Divisia Aggregates Research Articles

Nominal Stylized Facts of U.S. Business Cycles

The authors investigate the basic nominal stylized facts of business cycles in the United States, using monthly data from 1960:1 to 1993:4 and the methodology suggested by Kydland and Prescott (1990). They make comparisons among simple sum and Divisia aggregates, using the Thornton and Yue (1992) series of Divisia monetary aggregates, and they investigate the robustness of the results to relevant nonstochastic stationarity-inducing transformations.

Random Walks, Breaking Trend Functions, and the Chaotic Structure of the Velocity of Money

This article examines the times series properties of U.S. velocity series, using Zivot and Andrews's variation of Perron's test. It also tests for deterministic noisy chaos using the Nychka, Ellner, Gallant, and McCaffrey nonparametric test for positivity of the maximum Lyapunov exponent. Comparisons are made among simple-sum and Divisia aggregates using the Thornton and Yue series of Divisia monetary aggregates for an extended sample period (1960:1 to 1992:12). The conclusion is that the unit-root model cannot be rejected even if allowance is made for the possibility of a one-time break in the intercept and the slope of the trend function at an unknown point in time. There is tentative evidence, however, that the Divisia L velocity series is chaotic, implying that (nonlinearity-based) prediction might be possible (at least in the short run and provided that the actual generating mechanism is known exactly).

Breaking trend functions in the velocity of money: Evidence from the United States and Canada

This paper examines the times series properties of different velocity series, using Zivot and Andrews' (1992) variation of Perron's (1989) test. Comparisons are made among simple sum and Divisia aggregates using both United States and Canadian data. The overall conclusion is that the unit root model cannot be rejected even if allowance is made for the possibility of a one-time break in the intercept and the slope of the trend function at an unknown point in time.

PORTFOLIO DISEQUILIBRIUM: IMPLICATIONS FOR THE DIVISIA APPROACH TO MONETARY AGGREGATION*

The first part of the paper reviews the performance of the U.K.'s official monetary aggregates during the 1980s and argues that Divisia aggregation is, in principle, likely to offer a sounder basis for monetary analysis and policy. The central sections develop an econometric model of the demand for retail balances and examine the effect of portfolio disequilibrium, showing how this makes it appropriate to smooth the user costs in a particular way when using them to construct a Divisia aggregate. The final section of the paper shows that the resulting aggregate is closely associated with economic activity and prices once an allowance is made for the growth in the use of credit cards. Copyright 1994 by Blackwell Publishers Ltd and The Victoria University of Manchester

Rational expectations and the demand for money: A nonparametric approach

This paper tests the U.S. demand for money for evidence of the effect of rational expectations of the income and interest rate variables that enter as arguments into that function. The data employed are simple-sum and Divisia aggregates, and the nonparametric tests are of the identification and information orthogonality of the various monetary measures. The Akaike Criterion is used to distinguish among the alternative specifications. While non-rationality is the typical result, Divisia aggregates appear to be more “rational” than simple sum. There is evidence of mean-reversion in interest rates as well.

THE SUBSTITUTABILITY OF FINANCIAL ASSETS IN THE U.K. AND THE IMPLICATIONS FOR MONETARY AGGREGATION*

This paper assesses empirically the degree of substitutability between capital certain liquid financial assets in the United Kingdom by employing consumer demand theory. Translog share equations are specified and estimated for the various monetary assets. Expenditure elasticities, own and cross-price elasticities, and elasticities of substitution are then derived from the parameter estimates and these measures are used to provide information as to the appropriate asset components to be included in monetary aggregates. Finally, Divisia aggregation is employed to construct a monetary aggregate that is consistent with economic aggregation theory and the performance of this Divisia aggregate is then compared to simple sum monetary aggregates. Copyright 1992 by Blackwell Publishers Ltd and The Victoria University of Manchester

FINANCIAL INNOVATION AND DIVISIA MONETARY AGGREGATES*

Rapid financial innovation in the U.K. has altered the relative liquidity and productivity of financial assets. This paper shows that even a sophisticated (Divisia) monetary index does not adequately allow for the effects of financial innovation. Two modifications to Divisia monetary aggregates are proposed to capture the effects of: non-neutral transaction technology progress; and of the introduction of new financial assets. The empirical analysis reveals that the modified Divisia aggregates dominate the basic, innovation-neutral Divisia indices. The results presented in this paper strongly support the view that, because of the widespread financial innovations during the 1980s, the conventional broad monetary aggregates provide a misleading picture of the stance of monetary policy. Copyright 1992 by Blackwell Publishing Ltd

An Extended Series of Divisia Monetary Aggregates

Daniel L. Thornton and Piyu Yue discuss monetary aggregation and present an extended data series of Divisia monetary aggregates. They briefly analyze the behavior of five Divisia aggregates—M1A, M1, M2, M3, and L. Their analysis suggests that the method of aggregation is not likely to be empirically important for narrow monetary aggregates like M1A and M1 and that beyond some point, successively broader Divisia monetary aggregates are likely to behave similarly in applied work.

