Divisia Monetary Aggregates
Encyclopedia
In econometrics
and official statistics
, and particularly in banking, the Divisia monetary aggregates index is an index
of money supply
. It is a particular application of a Divisia index
to monetary aggregates.
currently in use by the Federal Reserve (and most other central bank
s around the world) are simple-sum indexes, in which all monetary components are assigned a unitary weight, as follows
where
is one of the 
monetary components of the monetary aggregate 
. 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
. It has been argued, however, that such an index
cannot, in general, represent a valid structural economic variable for the services of the quantity of money.
Over the years, there have been many attempts at properly weighting monetary components within a simple-sum aggregate. Without theory, however, any weighting scheme was questionable. Since 1980, 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
in his 1986 PhD dissertation.
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
formula for consumer goods 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
for
, where
is the expenditure share of asset
during period 
, and 
is the user cost of asset 
, derived by Barnett (1978),
which is just the opportunity cost
of holding a dollar's worth of the
th asset. In the last equation, 
is the market yield
on the
th asset, and 
is the yield available on a 'benchmark' asset that is held only to carry wealth
between different time periods.
In the literature on aggregation and index number theory, the Divisia approach to monetary aggregation,
, is widely viewed as a viable and theoretically appropriate alternative to the simple-sum approach. See, e.g., International Monetary Fund (2008), Macroeconomic Dynamics (2009), and Journal of Econometrics (2011). The simple-sum approach, 
, which is still in use by some central banks, adds up imperfect substitutes, such as currency and non-negotiable certificates of deposit, without weights reflecting differences in their contributions to the economy's liquidity. A primary source of theory, applications, and data from the aggregation-theoretic approach to monetary aggregation is the Center for Financial Stability in New York City. More details regarding the Divisia approach to monetary aggregation are provided by Barnett, Fisher, and Serletis (1992), Barnett and Serletis (2000), and Serletis (2007. Divisia Monetary Aggregates are available for the United Kingdom by the Bank of England, for the United States by the Federal Reserve Bank of St. Louis, and for Poland by the National Bank of Poland. Divisia monetary aggregates are maintained for internal use by the European Central Bank, the Bank of Japan, the Bank of Israel, and the International Monetary Fund.
Econometrics
Econometrics has been defined as "the application of mathematics and statistical methods to economic data" and described as the branch of economics "that aims to give empirical content to economic relations." More precisely, it is "the quantitative analysis of actual economic phenomena based on...
and official statistics
Official statistics
Official statistics are statistics published by government agencies or other public bodies such as international organizations. They provide quantitative or qualitative information on all major areas of citizens' lives, such as economic and social development, living conditions, health, education,...
, and particularly in banking, the Divisia monetary aggregates index is an index
Index (economics)
In economics and finance, an index is a statistical measure of changes in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices track economic health from...
of money supply
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...
. It is a particular application of a Divisia index
Divisia index
A Divisia index is a theoretical construct to create index number series for continuous-time data on prices and quantities of goods exchanged.It is designed to incorporate quantity and price changes over time from subcomponents which are measured in different units -- e.g...
to monetary aggregates.
Background
The monetary aggregatesMoney supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...
currently in use by the Federal Reserve (and most other central bank
Central bank
A central bank, reserve bank, or monetary authority is a public institution that usually issues the currency, regulates the money supply, and controls the interest rates in a country. Central banks often also oversee the commercial banking system of their respective countries...
s around the world) are simple-sum indexes, in which all monetary components are assigned a unitary weight, as follows
where
is one of the monetary components of the monetary aggregate . This summationSummation
Summation is the operation of adding a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed may be integers, rational numbers,...
index implies that all monetary components contribute equally to the money total, and it views all components as dollar for dollar perfect substitutes
Substitute good
In economics, one way we classify goods is by examining the relationship of the demand schedules when the price of one good changes. This relationship between demand schedules leads economists to classify goods as either substitutes or complements. Substitute goods are goods which, as a result...
