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The basic functions of money
Economics Letters 5 (1980) 353-357 0 North-Holland Publishing Company
THE BASIC FUNCTIONS OF MONEY An Application of the Input Independence
Transformation
*
Edward K. OFFENBACHER Federal Reserve System, Washington, DC 20551, Received
25 September
USA
1980
Theil’s input independence transformation is applied to consumer demand for components of newly defined M-3 to interpret an empirical formulation of the basic functions of money. The results are largely consist with conventional a priori notions, especially regarding importance of liquidity.
1. Introduction Economists have long sought to explain the basic functions of money in an economy. While previous attempts to understand money’s role have been based on a prioly approaches where basic functions are defined without direct appeal to quantitative evidence, one may also consider empirically based approaches where the data are used in some manner to suggest interpretations of the basic characteristics. In a somewhat different context, Friedman and Schwartz (1970, p. 90) advocate such an empirically oriented approach. Until recently, one of the problems with the empirical approach has been the lack of a formal, systematic methodology for organizing data in a way that is suitable for interpretation. The work by Theil and his associates on the input independence transformation (IIT) is an important contribution towards alleviating this difficulty in that it does propose a rigorous and general operational method for organizing data on prices and quantities of a given set of com-
* This paper is part of an ongoing project at the Federal Reserve Board concerned with the application of economic aggregation and index number theory to the problem of defining monetary quantity indexes. Barnett, Offenbacher and Spindt (1980) surveys the project. I am indebted to William A. Barnett, Richard D. Porter, Stephen P. Taylor and Henri Theil for helpful comments and suggestions but I am responsible for any remaining errors. The views expressed here are solely my own and do not necessarily represent those of the Board of Governors of the Federal Reserve System or of its staff members. 353
354
E.K. Offenbacher
/ The basic functions
of money
modities in a way that is likely to yield interesting interpretations. ’ This letter presents an application of IIT to the consumer sector holdings of monetary assets. 2 The application to money is of particular interest precisely because very strong prior expectations exist, yet the complete generality of IIT insures that the prior expectations do not influence the results. The findings suggest that the overwhelmingly dominant motive for holding money is a liquidity motive rather than store-of-value or some other motive. Some evidence of a weak, specific type of store-of-value motive is found and no additional motives could be discerned.
2. Methodology Application of IIT requires that prices and quantities of the underlying goods or assets be well and appropriately defined. In the monetary case, quantities are easily defined as real per capita amounts of consumer sector holdings of newly defined M-3. In order to construct consumer sector holdings, the Federal Reserve Board’s Demand Deposit Ownership Survey is used to determine the consumers’ share of demand deposits, the flow-of-funds data are used to determine the consumers’ share of large time deposits and the entire amount of the following components are assumed to be held by consumers: currency, other checkable deposits, savings accounts, small time accounts and money market mutual fund shares. 3 The data are monthly for 1972-1979. The specification of prices is not as straightforward and requires some elaboration. Since monetary assets are durable, the cost of holding a given monetary asset for a period shorter than its full life is its user cost, not its purchase price. Thus, in theory, it is incorrect to simply add together the quantities of different monetary assets on the grounds that a dollar’s worth of each asset costs a dollar because ‘that dollar’ is the purchase price, not the user cost [see Barnett (1979) and Fisher and McAleer (1980)]. The appropriate user cost for monetary assets is the interest bearing asset. Thus, for a given monetary asset, the user cost is defined operationally as the differential between the rate of return on a benchmark, non-monetary asset and the own rate of return on that monetary asset. While the specification of own rates is not particularly problematic, the problem of choosing an empirical proxy for the benchmark rate is difficult and is not yet resolved completely. The empirical proxy 1 See Theil (1977 and 1980) for discussion of the IIT. The present exposition in terms of the IIT, rather than the preference independence transformation, is motivated by a household production notion that views consumers as producers of monetary services using the monetary assets as inputs. This approach alleviates somewhat the conceptual problems associated with the terms ‘money in the utility function’ and ‘cardinal vs. ordinal’. 2 A more detailed exposition is in Offenbacher (1980). 3 The assignment of these total amounts to consumers is a reasonable reflection of reality, which probably accounts for the lack of disaggregated data.
