries in the less developed group, where financial assets are not important substitutes for holding money, one can infer from this result that the determinants of the behavior of real balances are likely to be income and expected prices. While in the industrial group only the substitution possibilities relating to financial assets seem to be important, for the less developed group substitution possibilities relating both to financial and to real assets seem to be important. If the finding for the industrial group is due to greater intersectoral integration, the results for the less developed group can be said to be due to little intersectoral integration.
It is now possible to relate these findings to the empirical hypotheses stated at the beginning of Section II. These results suggest that in the different economic environments, in developed and less developed countries, the demand for money is a predictable function of a limited number of variables. Variations of the basic hypothesis used here have been employed by others to explain the behavior of desired money balances in individual countries (especially the United States and the United Kingdom). The results of this study show that the hypothesis has a substantial degree of generality. As the estimates for all the countries combined show, diversity of circumstances is not so predominant as to render the relationship inapplicable to a wide range of countries.
At the same time, however, the findings show that particular specifications may be more appropriate to particular economic environments than to others. Thus, the findings support the hypothesis that the expectation variables are more appropriate in the demand relationship of the developed than in that of the less developed countries. It will be recalled that an expectation variable is considered to be more appropriate in A than in B if λA < λB. The estimates show that the price and the income expectation lambdas for the industrial countries are consistently smaller than those of the other developed countries, while those of the other developed countries are consistently smaller than those of the less developed countries. Thus, the conclusions reached in Section I about the implications of the structural differences between the less developed and developed countries for the comparative behavior of the money-demand function seem to be supported by the data.
As expected, the income elasticity of the demand for money is positive in all the economic environments; however, there is no evidence to suggest that the higher the level of development, the lower the income elasticity. Although in Tables 3 and 4 the estimates of the elasticity for the less developed countries are larger than that for the industrial group of countries, the estimated elasticity for the other developed countries is larger than the one for the less developed countries. More important, however, is the fact that none of these elasticities is significantly different from unity. This result, which contrasts with the a priori notions developed in Section I, may be due to the offsetting effects, in the less developed and developed countries, of the operation of the alternative motives for holding money. While in the less developed countries the level of living may be so low as not to permit significant marginal real balance holdings ascribable to the asset motive, in the developed countries the influence of this motive on the income elasticity may be such as to offset the influence of the possible existence of economies of scale (or efficiency) with respect to the holding of money for transactions purposes.
The results also suggest that opportunity costs of holding money involving real assets are more important in the less developed group of countries. Finally, as the findings reported for the United States have suggested, the results reported here support the view that in the developed group of countries all substitution possibilities can be subsumed under those of financial assets.
IV. Conclusions
This study has attempted to examine the degree of uniformity that exists across economic environments in the behavior of monetary relationships. Specifically, it has attempted to see what implications, if any, structural and other differences that separate developed from less developed economies imply for the money-demand function that is appropriate to each environment.
The demand-for-money relationship specified allows for nonstatic expectations with respect both to income and to the rate of change in prices. Thus, desired real balances are related to “expected” real income, current interest rate, and “expected” rate of change in prices. An adaptive expectations model that permits direct investigation of the manner in which expectations are formed is used to relate the “expected” variables to observables. A priori considerations suggest that the structural differences between the developed and less developed economies imply certain differences in the behavior of the demand for money. These considerations suggest, inter alia, that (1) the lag in expectation formation is longer in developed than in less developed countries; (2) strong (liquid) asset motives make for higher income elasticities in less developed economies; (3) opportunity costs of holding money involving real assets, as approximated by movements in the price level, are more important in the less developed economies; and (4) in the developed economies, most of the substitution effects may be subsumed under those of financial assets.
Empirical insights into these issues were sought by analyzing the data for 18 countries. As has been suggested at several points, the empirical findings are likely to suffer from some statistical limitations. Even if there are no statistical limitations, the conclusions implied by the findings cannot be considered as more than tentative. This is an exploratory study. In any event, it is appropriate to identify some of the sources of errors in the estimates. First, the estimates, because of the single equation approach, are subject to least-squares bias in simultaneous equation models. Further, although different elasticities of expectation were specified for the different variables, the expectation generating form used assumed geometrically declining weights, and the elasticity of expectation was assumed to be constant during the period of analysis. On the whole, these limitations are not believed to be such as to nullify the tentative conclusions reached about the “over-all properties of the system” applicable to each environment.
The 18 countries studied were grouped into three economic environments—industrial, other developed, and less developed—and the data for each group were pooled. The findings suggest that while there is wide room for generalizations about desired money holdings, there are differences in the form of the demand-for-money function that can be appropriately applied to each economic environment. The lag in expectation formation in the monetary sector does seem to be shorter in the less developed group. Or, more generally, the less developed the economic environment, the shorter the lag in expectation formation. For instance, the finding that income expectations are static in the less developed countries suggests that money balances should appropriately be related to current real income or rationalized on the basis of the transactions motive. On the other hand, the longer lag in income expectation formation in the industrial countries suggests, in agreement with recent theoretical and empirical formulations, that expected income or wealth (rather than current income) is the appropriate variable in the money-demand function.
While there appears to be little substitution between real assets and money balances in the industrial countries, this substitution effect seems to be important in the less developed countries. There has been much controversy in the literature over the contention that money is a luxury. The results provide little evidence to suggest that money is a luxury. All the estimated income elasticities of the demand for money are not significantly different from unity.
