Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T08:05:37.323Z Has data issue: false hasContentIssue false
  • English
  • Français

ADMISSIBLE CLUSTERING OF AGGREGATOR COMPONENTS: A NECESSARY AND SUFFICIENT STOCHASTIC SEMINONPARAMETRIC TEST FOR WEAK SEPARABILITY

Published online by Cambridge University Press:  15 September 2009

William A. Barnett  and
Philippe de Peretti
William A. Barnett
Affiliation:
Kansas University
Philippe de Peretti*
Affiliation:
Université Paris1 Panthéon-Sorbonne
*
Address correspondence to: Philippe de Peretti, Centre d'Economie de la Sorbonne (CES), Université Paris1 Panthéon-Sorbonne, Maison des Sciences Economiques, 106–112 Boulevard de l'Hôpital, 75647 Paris cedex 13, France; e-mail: philippe.de-peretti@univ-paris1.fr.
Get access Rights & Permissions [Opens in a new window]

Abstract

In aggregation theory, the admissibility condition for clustering 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 introduces a new class of weak separability tests, which is seminonparametric. Such tests are both based on a necessary and sufficient condition and are fully stochastic, allowing to take into account measurement error. Simulations show that the tests perform well, even for large measurement errors.

Keywords

Weak separabilitySeminonparametric tests
Type
Articles
Information
Macroeconomic Dynamics , Volume 13 , Supplement S2: Measurement with Theory , September 2009 , pp. 317 - 334
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barnett, W.A. (1979) Theoretical foundations for the Rotterdam model. Review of Economic Studies 46, 109–130.CrossRefGoogle Scholar
Barnett, W.A. (1980) Economic monetary aggregates: An application of index number and aggregation theory. Journal of Econometrics 14, 11–48. Reprinted in Barnett, W.A. and Serletis, A. (eds.) (2000) The Theory of Monetary Aggregation. Amsterdam: North Holland.Google Scholar
Barnett, W.A. and Choi, S.A. (1989) A Monte Carlo study of tests of blockwise weak separability. Journal of Business and Economic Statistics 7, 363–377. Reprinted in Barnett, W.A. and Binner, J. (eds.) (2004) Functional Structure and Approximation in Econometrics. Amsterdam: North Holland.CrossRefGoogle Scholar
Bell, W.R. and Hillmer, S.C. (1984) Issues involved with the seasonal adjustment of economic time series. Journal of Business and Economic Statistics 2, 291–320.CrossRefGoogle Scholar
Blackorby, C., Primont, D., and Russell, R.R. (1998) Separability: A survey. In Barbera, S., Hammond, P., and Seidl, C. (eds.) The Handbook of Utility Theory. Dordrecht, The Netherlands: Kluwer.Google Scholar
D'Agostino, R.B. and Stephens, M.A. (1986) Goodness-of-Fit Techniques. Statistics: Textbooks and Monographs. New York: Dekker.Google Scholar
Deaton, A. and Muellbauer, J. (1980) Economics and Consumer Behavior. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
de Jong, P. and Shephard, N. (1995) The simulation smoother for time series models. Biometrika 82, 339–350.CrossRefGoogle Scholar
de Peretti, P. (2005) Testing the significance of the departures from utility maximization. Macroeconomic Dynamics 9, 372–397.CrossRefGoogle Scholar
de Peretti, P. (2007) Testing the significance of the departures from weak separability. In Barnett, W.A. and Serletis, A. (eds.), International Symposia in Economic Theory and Econometrics: Functional Structure Inference. Amsterdam: Elsevier Press.Google Scholar
Durbin, J. and Koopman, S.J. (2001) Time Series Analysis by State Space Methods. Oxford Statistical Science Series. New York: Oxford University Press.Google Scholar
Embrecht, P., Klüppelberg, C., and Mikosch, T. (2003) Modelling extremal events. New York: Springer-Verlag.Google Scholar
Fisher, D. and Fleissig, A.R. (1997) Monetary aggregation and the demand for assets. Journal of Money, Credit and Banking 29, 458–475.CrossRefGoogle Scholar
Fleissig, A.R. and Whitney, G.A. (2003) New PC-based test for Varian's weak separability conditions. Journal of Business and Economic Statistics 21, 133–144.CrossRefGoogle Scholar
Fleissig, A.R. and Whitney, G.A. (2005) Testing for the significance of violations of Afriat's inequalities. Journal of Business and Economic Statistics 23, 355–362.CrossRefGoogle Scholar
Guégan, D. (2003) Introduction aux Valeurs extrêmes et à ses Applications. Working paper, Ecole Normale Supérieure de Cachan.Google Scholar
Harvey, A.C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge, UK: Cambridge University Press.Google Scholar
Harvey, A.C and Koopman, S.J. (1992) Diagnostic checking of unobserved-components time series models. Journal of Business and Economic Statistics 10, 377–389.CrossRefGoogle Scholar
Hosking, J.R.M. (1985) Maximum likelihood estimation of the parameter of the generalized extreme values distribution. Applied Statistics 34, 301–310.CrossRefGoogle Scholar
Hosking, J.R.M., Wallis, J.R, and Wood, E.F. (1985) Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics 27, 251–261.CrossRefGoogle Scholar
Hsiao, C. (1997) Statistical properties of the two-stage least squares estimator under cointegration. Review of Economic Studies 64, 385–398.CrossRefGoogle Scholar
Johnson, N.L., Kotz, L., and Balakrishnan, N. (1994) Continuous Univariate Distributions, Vols. I and II, 2nd ed.New York: Wiley.Google Scholar
Jones, B., Elger, T., Edgerton, D., and Dutkowsky, D. (2005) Toward a unified approach to testing for weak separability. Economics Bulletin 3, 1–7.Google Scholar
Kitamura, Y. and Phillips, P.C. (1997) Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments. Journal of Econometrics 80, 85–123.CrossRefGoogle Scholar
Koopman, S.J. (1997) Exact initial Kalman filtering and smoothing for nonstationary time series models. Journal of the American Statistical Association 92, 1630–1638.CrossRefGoogle Scholar
Rootzén, H. (1986) Extreme value theory for moving average processes. Annals of Probability 14, 612–652.CrossRefGoogle Scholar
Stoffer, D.S. and Wall, K. (1991) Bootstrapping state space models: Gaussian maximum likelihood estimation and the Kalman filter. Journal of the American Statistical Association 86, 1024–1033.CrossRefGoogle Scholar
Swofford, J.L. and Whitney, G.A. (1987) Non-parametric tests of utility maximization and weak separability for consumption, leisure, and money. Review of Economics and Statistics 69, 458–464.CrossRefGoogle Scholar
Swofford, J.L. and Whitney, G.A. (1994) A revealed preference test for weakly separable utility maximization with incomplete adjustment. Journal of Econometrics 60, 235–49.CrossRefGoogle Scholar
Varian, H. (1982) The nonparametric approach to demand analysis. Econometrica 50, 945–973.CrossRefGoogle Scholar
Varian, H. (1983) Nonparametric tests of consumer behavior. Review of Economic Studies 50, 99–110.CrossRefGoogle Scholar
Varian, H. (1985) Non-parametric analysis of optimizing behavior with measurement error. Journal of Econometrics 30, 445–458.CrossRefGoogle Scholar