E.K. Offenbacher
/ The basic functions
of money
355
used here is the maximum in each period of the returns on eight short-term financial assets and one long-term yield. The long-term yield is included as a proxy for the expected holding period yield on long-term bonds based on the finding that long-term yields tend to fall when they exceed short-term yields [see Shiller (1979)]. The high multi-collinearity of the own rates, as well as the fact that data for money market mutual funds begin only in 1974 necessitate some aggregation of the components prior to estimating the Rotterdam consumer demand model on which IIT is based. Accordingly, Divisia price and quantity indexes are constructed for three groups of components: (1) transactions balances comprised of currency and demand deposits, (2) a highly liquid alternative group including savings and small time accounts, other checkable deposits and money market mutual funds, and (3) a less liquid alternative group comprised of small and large time accounts. In order to apply IIT the relative price version of the Rotterdam model is estimated using Wymer’s RESIMUL program to obtain FIML estimates by the NewtonRaphson optimization procedure. The differential derived demand equation for the ith asset is wid(logqi)
= Oid(log
e>
+ @~k@ikd[b&-‘k/~‘>l
:
where pi, qi and wi = piqi/E are the price, quantity and budget share of the ith asset (E = Cpiqi), dlog Q = Ciwid(log gj), l/@~= the income elasticity of the marginal utility of income, d(log 8”) = CiBid(lOg pi) and tiii = the i, jth normalized price coefficient, a parameter that captures specific substitution effects. Estimation of the Bii requires the imposition of one arbitrary identifying restriction so that for applications where all over-identified models are statistically rejected, any just-identified model that satisfies all theoretical restrictions, e.g., concavity, is as plausible a model as any other such model. In the present application, all over-identifying combinations of zero restrictions on the off-diagonal elements of the 0 = {6’,} matrix, as well as all over-identifying equality restrictions on these elements were rejected by likelihood ratio tests at the 0.05 significance level. The results presented here are for the exactly identified model with 0 r2 = 0. While this model provided the cleanest interpretation, the interpretation of other exactly identified models is similar. 4 The IIT is a diagonalization of the normalized price coefficient matrix, 0, relative to a given budget share vector, chosen here as the mean budget share vector. The transformation changes observed assets to transformed assets (T-assets) that are neither specific substitutes nor specific complements for each other. The results of the transformation that are most useful for interpretation are the eigenvalues of the diagonalization (XJ, which can be interpreted as the elasticities of the T-assets with respect to the total foregone interest expense, and the composition matrix of the transformation, which is related to the eigenvectors. The elements of each row of 4 Results shifts.
for various
sub-periods
are also similar and do not suggest the presence
of structural
E.K. Offenbacher
356
/ The basic functions
of money
the composition matrix give the contribution of each observed asset to the budget share of the row’s T-asset. The row sums are budget shares of the T-assets; the column sums are budget shares of the observed goods. The composition matrix and expenditure elasticities for the three monetary assets are presented in table 1. The first T-asset, Tr, has by far the largest budget share and the largest contribution to this share comes from transactions balances with the magnitudes of the contributions of the two alternative groups being in the same order as their presumed liquidity. Thus, Tr can be interpreted as a liquidity function or motive. Note that its expenditure elasticity is near unity suggesting that, for consumers, production of liquidity is subject to constant returns to scale in the monetary assets. T2 is a contrast between transactions balances and the two alternative monetary assets, having a 14 percent budget share and a very low expenditure elasticity, 0.036. This T-asset can be interpreted as a special type of store-of-value motive that can be thought of as a rainy day nest egg. In other words consumers apparently wish to accumulate a given amount of wealth, mainly in time accounts, to serve as an accessible store of wealth in the sense that it is Federally insured and readily available even if pre-payment penalties are incurred. However, its small expenditure elasticity suggests that consumers do not wish to add to this nest egg as total expenditure rises. The third T-asset, Ta, is difficult to interpret, however, this is not overly surprising since the liquidity and store of wealth motives are the two most often discussed a priori basic characteristics. In conclusion, the evidence does confirm the a priori notions of the basic functions of money. While this finding is of interestin its own right, a clear understanding of the functions of monetary assets can be useful for the more practical purpose of assessing the likely impact of proposed changes in monetary institutions, e.g., introduction of new assets. Further research with more highly disaggregated systems is desirable in the hope that richer interpretations will be forthcoming.