These results may have implications that are of wider interest. The question of the general applicability of theoretical relationships developed to explain behavior in the industrial countries has often been raised. The results of this study suggest that these propositions have a fair amount of generality. Thus, the findings that in the industrial countries desired real balances are related to interest rates and expected income, while in the less developed countries they are related to interest rates, expected rates of change in prices, and current income are consistent with, or are special cases of, the general theoretical hypothesis developed in Section I.
However, the special variants of the general relationship that are applicable to the alternative types of environments differ enough to suggest that policy for one type of environment may not appropriately be based on empirical observations of behavior in the other type. For example, in the industrial countries price movements do not seem to play a significant role in explaining money holdings, but in the less developed countries they do. Thus, in the latter economic environment, changes in current rates of inflation not only tend to lead to adjustments in desired balances but also are more important in the formation of expectations about the future behavior of the price level. Given an acceleration in the rate of inflation, the consequent adjustments, in situations characterized by relatively inelastic supply conditions, are likely (depending on the size of money balances available for the purchase of assets for inflation hedging) to lead to still higher rates of price increase and the associated undesirable results. The effects of actual and expected inflation on the level and pattern of consumption and investment, on foreign balances, and on economic horizons are not likely to enhance the speed with which development targets are approached.
The finding that desired balances in less developed countries are related to current rather than to expected income does not make the job of monetary management in these countries any easier. It has been pointed out earlier that when expectations are nonstatic the expected value of a variable fluctuates less than its current value. Static income expectation in these countries means that desired balances are related to a variable which, especially because of the sensitivity of these countries to exogenously generated fluctuations, is likely to vary substantially from period to period. In this situation, where instruments of monetary policy are not fully developed and where there is a substantial lag in acquiring information about and interpreting developments in the level of economic activity, the added flexibility required of monetary management because of static income expectations may be especially difficult to achieve.
APPENDICES
I. Components of Money
Australia
Money: Monetary liabilities of the Reserve Bank other than to banks, Treasury coin outside banks, and the current deposits of the check-paying banks.
Canada
Money: Monetary liabilities of the Bank of Canada to the private sector, Treasury coin outside banks, and the monetary liabilities of the chartered banks to the private sector.
Ceylon
Money: Monetary liabilities of the Central Bank to the private sector and the demand deposits of the private sector with commercial banks.
China, Republic of
Money: Central Bank’s monetary liabilities to the private sector, and demand deposits with commercial banks and with the Post Office.
(The Bank of Taiwan was the central bank until July 1961 when it became a commercial bank.)
Costa Rica
Money: Monetary liabilities of the Central Bank to the private sector (including official entities and mortgage banks), and the monetary deposits of the private sector and official entities with the commercial banks (and Treasury coin issued through 1950).
Denmark
Money: Monetary liabilities of the National Bank to the private sector, Treasury coin outside banks, the monetary deposits of the commercial and savings banks, and postal checking deposits.
France
Money: Monetary liabilities of the Bank of France to the private sector, Treasury coin, and monetary deposits with the banks (registered banks, popular banks, agricultural credit institutions, and the Banque Française du Commerce Extérieur), the postal checking system, and the Treasury.
Germany
Money: Monetary liabilities of the federal bank to the private sector, Treasury coin in circulation outside banks, and private sector sight deposits with deposit money banks.
India
Money: Monetary liabilities of the Reserve Bank to the private sector, demand deposits of the commercial and the cooperative banks, and Treasury coin in circulation.
Mexico
Money: Bank of Mexico’s monetary liabilities to the private sector and related institutions (primarily mortgage banks), and checking deposits of the private sector and related institutions with deposit and savings banks.
Netherlands
Money: Treasury currency in circulation less bank holdings, private sector deposits with The Netherlands Bank, current accounts with the commercial and the agricultural credit banks, and deposits with the postal checking and giro systems.
New Zealand
Money: Monetary liabilities of the Reserve Bank to the private sector, Treasury coin outside the banks, and demand liabilities of the trading banks to the private sector.
Norway
Money: Monetary liabilities of the Bank of Norway to the private sector (all in the form of notes) and to official entities, Treasury coin in circulation, and private monetary deposits with deposit money banks (commercial and savings banks, plus Post Office).
South Africa
Money: Notes and coins in circulation outside the banks, and demand deposits of the domestic private sector with the Reserve Bank and commercial banks.
Sweden
Money: The Bank of Sweden’s monetary liabilities to the private sector, Treasury coin outside banks, and current deposits of the private sector with commercial and savings banks. The commercial banks’ current deposits include money orders issued and giro deposits, but are net of their holdings of checks and money orders in course of collection.
Switzerland
Money: The note issue of the National Bank, sight deposits with deposit money banks, Treasury coin, and checking deposits with the Post Office.
Turkey
Money: Central Bank monetary liabilities to the private sector, private sector monetary deposits with the deposit money banks, and Treasury coin in circulation.
United States
Money: Monetary authorities’ liabilities to the private sector and commercial banks’ demand deposits (net of “cash items in process of collection”) held by the private sector, local governments, and foreign business and individuals, less Federal Reserve float.
