The monetary aggregates currently in use by the Federal Reserve (and most other central banks around the world) are simple-sum indices in which all monetary components are assigned a unitary weight, as follows This article or section does not cite any references or sources. ... This article or section does not cite any references or sources. ...

where x_jt is one of the n monetary components of the monetary aggregate M_t. This summation index implies that all monetary components contribute equally to the money total and it views all components as dollar for dollar perfect substitutes. Such an index, however cannot, in general, represent a valid structural economic variable for the services of the quantity of money. For evaluation of sums in closed form see evaluating sums. ... In economics, one kind of good (or service) is said to be a substitute good for another kind insofar as the two kinds of goods can be consumed or used in place of one another in at least some of their possible uses. ... In economics and finance an index (for example a price index, a stockmarket index) is a benchmark of activity, performance or any evolution in general. ...

Over the years, there have been many attempts at properly weighting monetary components within a simple-sum aggregate. With no theory, however, any weighting scheme is questionable. Recently, however, attention has been focused on the gains that can be achieved by a rigorous use of microeconomic- and aggregation-theoretic foundations in the construction of monetary aggregates. This new approach to monetary aggregation was derived and advocated by William A. Barnett (1980) and has led to the construction of monetary aggregates based on Diewert's (1976) class of superlative quantity index numbers. The new aggregates are called the Divisia aggregates or Monetary Services Indexes. Early research with those aggregates using American data was done by Salam Fayyad. Microeconomics is the study of the economic behaviour of individual consumers, firms, and industries and the distribution of production and income among them. ... This article or section does not cite any references or sources. ... William Arnold Barnett is an American economist whose current work is in the field of chaos and nonlinearity in socioeconomic contexts, as well as the study of the aggregation problem. ... Dr. Salam Fayyad (Arabic: ; b. ...

The Divisia index (in discrete time) is defined as

according to which the growth rate of the aggregate is the weighted average of the growth rates of the component quantities. The original continuous time Divisia index was derived by Francois Divisia in his classic paper published in French in 1925 in the Revue d'Economie Politique. The discrete time Divisia weights are defined as the expenditure shares averaged over the two periods of the change In statistics, given a set of data, X = { x1, x2, ..., xn} and corresponding weights, W = { w1, w2, ..., wn} the weighted mean is calculated as Note that if all the weights are equal, the weighted mean is the same as the arithmetic mean. ...

for j = 1,...,n, where

is the expenditure share of asset j during period t, and π_jt is the user cost of asset j, derived in Banett (1978), In business and accounting an asset is anything owned which can produce future economic benefit, whether in possession or by right to take possession, by a person or a group acting together, e. ...

which is just the opportunity cost of holding a dollar's worth of the jth asset. In the last equation, r_jt is the market yield on the jth asset, and R_t is the yield available on a 'benchmark' asset that is held only to carry wealth between multiperiods. In economics, opportunity cost, or economic cost, is the cost of something in terms of an opportunity forgone (and the benefits which could be received from that opportunity), or the most valuable forgone alternative (or highest-valued option forgone), i. ... In financial economics, the yield of a financial instrument/security (finance), usually a debt instrument, or other investment is the rate of return the holder earns on that instrument. ... Wealth from the old English word weal, which means well-being or welfare. The term was originally an adjective to describe the possession of such qualities. ...

The Divisia approach to monetary aggregation represents a viable and theoretically appropriate alternative to the simple-sum approach, which is unfortunately still in use by some central banks. Barnett, Fisher, and Serletis (1992), Barnett and Serletis (2000), and Serletis (2007) provide more details regarding the Divisia approach to monetary aggregation. Divisia Monetary Aggregates are available for the United Kingdom by the Bank of England and for the United States by the Federal Reserve Bank of St. Louis.

References

• Barnett, William A. "The User Cost of Money". Economics Letters (1978), 145-149.

• Barnett, William A. "Economic Monetary Aggregates: An Application of Aggregation and Index Number Theory", Journal of Econometrics 14 (1980), 11-48.

• Barnett, William A. and Apostolos Serletis. The Theory of Monetary Aggregation. Contributions to Economic Analysis 245. Amsterdam: North-Holland (2000).

• Barnett, William A., Douglas Fisher, and Apostolos Serletis. "Consumer Theory and the Demand for Money". Journal of Economic Literature 30 (1992), 2086-2119.

• Diewert, W. Erwin. "Exact and Superlative Index Numbers". Journal of Econometrics 4 (1976), 115-146.

• Serletis, Apostolos. The Demand for Money: Theoretical and Empirical Approaches. Springer (2007).