Table 1 Results of input independence Composition Transactions
Tl T2 T3
2 cols
transformation.
matrix Very liquid
c rows
Expenditure elasticity
0.78 0.14 0.08
1.12 0.04 1.57
Less liquid
0.47 -0.08 -0.04
0.17 0.05 0.16
0.13 0.17 -0.05
0.35
0.39
0.26
1
E.K. Offenbacher
/ The basic functions
of money
357
References Barnett, William A., 1979, The user cost of money, Economics Letters 1, 1455149. Barnett, William A., Edward K. Offenbacher and Paul A. Spindt, 1980, New concepts of aggregated money, Journal of Finance (forthcoming in Papers and Proceedings issue). Fisher, Gordon and Michael McAleer, 1980, Theory and econometric evaluation of a systems approach to the demand for money: The Canadian case, Paper presented at the ASSA convention, Sept. (Denver, CO). Friedman, Milton and Anna J. Schwartz, 1970, Monetary statistics of the United States (Columbia University Press for N.B.E.R., New York). Offenbacher, Edward, 1980, Disaggregated monetary asset demand systems: Estimation and an application of the preference independence transformation, Board of Governors of the Federal Reserve System, Special Studies Paper no. 144. Shiller, Robert J., 1979, The volatility of long-term interest rates and expectations models of the term structure, Journal of Political Economy 87, 1190-1219. Theil, Henri, 1977, The independent inputs of production, Econometrica 45,1303-1327. Theil, Henri, 1980, The system-wide approach to micro-economics (University of Chicago Press, Chicago, IL).
THE BASIC FUNCTIONS OF MONEY An Application of the Input Independence
Transformation
*
Edward K. OFFENBACHER Federal Reserve System, Washington, DC 20551, Received
25 September
USA
1980
Theil’s input independence transformation is applied to consumer demand for components of newly defined M-3 to interpret an empirical formulation of the basic functions of money. The results are largely consist with conventional a priori notions, especially regarding importance of liquidity.
1. Introduction Economists have long sought to explain the basic functions of money in an economy. While previous attempts to understand money’s role have been based on a prioly approaches where basic functions are defined without direct appeal to quantitative evidence, one may also consider empirically based approaches where the data are used in some manner to suggest interpretations of the basic characteristics. In a somewhat different context, Friedman and Schwartz (1970, p. 90) advocate such an empirically oriented approach. Until recently, one of the problems with the empirical approach has been the lack of a formal, systematic methodology for organizing data in a way that is suitable for interpretation. The work by Theil and his associates on the input independence transformation (IIT) is an important contribution towards alleviating this difficulty in that it does propose a rigorous and general operational method for organizing data on prices and quantities of a given set of com-
* This paper is part of an ongoing project at the Federal Reserve Board concerned with the application of economic aggregation and index number theory to the problem of defining monetary quantity indexes. Barnett, Offenbacher and Spindt (1980) surveys the project. I am indebted to William A. Barnett, Richard D. Porter, Stephen P. Taylor and Henri Theil for helpful comments and suggestions but I am responsible for any remaining errors. The views expressed here are solely my own and do not necessarily represent those of the Board of Governors of the Federal Reserve System or of its staff members. 353
354
E.K. Offenbacher
/ The basic functions
of money
modities in a way that is likely to yield interesting interpretations. ’ This letter presents an application of IIT to the consumer sector holdings of monetary assets. 2 The application to money is of particular interest precisely because very strong prior expectations exist, yet the complete generality of IIT insures that the prior expectations do not influence the results. The findings suggest that the overwhelmingly dominant motive for holding money is a liquidity motive rather than store-of-value or some other motive. Some evidence of a weak, specific type of store-of-value motive is found and no additional motives could be discerned.