II. Interest Rates Used
It will be recalled that interest rates are used in this study as proxies for the yields on financial assets. There is the largely empirical problem of the interest rate, a short-term or a long-term rate, that should appropriately be used in the demand relation.54 For about half of the countries examined in this paper, the issue does not arise because there is only one—a short-term or a long-term—rate available. For the remaining countries, however, data on both types of rates are available. In these cases the choice of which rate to use was approached empirically, and that rate was used which performs better in the individual country’s demand relationship. Where both rates perform equally well, the choice was arbitrary. For countries with two rates, the one used is designated by r.
Australia
r is the long-term government bond yield. The data re theoretical yields of 12-year bonds, read from a calculated schedule of yields of all issues taxable at current rates and maturing in 10 to 15 years. Data are averages of the monthly data.
Canada
r is the Treasury bill rate. The rate is a weighted average of the tender rate on new three-month bills issued every Thursday.
r1 is the long-term government bond yield. This is the average yield of Wednesday quotations for 3¾ per cent bonds maturing on March 15, 1998. Data for the Treasury bill rate and long-term government bond yield are averages of monthly data.
Ceylon
r is the advance rate. It is the rate at which the Central Bank makes advances to the commercial banks against the pledge of government securities.
r1 is the long-term government bond yield. It is the yield to maturity (or to first call date when price is above par) of the 3 per cent National Development Loan, 1965-70.
China, Republic of
r is the call loan rate. It is the rate of the Central Bank of China (before July 1, 1961, the “basic” rate of the Bank of Taiwan) on its call loans to the commercial banks.
Costa Rica
r is the government bond yield. The data show the yields to maturity (averages of daily rates) of the 7 per cent Refunded Internal Debt bonds of 1959 maturing in 1979.
Denmark
r is the discount rate. It is the rate at which the National Bank discounts eligible commercial paper for the deposit money banks.
r1 is the long-term government bond yield. It is the yield of 3½ per cent perpetual government bonds quoted. Data are averages of the monthly data.
France
r is the discount rate. This is the basic rate at which the Bank of France discounts, up to a ceiling set for each deposit money bank, eligible paper (mainly commercial paper).
r1 is the long-term government bond yield. It is the yield of 5 per cent Perpetual Government Bonds issued in 1949 (averages of daily quotations).
Germany
r is the discount rate. It is the rate at which the federal bank discounts eligible commercial paper and, to a small extent, Treasury bills, for the deposit money banks.
India
r is the government bond yield. Current yields (averages of daily quotations) of the 3 per cent Conversion Loan of 1945-46 (no final maturity data but callable at any time after 1986) are quoted.
rs is the call money rate. Data are averages of monthly data.
Mexico
r is the market discount rate. It is the average discount rate of leading banks of Mexico City for commercial paper of up to 180 days’ maturity. Data are unweighted averages of daily rates.
Netherlands
r is the long-term government bond yield. This is the yield to maturity of 3¼ per cent government bonds maturing in 1998. Data are averages of Wednesday quotations.
rs is the Treasury bill rate. It is the unweighted average of daily market prices for all types of Treasury paper then three months from maturity.
New Zealand
r is the long-term government bond yield. It is the yield to maturity of 3¼ per cent government bonds maturing in 1998. Data are averages of Wednesday quotations.
Norway
r is the long-term government bond yield. It is the average yield to maturity of 4 per cent 1955-75 government bonds. Data are averages of monthly quotations.
South Africa
r is the long-term government bond yield, i.e., the yield to maturity (averages of daily rates) of 4#189; per cent government bonds of 1954, maturing in 1974.
rs is the Treasury bill rate. It is the weighted average of discount rates on 91-day bills allotted at the weekly tenders instituted in June 1958. Earlier rates are tap rates on three-month bills.
Sweden
r is the long-term government bond yield. It is the yield of 3 per cent perpetual bonds (averages of daily rates).
rs is the discount rate. The Bank of Sweden quotes a discount rate for its own discounts and a rediscount rate for discounts of eligible commercial bank paper.
Switzerland
r is the long-term government bond yield. This is the weighted average of the yields to maturity of 12 government and federal railway bonds with maturities of at least 5 years. Data are averages of daily quotations.
rs is the call money rate. The call money rate is the rate for interbank loans. Data are period averages of highest and lowest quotations of each week in Zürich.
Turkey
r is the long-term government bond yield. Data are the yields to maturity of 5 per cent Treasury bonds issued in 1951 and maturing in 1972. Annual data are averages of end-of-month quotations.
United States
r is the long-term government bond yield. Unweighted averages of yields to first call or maturity of all fully taxable bonds callable or maturing in 12 years or more. Adjusted for accrued interest.
rs, is the Treasury bill rate. This is the unweighted average tender rate on new three-month bills issued within the period.
III. Period Covered
1950-61 for Australia, Canada, Ceylon, Costa Rica, Denmark, Mexico, New Zealand, South Africa, Sweden, Turkey, and the United States.
1951-62 for France, India, and the Netherlands.
1952-63 for Germany and Norway.
1953-64 for the Republic of China and Switzerland.
IV. Individual Country Results from Model I and Estimates from Model III
Tables 5 and 6 present, respectively, the individual country estimates of Model I and the group and over-all estimates from the unrestricted version of Model III.
Model I: Regression and Correlation Estimates of Equation (2.5) for Individual Countries
Durbin-Watson test statistic.
