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Admissible clustering of aggregator components: a necessary and sufficient stochastic semi-nonparametric test for weak separability

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  • Barnett, William A.
  • de Peretti, Philippe

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 sufficient 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 Library of Munich, Germany in its series MPRA Paper with number 12503.

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Date of creation: 03 Nov 2008
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Handle: RePEc:pra:mprapa:12503

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

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  1. 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, vol. 80(1), pages 85-123, September.
  2. 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, vol. 2(4), pages 291-320, October.
  3. 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, vol. 23, pages 355-362, July.
  4. Varian, Hal R., 1985. "Non-parametric analysis of optimizing behavior with measurement error," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 445-458.
  5. Swofford, James L. & Whitney, Gerald A., 1994. "A revealed preference test for weakly separable utility maximization with incomplete adjustment," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 235-249.
  6. Jones, Barry & Elger, Thomas & Edgerton, David & Dutkowsky, Donald, 2004. "Toward a Unified Approach to Testing for Weak Separability," Working Papers 2004:1, Lund University, Department of Economics.
  7. de PERETTI, PHILIPPE, 2005. "Testing The Significance Of The Departures From Utility Maximization," Macroeconomic Dynamics, Cambridge University Press, vol. 9(03), pages 372-397, June.
  8. Harvey, Andrew C & Koopman, Siem Jan, 1992. "Diagnostic Checking of Unobserved-Components Time Series Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(4), pages 377-89, October.
  9. Fisher, Douglas & Fleissig, Adrian R, 1997. "Monetary Aggregation and the Demand for Assets," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(4), pages 458-75, November.
  10. Hsiao, Cheng, 1997. "Statistical Properties of the Two-Stage Least Squares Estimator under Cointegration," Review of Economic Studies, Wiley Blackwell, vol. 64(3), pages 385-98, July.
  11. Barnett, William A & Choi, Seungmook, 1989. "A Monte Carlo Study of Tests of Blockwise Weak Separability," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 363-77, July.
  12. Varian, Hal R, 1982. "The Nonparametric Approach to Demand Analysis," Econometrica, Econometric Society, vol. 50(4), pages 945-73, July.
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Cited by:
  1. Barnett, William A. & Chauvet, Marcelle, 2010. "How better monetary statistics could have signaled the financial crisis," MPRA Paper 24721, University Library of Munich, Germany.
  2. William Barnett & W. Erwin Diewert & Arnold Zellner, 2009. "Introduction to Measurement with Theory," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200906, University of Kansas, Department of Economics, revised Apr 2009.

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