2. Methodology Application of IIT requires that prices and quantities of the underlying goods or assets be well and appropriately defined. In the monetary case, quantities are easily defined as real per capita amounts of consumer sector holdings of newly defined M-3. In order to construct consumer sector holdings, the Federal Reserve Board’s Demand Deposit Ownership Survey is used to determine the consumers’ share of demand deposits, the flow-of-funds data are used to determine the consumers’ share of large time deposits and the entire amount of the following components are assumed to be held by consumers: currency, other checkable deposits, savings accounts, small time accounts and money market mutual fund shares. 3 The data are monthly for 1972-1979. The specification of prices is not as straightforward and requires some elaboration. Since monetary assets are durable, the cost of holding a given monetary asset for a period shorter than its full life is its user cost, not its purchase price. Thus, in theory, it is incorrect to simply add together the quantities of different monetary assets on the grounds that a dollar’s worth of each asset costs a dollar because ‘that dollar’ is the purchase price, not the user cost [see Barnett (1979) and Fisher and McAleer (1980)]. The appropriate user cost for monetary assets is the interest bearing asset. Thus, for a given monetary asset, the user cost is defined operationally as the differential between the rate of return on a benchmark, non-monetary asset and the own rate of return on that monetary asset. While the specification of own rates is not particularly problematic, the problem of choosing an empirical proxy for the benchmark rate is difficult and is not yet resolved completely. The empirical proxy 1 See Theil (1977 and 1980) for discussion of the IIT. The present exposition in terms of the IIT, rather than the preference independence transformation, is motivated by a household production notion that views consumers as producers of monetary services using the monetary assets as inputs. This approach alleviates somewhat the conceptual problems associated with the terms ‘money in the utility function’ and ‘cardinal vs. ordinal’. 2 A more detailed exposition is in Offenbacher (1980). 3 The assignment of these total amounts to consumers is a reasonable reflection of reality, which probably accounts for the lack of disaggregated data.
E.K. Offenbacher
/ The basic functions
of money
355
used here is the maximum in each period of the returns on eight short-term financial assets and one long-term yield. The long-term yield is included as a proxy for the expected holding period yield on long-term bonds based on the finding that long-term yields tend to fall when they exceed short-term yields [see Shiller (1979)]. The high multi-collinearity of the own rates, as well as the fact that data for money market mutual funds begin only in 1974 necessitate some aggregation of the components prior to estimating the Rotterdam consumer demand model on which IIT is based. Accordingly, Divisia price and quantity indexes are constructed for three groups of components: (1) transactions balances comprised of currency and demand deposits, (2) a highly liquid alternative group including savings and small time accounts, other checkable deposits and money market mutual funds, and (3) a less liquid alternative group comprised of small and large time accounts. In order to apply IIT the relative price version of the Rotterdam model is estimated using Wymer’s RESIMUL program to obtain FIML estimates by the NewtonRaphson optimization procedure. The differential derived demand equation for the ith asset is wid(logqi)
= Oid(log
e>
+ @~k@ikd[b&-‘k/~‘>l
:
where pi, qi and wi = piqi/E are the price, quantity and budget share of the ith asset (E = Cpiqi), dlog Q = Ciwid(log gj), l/@~= the income elasticity of the marginal utility of income, d(log 8”) = CiBid(lOg pi) and tiii = the i, jth normalized price coefficient, a parameter that captures specific substitution effects. Estimation of the Bii requires the imposition of one arbitrary identifying restriction so that for applications where all over-identified models are statistically rejected, any just-identified model that satisfies all theoretical restrictions, e.g., concavity, is as plausible a model as any other such model. In the present application, all over-identifying combinations of zero restrictions on the off-diagonal elements of the 0 = {6’,} matrix, as well as all over-identifying equality restrictions on these elements were rejected by likelihood ratio tests at the 0.05 significance level. The results presented here are for the exactly identified model with 0 r2 = 0. While this model provided the cleanest interpretation, the interpretation of other exactly identified models is similar. 4 The IIT is a diagonalization of the normalized price coefficient matrix, 0, relative to a given budget share vector, chosen here as the mean budget share vector. The transformation changes observed assets to transformed assets (T-assets) that are neither specific substitutes nor specific complements for each other. The results of the transformation that are most useful for interpretation are the eigenvalues of the diagonalization (XJ, which can be interpreted as the elasticities of the T-assets with respect to the total foregone interest expense, and the composition matrix of the transformation, which is related to the eigenvectors. The elements of each row of 4 Results shifts.