Model I: Regression and Correlation Estimates of Equation (2.5) for Individual Countries
| Countries | a | b1 | b2 | ba | R2 | D-W Test1 | |
|---|---|---|---|---|---|---|---|
| Industrial | |||||||
| Canada | –1.8208 | 0.8678 | –0.0775 | 0.1367 | 0.9424 | 2.323 | |
| (0.2005) | (0.1451) | (0.0385) | (0.3112) | ||||
| Denmark | –0.5745 | 0.9924 | –0.5270 | 0.9351 | 0.8863 | 1.167 | |
| (0.6577) | (0.1571) | (0.1629) | (0.5020) | ||||
| France | –0.7097 | 1.2924 | –0.2175 | –0.2757 | 0.9791 | 1.266 | |
| (0.1696) | (0.0750) | (0.1191) | (0.3650) | ||||
| Germany | –1.4071 | 1.1641 | –0.3146 | –3.2497 | 0.9799 | 2.193 | |
| (0.1022) | (0.0880) | (0.0799) | (1.4947) | ||||
| Netherlands | –1.6322 | 0.5909 | –0.3395 | –0.5990 | 0.9490 | 1.334 | |
| (0.1853) | (0.0522) | (0.0771) | (0.3999) | ||||
| Norway | –2.5267 | 0.5230 | –0.1898 | –0.1717 | 0.9173 | 1.791 | |
| (0.2201) | (0.0618) | (0.0321) | (0.2394) | ||||
| Sweden | –0.8512 | 1.0461 | –0.4917 | 0.0382 | 0.8407 | 1.476 | |
| (0.8216) | (0.2706) | (0.1941) | (0.2662) | ||||
| Switzerland | –0.3195 | 1.0826 | –0.1599 | –0.0381 | 0.9955 | 1.556 | |
| (0.1345) | (0.0378) | (0.0561) | (0.4928) | ||||
| United States | 0.0614 | 0.3871 | –0.1944 | –0.5929 | 0.8109 | 0.952 | |
| (0.1256) | (0.1410) | (0.0815) | (0.2667) | ||||
| Other Developed | |||||||
| Australia | –2.7557 | 0.0842 | –0.1401 | –0.2215 | 0.3798 | 1.300 | |
| (0.3897) | (0.1513) | (0.0888) | (0.3157) | ||||
| New Zealand | –2.5278 | 0.3066 | –0.5531 | –2.6211 | 0.8001 | 1.731 | |
| (0.7083) | (0.1954) | (0.1237) | (0.7541) | ||||
| South Africa | –4.2518 | –0.2349 | –0.2676 | –0.7648 | 0.9763 | 2.474 | |
| (0.2635) | (0.0690) | (0.0658) | (0.2435) | ||||
| Turkey | –2.2235 | 0.9363 | –0.1241 | 0.2114 | 0.8691 | 1.079 | |
| (0.7540) | (0.1785) | (0.5019) | (0.4470) | ||||
| Less Developed | |||||||
| Ceylon | –2.4210 | 0.7730 | –0.2348 | –0.2915 | 0.8093 | 1.556 | |
| (0.7087) | (0.1606) | (0.1942) | (0.9797) | ||||
| China, Republic of | –0.6132 | 0.8096 | –0.8892 | 0.1239 | 0.9095 | 3.039 | |
| (0.7980) | (0.2320) | (0.3568) | (0.7511) | ||||
| Costa Rica | –1.9812 | 0.9443 | –0.1021 | –0.4387 | 0.9925 | 1.257 | |
| (0.2142) | (0.0316) | (0.0384) | (0.2324) | ||||
| India | –1.2113 | 1.3480 | 0.0171 | –0.2864 | 0.7520 | 1.454 | |
| (0.7112) | (0.4799) | (0.0884) | (0.5301) | ||||
| Mexico | –3.2901 | 0.6086 | 0.1100 | –0.4561 | 0.9809 | 1.205 | |
| (0.6544) | (0.0578) | (0.2313) | (0.1427) | ||||
Durbin-Watson test statistic.