. It has been argued, however, that such an index
Index (economics)
In economics and finance, an index is a statistical measure of changes in a representative group of individual data points. These data may be derived from any number of sources, including company performance, prices, productivity, and employment. Economic indices track economic health from...
cannot, in general, represent a valid structural economic variable for the services of the quantity of money.
Over the years, there have been many attempts at properly weighting monetary components within a simple-sum aggregate. Without theory, however, any weighting scheme was questionable. Since 1980, 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
Money supply
In economics, the money supply or money stock, is the total amount of money available in an economy at a specific time. There are several ways to define "money," but standard measures usually include currency in circulation and demand deposits .Money supply data are recorded and published, usually...
. This new approach to monetary aggregation was derived and advocated by William A. Barnett
William A. Barnett
William Arnold Barnett is an American economist whose current work is in the field of chaos, bifurcation, and nonlinearity in socioeconomic contexts, as well as the study of the aggregation problem....
(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
Salam Fayyad
Salam Fayyad is a Palestinian politician and Prime Minister of the Palestinian National Authority of the Palestinian National Authority. His first appointment, on 15 June 2007, which was justified by President Mahmoud Abbas on the basis of "national emergency", has not been confirmed by the...
in his 1986 PhD dissertation.
The Divisia index (in discrete time) is defined as
according to which the growth rate of the aggregate is the weighted average
Weighted mean
The weighted mean is similar to an arithmetic mean , where instead of each of the data points contributing equally to the final average, some data points contribute more than others...
of the growth rates of the component quantities. The original continuous time Divisia index
Divisia index
A Divisia index is a theoretical construct to create index number series for continuous-time data on prices and quantities of goods exchanged.It is designed to incorporate quantity and price changes over time from subcomponents which are measured in different units -- e.g...
formula for consumer goods 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
for
, whereis the expenditure share of asset
Asset
In financial accounting, assets are economic resources. Anything tangible or intangible that is capable of being owned or controlled to produce value and that is held to have positive economic value is considered an asset...
during period , and is the user cost of asset , derived by Barnett (1978),which is just the opportunity cost
Opportunity cost
Opportunity cost is the cost of any activity measured in terms of the value of the best alternative that is not chosen . It is the sacrifice related to the second best choice available to someone, or group, who has picked among several mutually exclusive choices. The opportunity cost is also the...
of holding a dollar's worth of the
th asset. In the last equation, is the market yieldYield (finance)
In finance, the term yield describes the amount in cash that returns to the owners of a security. Normally it does not include the price variations, at the difference of the total return...
on the
th asset, and is the yield available on a 'benchmark' asset that is held only to carry wealthWealth
Wealth is the abundance of valuable resources or material possessions. The word wealth is derived from the old English wela, which is from an Indo-European word stem...
between different time periods.
In the literature on aggregation and index number theory, the Divisia approach to monetary aggregation,
, is widely viewed as a viable and theoretically appropriate alternative to the simple-sum approach. See, e.g., International Monetary Fund (2008), Macroeconomic Dynamics (2009), and Journal of Econometrics (2011). The simple-sum approach, , which is still in use by some central banks, adds up imperfect substitutes, such as currency and non-negotiable certificates of deposit, without weights reflecting differences in their contributions to the economy's liquidity. A primary source of theory, applications, and data from the aggregation-theoretic approach to monetary aggregation is the Center for Financial Stability in New York City. More details regarding the Divisia approach to monetary aggregation are provided by Barnett, Fisher, and Serletis (1992), Barnett and Serletis (2000), and Serletis (2007. Divisia Monetary Aggregates are available for the United Kingdom by the Bank of England, for the United States by the Federal Reserve Bank of St. Louis, and for Poland by the National Bank of Poland. Divisia monetary aggregates are maintained for internal use by the European Central Bank, the Bank of Japan, the Bank of Israel, and the International Monetary Fund.