An Admissible Monetary Aggregate for the United Kingdom

This paper evaluates the performance of a monetary aggregate that is constructed from principles of economic and index number theory. Results from tests for weak separability indicate that wholesale deposits should not be aggregated with other U.K. financial assets; they currently are included, however, in broad monetary aggregates published by the Bank of England. Financial asset groupings passing the weak separability tests then were aggregated using both simple-sum and Divisia weights. In each case, the Divisia aggregates were more closely related to the growth of nominal GDP and had stable demand for money functions. Copyright 1991 by MIT Press. (This abstract was borrowed from another version of this item.)

Velocity effects of anticipated and unanticipated money growth and its variability

The purpose of this paper is to empirically test the relationship between velocity growth and anticipated and unanticipated money growth and its variability. In particular, by decomposing actual monetary growth into anticipated and unanticipated components, the study investigates whether knowledge of past variability of anticipated and unanticipated monetary growth improves the prediction of future velocity growth beyond predictions that are based on past velocity growth alone. This is the empirical definition of Granger causality. Comparasions are made, in all tests, among simple sum and Divisia aggregates (of M1, M2, M3, and L) and with Spindt's monetary velocity (MQ) aggregate.

On the demand for money in the United States

One of the current issues in the literature on the demand for money is whether the adjustment of actual to desired money holdings is in real or nominal terms. This paper tests the real against the nominal adjustment hypothesis using United States data. Comparisons are made among simple sum and Divisia aggregates (of M1, M2, M3, and L) and with Spindt's monetary velocity (MQ) aggregate. The results strongly support the nominal adjustment hypothesis, but they do not reveal a single uniformly best monetary aggregate.

Divisia Aggregation and Substitutability among Monetary Assets

In this paper the authors estimate the degree of substitutability among the services of money, checkable deposits, savings deposits, and time deposits in a quasi-homothetic translog utility framework for Canada. The four composites mentioned are formed by aggregating more basic assets such as checkable deposits at banks, checkable deposits at trust companies, etc. Traditionally the simple-sum aggregation has been used in this context. The authors investigate both this alternative and Divisia aggregation of the assets. They find a low degree of substitution among the services of monetary assets and provide some evidence favoring Divisia aggregation over simple-sum aggregation. Copyright 1986 by Ohio State University Press.

The Changing Empirical Definition of Money: Some Estimates from a Model of the Demand for Money Substitutes

Interest-bearing checkable deposits are examined to test whether they should be included in measures of the U.S. money stock. Both Divisia and traditional simple-sum aggregates are constructed on the basis of tests for weak separability in a model of the demand for financial assets. Using nonparametric demand analysis, we find that several groups of assets are compatible with aggregation theory. We find empirical support for a narrow measure consisting of the components of current MIA. In tests based on a St. Louis equation and in terms of controllability, a Divisia aggregate performs better than the simple-sum MIA measure.

Turnover Statistics and Federal Government Balances in Money Supply Targets

In the middle of the last decade, Congress mandated that the Federal Reserve announce its goals for monetary aggregates. This increased emphasis on aggregates combined with the more recent financial innovations and deregulation has led to considerable discussion about the best monetary aggregate. Today, arguments abound for every conceivable money stock or credit aggregate, ranging from Davidson and Hafer's support of M I [5] to Friedman's support of total net credit [7]. Given such a range of disagreement, one can empathize with the frustration that prompted a Congressional committee to ask, Can we identify a particular conception of 'money' (Ml, M2 or whatever) with sufficient precision to allow its use as a proxy for economic performance?' A promising approach to the resolution of this problem has been the substitution of weighted-sum monetary aggregates for the conventional simple-sum aggregates. In a simple-sum aggregate, each component is assigned a weight of one. For instance, one dollar of currency carries the same weight as one dollar of passbook savings. But in the Divisia aggregate approach [2], each component is assigned a weight which is proportional to the opportunity cost of holding that financial asset. Consequently, a dollar of currency, which earns no interest, carries greater weight than a dollar of passbook savings. The higher cost of holding currency directly reflects the value of its services as a medium of exchange, the basic function of money. A study by Spindt [19] uses a second weighting system based on turnover statistics. The basic assumption is that the more often a financial asset changes hands, the greater its services as a medium of exchange. Using a St. Louis type reduced-form model, Spindt discovered that his turnover-weighted aggregate bore a closer relationship to GNP than did the Federal Reserve's MI. In his detailed analysis, Spindt estimates some time series that are not directly measured, for example, the turnover of currency. As a result, he does not advocate the substitution of his aggregate index for the conventional aggregates. Nevertheless, he does point out that the integration of the turnover statistics may be helpful in explaining certain anomalies in the behavior of the conventional aggregates [19, 24].

The monetary multiplier when money is measured as a Divisia quantity index

Abstract The traditional algebraic derivation of the monetary multiplier for conventional simple sum monetary aggregates is extended to cover the case of money defined as a Divisia monetary quantity index. Thus, the procedures developed by Johannes and Rasche for assessing the controllability of money can be applied to the issue of controllability of the Divisia aggregates.

The velocity behavior and information content of Divisia monetary aggregates

Monetary aggregates are commonly sums, although summation quantity aggregation is disreputable. We compare summation versus Divisia aggregation of monetary assets. The velocity behavior and the information content of the Divisia index are superior to those of the summation index.