Model I: Regression and Correlation Estimates of Equation (2.5) for Individual Countries
| Countries | a | b1 | b2 | ba | R2 | D-W Test1 | |
|---|---|---|---|---|---|---|---|
| Industrial | |||||||
| Canada | –1.8208 | 0.8678 | –0.0775 | 0.1367 | 0.9424 | 2.323 | |
| (0.2005) | (0.1451) | (0.0385) | (0.3112) | ||||
| Denmark | –0.5745 | 0.9924 | –0.5270 | 0.9351 | 0.8863 | 1.167 | |
| (0.6577) | (0.1571) | (0.1629) | (0.5020) | ||||
| France | –0.7097 | 1.2924 | –0.2175 | –0.2757 | 0.9791 | 1.266 | |
| (0.1696) | (0.0750) | (0.1191) | (0.3650) | ||||
| Germany | –1.4071 | 1.1641 | –0.3146 | –3.2497 | 0.9799 | 2.193 | |
| (0.1022) | (0.0880) | (0.0799) | (1.4947) | ||||
| Netherlands | –1.6322 | 0.5909 | –0.3395 | –0.5990 | 0.9490 | 1.334 | |
| (0.1853) | (0.0522) | (0.0771) | (0.3999) | ||||
| Norway | –2.5267 | 0.5230 | –0.1898 | –0.1717 | 0.9173 | 1.791 | |
| (0.2201) | (0.0618) | (0.0321) | (0.2394) | ||||
| Sweden | –0.8512 | 1.0461 | –0.4917 | 0.0382 | 0.8407 | 1.476 | |
| (0.8216) | (0.2706) | (0.1941) | (0.2662) | ||||
| Switzerland | –0.3195 | 1.0826 | –0.1599 | –0.0381 | 0.9955 | 1.556 | |
| (0.1345) | (0.0378) | (0.0561) | (0.4928) | ||||
| United States | 0.0614 | 0.3871 | –0.1944 | –0.5929 | 0.8109 | 0.952 | |
| (0.1256) | (0.1410) | (0.0815) | (0.2667) | ||||
| Other Developed | |||||||
| Australia | –2.7557 | 0.0842 | –0.1401 | –0.2215 | 0.3798 | 1.300 | |
| (0.3897) | (0.1513) | (0.0888) | (0.3157) | ||||
| New Zealand | –2.5278 | 0.3066 | –0.5531 | –2.6211 | 0.8001 | 1.731 | |
| (0.7083) | (0.1954) | (0.1237) | (0.7541) | ||||
| South Africa | –4.2518 | –0.2349 | –0.2676 | –0.7648 | 0.9763 | 2.474 | |
| (0.2635) | (0.0690) | (0.0658) | (0.2435) | ||||
| Turkey | –2.2235 | 0.9363 | –0.1241 | 0.2114 | 0.8691 | 1.079 | |
| (0.7540) | (0.1785) | (0.5019) | (0.4470) | ||||
| Less Developed | |||||||
| Ceylon | –2.4210 | 0.7730 | –0.2348 | –0.2915 | 0.8093 | 1.556 | |
| (0.7087) | (0.1606) | (0.1942) | (0.9797) | ||||
| China, Republic of | –0.6132 | 0.8096 | –0.8892 | 0.1239 | 0.9095 | 3.039 | |
| (0.7980) | (0.2320) | (0.3568) | (0.7511) | ||||
| Costa Rica | –1.9812 | 0.9443 | –0.1021 | –0.4387 | 0.9925 | 1.257 | |
| (0.2142) | (0.0316) | (0.0384) | (0.2324) | ||||
| India | –1.2113 | 1.3480 | 0.0171 | –0.2864 | 0.7520 | 1.454 | |
| (0.7112) | (0.4799) | (0.0884) | (0.5301) | ||||
| Mexico | –3.2901 | 0.6086 | 0.1100 | –0.4561 | 0.9809 | 1.205 | |
| (0.6544) | (0.0578) | (0.2313) | (0.1427) | ||||
Durbin-Watson test statistic.
Model III: Estimates from the Unrestricted Version of Equation (2.1)
Degrees of Freedom.
Durbin-Watson test statistic.
Model III: Estimates from the Unrestricted Version of Equation (2.1)
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| B0 | 0.0130 | 0.0109 | –0.2762 | –0.1757 |
| (0.0247) | (0.0739) | (0.0916) | (0.0118) | |
| B1 | 1.2596 | 1.4194 | 1.1048 | 1.3999 |
| (0.0926) | (0.1671) | (0.1436) | (0.0628) | |
| B2 | 0.2671 | –0.4788 | –0.3145 | –0.4238 |
| (0.0920) | (0.1527) | (0.1225) | (0.0605) | |
| B3 | 0.5020 | 0.2345 | 0.2453 | 0.2966 |
| (0.1466) | (0.1541) | (0.0935) | (0.0588) | |
| B4 | –0.4941 | –0.1969 | –0.0331 | –0.2704 |
| (0.1468) | (0.1575) | (0.0914) | (0.0594) | |
| B5 | –0.1399 | –0.2126 | –0.1356 | –0.1104 |
| (0.0241) | (0.0967) | (0.0499) | (0.0193) | |
| B6 | 0.0777 | 0.2194 | 0.0663 | 0.0852 |
| (0.0285) | (0.1347) | (0.0799) | (0.0256) | |
| B7 | 0.0539 | –0.1016 | 0.0370 | 0.0302 |
| (0.0211) | (0.0876) | (0.0483) | (0.0185) | |
| B8 | –0.5420 | –0.8682 | –1.1212 | –0.9140 |
| (0.2133) | (0.1781) | (0.1550) | (0.0932) | |
| B9 | 0.4208 | 0.3961 | 0.2048 | 0.5355 |
| (0.1459) | (0.2176) | (0.1936) | (0.0874) | |
| DF1 | 80 | 30 | 40 | 170 |
| R2 | 0.9994 | 0.9982 | 0.9990 | 0.9996 |
| D-W Test2 | 1.881 | 1.764 | 1.518 | 1.780 |
Degrees of Freedom.
Durbin-Watson test statistic.