for various
sub-periods
are also similar and do not suggest the presence
of structural
E.K. Offenbacher
356
/ The basic functions
of money
the composition matrix give the contribution of each observed asset to the budget share of the row’s T-asset. The row sums are budget shares of the T-assets; the column sums are budget shares of the observed goods. The composition matrix and expenditure elasticities for the three monetary assets are presented in table 1. The first T-asset, Tr, has by far the largest budget share and the largest contribution to this share comes from transactions balances with the magnitudes of the contributions of the two alternative groups being in the same order as their presumed liquidity. Thus, Tr can be interpreted as a liquidity function or motive. Note that its expenditure elasticity is near unity suggesting that, for consumers, production of liquidity is subject to constant returns to scale in the monetary assets. T2 is a contrast between transactions balances and the two alternative monetary assets, having a 14 percent budget share and a very low expenditure elasticity, 0.036. This T-asset can be interpreted as a special type of store-of-value motive that can be thought of as a rainy day nest egg. In other words consumers apparently wish to accumulate a given amount of wealth, mainly in time accounts, to serve as an accessible store of wealth in the sense that it is Federally insured and readily available even if pre-payment penalties are incurred. However, its small expenditure elasticity suggests that consumers do not wish to add to this nest egg as total expenditure rises. The third T-asset, Ta, is difficult to interpret, however, this is not overly surprising since the liquidity and store of wealth motives are the two most often discussed a priori basic characteristics. In conclusion, the evidence does confirm the a priori notions of the basic functions of money. While this finding is of interestin its own right, a clear understanding of the functions of monetary assets can be useful for the more practical purpose of assessing the likely impact of proposed changes in monetary institutions, e.g., introduction of new assets. Further research with more highly disaggregated systems is desirable in the hope that richer interpretations will be forthcoming.
Table 1 Results of input independence Composition Transactions
Tl T2 T3
2 cols
transformation.
matrix Very liquid
c rows
Expenditure elasticity
0.78 0.14 0.08
1.12 0.04 1.57
Less liquid
0.47 -0.08 -0.04
0.17 0.05 0.16
0.13 0.17 -0.05
0.35
0.39
0.26
1
E.K. Offenbacher
/ The basic functions
of money
357
References Barnett, William A., 1979, The user cost of money, Economics Letters 1, 1455149. Barnett, William A., Edward K. Offenbacher and Paul A. Spindt, 1980, New concepts of aggregated money, Journal of Finance (forthcoming in Papers and Proceedings issue). Fisher, Gordon and Michael McAleer, 1980, Theory and econometric evaluation of a systems approach to the demand for money: The Canadian case, Paper presented at the ASSA convention, Sept. (Denver, CO). Friedman, Milton and Anna J. Schwartz, 1970, Monetary statistics of the United States (Columbia University Press for N.B.E.R., New York). Offenbacher, Edward, 1980, Disaggregated monetary asset demand systems: Estimation and an application of the preference independence transformation, Board of Governors of the Federal Reserve System, Special Studies Paper no. 144. Shiller, Robert J., 1979, The volatility of long-term interest rates and expectations models of the term structure, Journal of Political Economy 87, 1190-1219. Theil, Henri, 1977, The independent inputs of production, Econometrica 45,1303-1327. Theil, Henri, 1980, The system-wide approach to micro-economics (University of Chicago Press, Chicago, IL).