Divisia Second Moments: An Application of Stochastic Index Number Theory

Barnett, William A.; Jones, Barry E. and Nesmith, Travis D. (2008): Divisia Second Moments: An Application of Stochastic Index Number Theory. Unpublished.

Abstract

W. A. Barnett originated the Divisia monetary aggregates, using Diewert's results on superlative index numbers and Barnett's derivation of the user cost of monetary asset services. The resulting Divisia index can be interpreted as a first moment aggregating over growth rates with expenditure shares serving as probabilities. But Theil showed that there are analogous higher order Divisia moments providing distributional information. In this paper we use the Divisia second moments to investigate distributional information in the monetary aggregate growth rates and to measure aggregation error in the Divisia first moments.

• Item Type: MPRA Paper
• Language: English
• Keywords: Divisia monetary aggregates; Divisia second moments; monetary aggregation; monetary policy; distribution effects
• Subjects: E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E51 - Money Supply; Credit; Money Multipliers; E - Macroeconomics and Monetary Economics > E5 - Monetary Policy, Central Banking, and the Supply of Money and Credit > E52 - Monetary Policy (Targets, Instruments, and Effects); E - Macroeconomics and Monetary Economics > E0 - General > E01 - Measurement and Data on National Income and Product Accounts and Wealth; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates; G - Financial Economics > G0 - General; E - Macroeconomics and Monetary Economics > E4 - Money and Interest Rates > E41 - Demand for Money; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods: General

References

Barnett, W. A. 1978, “The User Cost of Money,” Economics Letters 1: 145-149.

Barnett, W. A. 1980, “Economic Monetary Aggregates: An Application of Index Number and Aggregation Theory, Journal of Econometrics 14: 11-48.

Barnett, W. A., E. K. Offenbacher, and P. A. Spindt, 1984. “The New Divisia Monetary Aggregates,” Journal of Political Economy 29 (6): 1049-1085.

Barnett, W. A., and A. Serletis. 1990. “A Dispersion-Dependency Diagnostic Test for Aggregation Error: With Applications to Monetary Economics and Income Distribution.” Journal of Econometrics 43: 5-34.

Chrystal, K. A., and R. MacDonald. 1984. “Empirical Evidence on the Recent Behavior and Usefulness of Simple Sum and Weighted Measures of the Money Stock.” Federal Reserve Bank of St. Louis Review (March/April): 73-109.

Diewert, E. W. 1976. “Exact and Superlative Index Numbers.” Journal of Econometrics 4: 115-145.

Gorman, W. M. 1953. “Community Preference Fields. Econometrica 21: 63-80.

Theil, H. 1967. Economics and Information Theory. Amsterdam: North Holland.

Thornton, D. L., and P. Yue. 1992. “An Extended Series of Divisia Monetary Aggregates.” Federal Reserve Bank of St. Louis Review (November/December): 35-52.