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

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  • William Barnett

    (Department of Economics, The 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.

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Bibliographic Info

Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 200904.

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Length: 26 pages
Date of creation: Jan 2009
Date of revision: Jan 2009
Handle: RePEc:kan:wpaper:200904

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Keywords: weak separability; quantity aggregation; clustering; sectors; index number theory; semi-nonparametrics;

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  1. David Edgerton & Donald Dutkowsky & Thomas Elger & Barry Jones, 2005. "Toward a unified approach to testing for weak separability," Economics Bulletin, AccessEcon, vol. 3(20), pages 1-7.
  2. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 945-73, July.
  3. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 10(4), pages 377-89, October.
  4. de PERETTI, PHILIPPE, 2005. "Testing The Significance Of The Departures From Utility Maximization," Macroeconomic Dynamics, Cambridge University Press, Cambridge University Press, vol. 9(03), pages 372-397, June.
  5. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 2(4), pages 291-320, October.
  6. Swofford, James L. & Whitney, Gerald A., 1994. "A revealed preference test for weakly separable utility maximization with incomplete adjustment," Journal of Econometrics, Elsevier, Elsevier, vol. 60(1-2), pages 235-249.
  7. Fisher, Douglas & Fleissig, Adrian R, 1997. "Monetary Aggregation and the Demand for Assets," Journal of Money, Credit and Banking, Blackwell Publishing, Blackwell Publishing, vol. 29(4), pages 458-75, November.
  8. Kitamura, Yuichi & Phillips, Peter C. B., 1997. "Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments," Journal of Econometrics, Elsevier, Elsevier, vol. 80(1), pages 85-123, September.
  9. Fleissig, Adrian R. & Whitney, Gerald A., 2005. "Testing for the Significance of Violations of Afriat's Inequalities," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 23, pages 355-362, July.
  10. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, Elsevier, vol. 30(1-2), pages 445-458.
  11. Hsiao, Cheng, 1997. "Statistical Properties of the Two-Stage Least Squares Estimator under Cointegration," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 64(3), pages 385-98, July.
  12. Barnett, William A & Choi, Seungmook, 1989. "A Monte Carlo Study of Tests of Blockwise Weak Separability," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 7(3), pages 363-77, July.
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Cited by:
  1. Barnett, William A. & Chauvet, Marcelle, 2011. "How better monetary statistics could have signaled the financial crisis," Journal of Econometrics, Elsevier, Elsevier, vol. 161(1), pages 6-23, March.
  2. Barnett, William A. & Diewert, W. Erwin & Zellner, Arnold, 2009. "Introduction to Measurement with Theory," MPRA Paper 14868, University Library of Munich, Germany.

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