Model III: Estimates from the Unrestricted Version of Equation (2.1)
| Quantity Estimated | Industrial Countries | Other Developed Countries | Less Developed Countries | All Countries |
|---|---|---|---|---|
| B0 | 0.0130 | 0.0109 | –0.2762 | –0.1757 |
| (0.0247) | (0.0739) | (0.0916) | (0.0118) | |
| B1 | 1.2596 | 1.4194 | 1.1048 | 1.3999 |
| (0.0926) | (0.1671) | (0.1436) | (0.0628) | |
| B2 | 0.2671 | –0.4788 | –0.3145 | –0.4238 |
| (0.0920) | (0.1527) | (0.1225) | (0.0605) | |
| B3 | 0.5020 | 0.2345 | 0.2453 | 0.2966 |
| (0.1466) | (0.1541) | (0.0935) | (0.0588) | |
| B4 | –0.4941 | –0.1969 | –0.0331 | –0.2704 |
| (0.1468) | (0.1575) | (0.0914) | (0.0594) | |
| B5 | –0.1399 | –0.2126 | –0.1356 | –0.1104 |
| (0.0241) | (0.0967) | (0.0499) | (0.0193) | |
| B6 | 0.0777 | 0.2194 | 0.0663 | 0.0852 |
| (0.0285) | (0.1347) | (0.0799) | (0.0256) | |
| B7 | 0.0539 | –0.1016 | 0.0370 | 0.0302 |
| (0.0211) | (0.0876) | (0.0483) | (0.0185) | |
| B8 | –0.5420 | –0.8682 | –1.1212 | –0.9140 |
| (0.2133) | (0.1781) | (0.1550) | (0.0932) | |
| B9 | 0.4208 | 0.3961 | 0.2048 | 0.5355 |
| (0.1459) | (0.2176) | (0.1936) | (0.0874) | |
| DF1 | 80 | 30 | 40 | 170 |
| R2 | 0.9994 | 0.9982 | 0.9990 | 0.9996 |
| D-W Test2 | 1.881 | 1.764 | 1.518 | 1.780 |
Degrees of Freedom.
Durbin-Watson test statistic.
La demande de monnaie : les enseignements des économies développées et moins développées
Résumé
Dans la présente étude, l’auteur examine l’incidence que peuvent avoir, pour le comportement de la demande de monnaie, les différences structurelles et autres entre économies développées et moins développées. La fonction spécifiée régissant la demande de monnaie fait intervenir certains éléments dynamiques, à savoir les prévisions relatives au revenu et à la rapidité de variation des prix. On établit ainsi un rapport entre les encaisses réelles désirées d’une part, et le revenu réel “attendu”, le taux d’intérêt courant et le rythme “attendu” des variations des prix, d’autre part. Pour rattacher ces variables que sont les prévisions aux phénomènes observables, on utilise un modèle permettant d’adapter les prévisions et d’observer directement la manière dont elles s’élaborent. Un premier examen de la question laisse supposer qu’il existe certaines différences entre économies développées et moins développées en ce qui concerne le comportement de cette fonction spécifiée.
On a cherché à préciser la nature de ces différences d’une manière empirique en analysant les données relatives à 18 pays. Ceux-ci ont été regroupés en trois catégories de contextes économiques – pays industriels, autres pays développés et pays moins développés – et les données relatives à chaque catégorie ont été rassemblées. Il ressort de cette analyse qu’il y a amplement matière à généralisation au sujet des encaisses monétaires désirées, mais que la fonction déterminant la demande de monnaie s’exprime toutefois sous une forme différente selon le contexte économique. On a constaté que les prévisions relatives au revenu et au taux de variation des prix s’effectuent d’autant plus rapidement que l’économie est moins développée : en ce qui concerne la catégorie des pays moins développés, on a découvert que l’élasticité des prévisions en matière de revenu était proche de l’unité. Il semble qu’il n’y ait pratiquement aucun effet de substitution entre les encaisses monétaires et les avoirs réels dans les pays industriels, alors que cet effet de substitution paraît important dans les pays moins développés. D’après les estimations, l’élasticité du revenu dans chacun des groupes ne s’écarte guère de l’unité.
La demanda de dinero: comprobación en las economías desarrolladas y en las menos desarrolladas
Resumen
En este artículo se examinan las implicaciones que, en cuanto al comportamiento de la demanda de dinero, tienen las diferencias estructurales y de otro tipo, entre las economías desarrolladas y las menos desarrolladas. La función de demanda de dinero especificada da cabida a expectativas no estáticas, con respecto tanto al ingreso como a la tasa de variación de los precios. Así es que los saldos reales deseados están relacionados con el ingreso real “esperado”, la tasa actual de interés, y la tasa “esperada” de variación de precios. Se utiliza un modelo de expectativa adaptante, que permite una investigación directa sobre la manera en que se forman las expectativas, con objeto de relacionar las variables esperadas y las magnitudes observables. Las consideraciones apriorísticas sugieren ciertas diferencias entre las economías desarrolladas y las menos desarrolladas, en cuanto al comportamiento de la función especificada.
Se ha tratado de obtener una visión empírica, analizando los datos correspondientes a 18 países. A los 18 países estudiados se les ha agrupado según tres ambientes económicos—industriales, otros desarrollados, y menos desarrollados—y se han agrupado los datos para cada una de esas categorías. Los resultados obtenidos sugieren que, aun habiendo un amplio margen para poder generalizar sobre las cantidades de dinero que se desean guardar, hay diferencias en cuanto a la forma de la función de demanda de dinero que mejor se ajuste a cada uno de los ambientes económicos. Se ha encontrado que cuanto menos desarrollada es la economía, más cortos son los desfases en la formación de expectativa con respecto al ingreso y a la tasa de variación de los precios. En el grupo de los menos desarrollados, el resultado obtenido para la elasticidad de expectativa del ingreso fue próximo a la unidad. Mientras que en los países industriales no parece haber una substitución significativa entre el dinero retenido y los activos reales, parece ser que dicha substitución es importante en los países menos desarrollados. Las elasticidades con respecto al ingreso halladas para los distintos grupos no se separan mucho de la unidad.
