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Admissible Clustering of Aggregator Components: A Necessary and Sufficient Stochastic Semi-Nonparametric Test for Weak Separability

Author

Listed:
  • William Barnett

    (Department of Economics, University of Kansas)

  • Philippe de Peretti

    (Universite de la Sorbonne)

Abstract

In aggregation theory, the admissibility condition for clustering together components to be aggregated is blockwise weak separability, which also is the condition needed to separate out sectors of the economy. Although weak separability is thereby of central importance in aggregation and index number theory and in econometrics, prior attempts to produce statistical tests of weak separability have performed poorly in Monte Carlo studies. This paper deals with semi- nonparametric tests for weak separability. It introduces both a necessary and su¢ cient test, and a fully stochastic procedure allowing to take into account measurement error. Simulations show that the test performs well, even for large measurement errors.

Suggested Citation

  • William Barnett & Philippe de Peretti, 2009. "Admissible Clustering of Aggregator Components: A Necessary and Sufficient Stochastic Semi-Nonparametric Test for Weak Separability," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200904, University of Kansas, Department of Economics, revised Jan 2009.
    • Handle: RePEc:kan:wpaper:200904
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    File URL: http://www2.ku.edu/~kuwpaper/2009Papers/200904.pdf
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    References listed on IDEAS

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    Cited by:

    1. Barnett, William A. & Erwin Diewert, W. & Zellner, Arnold, 2011. "Introduction to measurement with theory," Journal of Econometrics, Elsevier, vol. 161(1), pages 1-5, March.
    2. Serletis, Apostolos & Xu, Libo, 2021. "Consumption, Leisure, And Money," Macroeconomic Dynamics, Cambridge University Press, vol. 25(6), pages 1412-1441, September.
    3. Ryan S. Mattson & Philippe de Peretti, 2014. "Investigating the Role of Real Divisia Money in Persistence-Robust Econometric Models," Working Papers hal-00984827, HAL.
    4. Ali Jadidzadeh & Apostolos Serletis, 2019. "The Demand for Assets and Optimal Monetary Aggregation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(4), pages 929-952, June.
    5. Barnett, William A. & Chauvet, Marcelle, 2011. "How better monetary statistics could have signaled the financial crisis," Journal of Econometrics, Elsevier, vol. 161(1), pages 6-23, March.

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    More about this item

    Keywords

    weak separability; quantity aggregation; clustering; sectors; index number theory; semi-nonparametrics;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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