It has been argued that such an index does not weight such components in a way that properly summarizes the services of the quantities of money.
An index can rigorously apply microeconomic- and aggregation-theoretic foundations in the construction of monetary aggregates.
That 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.
Salam Fayyad's 1986 PhD dissertation did early research with those aggregates using U.S. data.
The discrete time Divisia weights are defined as the expenditure shares averaged over the two periods of the change for
, derived by Barnett (1978), Which is the opportunity cost of holding a dollar's worth of the
is the yield available on a benchmark asset, held only to carry wealth between different time periods.
, is widely viewed as a viable and theoretically appropriate alternative to the simple-sum approach.
See, for example, International Monetary Fund (2008), Macroeconomic Dynamics (2009), and Journal of Econometrics (2011).
, 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.
Keating et al. (2019)[1] develop an econometric framework to evaluate monetary policy transmission mechanisms, conducting a systematic comparison between the federal funds rate and Divisia M4 over the period 1960-2017.
Their findings suggest that Divisia M4 may provide more theoretically consistent counterfactuals across both crisis and non-crisis periods, whereas federal funds rate specifications sometimes produce empirical puzzles.
The authors' model incorporating Divisia M4 appears to capture certain aspects of temporal heterogeneity in policy shock effects.