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.
Edgar L. Feige, “Expectations and Adjustments in the Monetary Sector,” The American Economic Review, May 1967, pp. 462–73.
See, for example, Marc Nerlove, Distributed Lags and Demand Analysis for Agricultural and Other Commodities (U.S. Department of Agriculture, Agriculture Handbook No. 141, Washington, June 1958); Phillip Cagan, “The Monetary Dynamics of Hyperinflation,” in Studies in the Quantity Theory of Money, ed. by Milton Friedman (University of Chicago Press, 1957), pp. 25–117; Milton Friedman, A Theory of the Consumption Function(Princeton University Press, 1957).
Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote 1).
For a full development of adaptive adjustment, see Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote 1).
Nerlove, op. cit.
Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote 1).
See Milton Friedman, “The Demand for Money: Some Theoretical and Empirical Results,” The Journal of Political Economy, Vol. LXVII (August 1959), pp. 327–51, and Richard T. Selden, “Monetary Velocity in the United States,” in Studies in the Quantity Theory of Money (cited in footnote 2). For examples of hyperinflation, see Cagan, op. cit.
For example, Anthony Bottomley, “Keynesian Monetary Theory and the Developing Countries,” The Indian Economic Journal, Vol. XII (1965), pp. 535–46.
See, for example, Rudolf R. Rhomberg, “Money, Income, and the Foreign Balance,” in Economic Development in Africa, ed. by E. F. Jackson (Oxford, 1965), pp. 254–56.
Peter T. Bauer and Basil S. Yamey, The Economics of Under-Developed Countries (University of Chicago Press, 1957), p. 8.
See, for example, Harvey Leibenstein, Economic Backwardness and Economic Growth (New York, 1957), especially pp. 40–41; David Horowitz, “Monetary Policy in Underdeveloped Countries,” in The Challenge of Development: A Symposium Held in Jerusalem, June 26–27, 1957 (Jerusalem, 1958), pp. 99–105; Arnold C. Harberger, “Some Notes on Inflation,” in Inflation and Growth in Latin America, ed. by Werner Baer and Isaac Kerstenetzky (Homewood, Illinois, 1964), pp. 319–51; Hugh T. Patrick, “Financial Development and Economic Growth in Underdeveloped Countries,” Economic Development and Cultural Change, Vol. XIV (1966), pp. 174–89; Arthur I. Bloomfield, “Monetary Policy in Underdeveloped Countries,” in Public Policy, Vol. VII, ed. by Carl J. Friedrich and Seymour E. Harris (Cambridge, Massachusetts, 1956), pp. 232–74; and D. Bright Singh, Economics of Development(New York, 1966).
Milton Friedman, “The Demand for Money: Some Theoretical and Empirical Results” (cited in footnote 7), p. 333.
John F. Muth, “Optimal Properties of Exponentially Weighted Forecasts,” Journal of the American Statistical Association, Vol. LV (1960), pp. 299–306.
Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote l), p. 465.
Nerlove, op. ext., p. 23.
See the references cited in footnote 11, p. 226; Henry G. Aubrey, “Investment Decisions in Underdeveloped Countries,” in Capital Formation and Economic Growth, National Bureau of Economic Research (Princeton University Press, 1955), pp. 397–440; Marion J. Levy, Jr., “Some Social Obstacles to ‘Capital Formation’ in ‘Underdeveloped Areas,’” in Capital Formation and Economic Growth, pp. 441–520; Baldwin, “Investment Policy in Underdeveloped Countries,” in Economic Development in Africa(cited in footnote 9), pp. 236–53.
See, for example, Irma Adelman and Cynthia Taft Morris, “Factor Analysis of the Interrelationship between Social and Political Variables and Per Capita Gross National Product,” The Quarterly Journal of Economics, Vol. LXXIX (1965), pp. 555–78.
That this has some operative significance is suggested, e.g., by the following statement, “The main justification usually given by planners is that the present generation does not give sufficient weight in its saving and investment decisions to future generations. Contemporary households are too shortsighted and consequently devote too large a share of their income to consumption purposes rather than to saving. It is the duty of the government—so the argument goes—to represent the welfare interests of future generations as well as contemporary households.” Baldwin, “Investment Policy in Underdeveloped Countries” (cited in footnote 16), p. 247.
“Although aversion to risk influences all producers no matter what their income levels, a rise in income seems to reduce the degree of risk aversion,” ibid., p. 242.
Aubrey, “Investment Decisions in Underdeveloped Countries” (cited in footnote 16), p. 409.
See, for example, ibid., p. 410; Bloomfield, op. cit., p. 236; and Gerald M. Meier and Robert E. Baldwin, Economic Development: Theory, History, Policy(New York, 1957), pp. 310–14.
In a study, under preparation by the author, of the behavior of inflation during the period 1949–65 in 53 countries, 30 of which are less developed, it was found that an important difference between the two groups is that variations in the year-to-year rates of inflation are wider in the less developed countries. The contrast in behavior implied, for instance, by Stephen Enke is not based on an examination of the data; in Economics for Development(Englewood Cliffs, N.J., 1963), page 219, he asserts that “There are few underdeveloped countries that do not experience at least a 5 per cent inflation of price level each year. …” In fact, outside some notable exceptions, especially in Latin America, less developed countries have not, in the period after World War II, had higher average annual rates of inflation than the developed countries.
Cagan, op. cit., p. 29.
Patrick, op. cit., pp. 174–89.
Milton Friedman and Anna Jacobson Schwartz, A Monetary History of the United States, 1867–1960(Princeton University Press, 1963), p. 660.
Raymond W. Goldsmith, The Determinants of Financial Structure(Organization for Economic Cooperation and Development, Development Centre Studies, Paris, 1966), p. 24.
Friedman and Schwartz, op. cit., p. 673.
Writing about behavior in Pakistan, Richard C. Porter has argued that because of existence near the subsistence level and the unreliability of markets for the conversion of assets into money, precautionary money balances probably form an important proportion of total wealth. “Income Velocity and Pakistan’s Second Plan,” The Pakistan Development Review, Vol. 1 (1961), pp. 24–25.
Irving Fisher, The Purchasing Power of Money (New York, 1911), p. 167.
George Garvy, “Money, Liquid Assets, Velocity and Monetary Policy,” Banca Nazionale del Lavoro, Quarterly Review, December 1964, pp. 323–38.
Clark Warburton, “The Secular Trend in Monetary Velocity,” The Quarterly Journal of Economics, Vol. LXIII (1949), p. 90.
Milton Friedman, “The Quantity Theory of Money—A Restatement,” in Studies in the Quantity Theory of Money, ed. by Milton Friedman (University of Chicago Press, 1957), pp. 5–10.
Cagan, op. cit., p. 31.
Bloomfield, op. cit.; Graeme S. Dorrance, “The Instruments of Monetary Policy in Countries Without Highly Developed Capital Markets,” Staff Papers, Vol. XII (1965), pp. 272–81; Richard C. Porter, “Narrow Security Markets and Monetary Policy: Lessons from Pakistan,” Economic Development and Cultural Change, Vol. XIV (1965), pp. 48–60.
U Tun Wai, “Interest Rates Outside the Organized Money Markets of Underdeveloped Countries,” Staff Papers, Vol. VI (1957), pp. 81–82.
Ibid., pp. 94–98.
For a discussion, see Edgar L. Feige, The Demand for Liquid Assets: A Temporal Cross-Section Analysis(Englewood Cliffs, N.J., 1964).
Harry G. Johnson, “Monetary Theory and Policy,” The American Economic Review, Vol. LII (1962), p. 351.
The relationship of the inclusiveness of the definition of money to the level of development has been examined empirically by the author in “The Demand for Money: An International Comparison,” forthcoming in The Indian Economic Journal, and in “A Note on the Friedman-Meiselman Approach to the Definition of Money,” mimeographed, May 1967. No such relationship was found to exist. Further, the conventional definition was found to be generally more appropriate. For the United States, certain studies showed that the conventional definition is appropriate, e.g., those by Feige in The Demand for Liquid Assets: A Temporal Cross-Section Analysis (cited in footnote 37), and by Allan H. Meltzer, “The Demand for Money: The Evidence from the Time Series,” The Journal of Political Economy, Vol. LXXI (1963), pp. 219–46.
Cagan, op. cit., p. 31.
For a similar approach, see Friedman, “The Quantity Theory of Money—A Restatement” (cited in footnote 32), p. 7.
Graeme S. Dorrance, “The Effect of Inflation on Economic Development,” Staff Papers, Vol. X (1963), p. 6.
For example, Austria, Germany, and Greece.
See Friedman, “The Demand for Money: Some Theoretical and Empirical Results” (cited in footnote 7); Selden, op. cit.; Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote 1).
On the effect of expected inflation on interest rates and on the behavior of businesses and households, see Martin J. Bailey, National Income and the Price Level: A Study in Macrotheory (New York, 1962). See also Reuben A. Kessel and Armen A. Alchian, “Effects of Inflation,” The Journal of Political Economy. Vol. LXX (1962), pp. 521–37.
L. M. Koyck, Distributed Lags and Investment Analysis (Amsterdam, North-Holland Publishing Co., 1954). See also Nerlove, op. cit., pp. 25–31.
International Monetary Fund, An Introduction to IFS: Reprints of introductory articles published in the January to May 1960 issues(Washington, 1960), p. 8.
H. S. Houthakker, “New Evidence on Demand Elasticities,” Econometrica, Vol. 33 (1965), p. 277.
Ibid.
Statistical significance tests are performed at the 5 per cent level.
Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote 1).
Friedman, “The Demand for Money: Some Theoretical and Empirical Results” (cited in footnote 7), p. 335.
Feige, “Expectations and Adjustments in the Monetary Sector” (cited in footnote 1).
See, for example, the discussions in H. R. Heller, “The Demand for Money: The Evidence from the Short-Run Data,” The Quarterly Journal of Economics Vol. LXXIX (1965), pp. 296-97.