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

Barnett, William A. and de Peretti, Philippe (2008): Admissible clustering of aggregator components: a necessary and sufficient stochastic semi-nonparametric test for weak separability.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: weak separability; quantity aggregation; clustering; sectors; index number theory; semi-nonparametrics
• Subjects: C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C43 - Index Numbers and Aggregation; D - Microeconomics > D1 - Household Behavior and Family Economics > D12 - Consumer Economics: Empirical Analysis; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General

References

[1] Barnett, W.A. and S.A. Choi (1989): A Monte Carlo study of tests of blockwise weak separability, Journal of Business & Economic Statistics, Vol. 7, 363-�377.

[2] Blackorby, C., Russell, R.R. and D. Primont (1998): Separability: A survey, in The Handbook of Utility Theory Vol. 1, S. Barbera, P. Hammond, and C. Seidl eds, Kluwer: Dordrecht, 49-92.

[3] Bell, W.R. and S.C. Hillmer (1984): Issues involved with the seasonal adjustment of economic time series, Journal of Business & Economic Statistics, Vol. 2, 291�-320.

[4] de Peretti, P. (2005): Testing the signifi�cance of the departures from utility maximization, Macroeconomic Dynamics 9, 372-397.

[5] de Peretti, P. (2007): Testing the signi�ficance of the departures from weak separability, International Symposia in Economic Theory and Econometrics: Functional Structure Inference, William Barnett and Apostolos Serletis, Eds. Elsevier Press.

[6] D'�Agostino, R.B and M.A. Stephens (1986): Goodness-of-�fit techniques, Statistics: Textbooks and Monographs, New York: Dekker, D�'Agostino and Stephens, Eds.

[7] Deaton, A. and J. Muellbauer (1980): Economics and consumer behavior, Cambridge University Press.

[8] Durbin, J. and S.J. Koopman (2001: Time Series Analysis by State Space Methods. Oxford Statistical Science Series, Oxford University Press.

[9] Embrecht, P., Klüppelberg, C. and T. Mikosch (2003): Modelling extremal events, Springer-Verlag, New York.

[10] Fisher, D. and A.R. Fleissig (1997): Monetary aggregation and the demand for assets, Journal of Money, Credit and Banking 29,458�-75.

[11] Fleissig, A. R. and G.A. Whitney (2003): New PC-Based test for Varian'�s weak separability conditions, Journal of Business & Economic Statistics, Vol. 21, No. 3, 133-�144.

[12] Fleissig, A. R. and G.A. Whitney (2005): Testing for the signi�ficance of violations of Afriat�'s inequalities, Journal of Business & Economic Statistics, Vol. 23, No. 3, 355-�362.

[13] Guégan, D. (2003): Introduction aux valeurs extrêmes et à ses applications, working paper, Ecole Normale Supérieure de Cachan.

[14] Harvey, A.C. (1989): Forecasting, structural time series models and the Kalman �filter, Cambridge, U.K., Cambridge University Press.

[15] Harvey, A.C and S.J. Koopman (1992): Diagnostic checking of unobserved-components time series models, Journal of Business & Economic Statistics, Vol. 10, No.4, 377�-389.

[16] Hosking, J.R.M. (1985): Maximum likelihood estimation of the parameter of the generalized extreme values distribution, Applied Statistics, 34, 301�-310.

[17] Hosking, J.R.M., Wallis, J.R and E.F.Wood (1985): Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics, 27, 251-261.

[18] Hsiao, C. (1997): Statistical properties of the two-stage least squares estimator under cointegration, The Review of Economic Studies, vol. 64, No. 3, 385�-398.

[19] Johnson, N.L, Kotz, L. and N. Balakrishnan (1994): Continuous Univariate Distributions, Vol. I and II, 2nd. edition, Eds.: John Wiley and Sons.

[20] Jones, B., Elger, T., Edgerton, D. and D. Dutkowsky (2005): Toward a unifi�ed approach to testing for weak separability, Economic Bulletin, Vol. 3, 1�-7.

[21] Rootzén, H. (1986): Extreme value theory for moving average processes, The Annals of Probability, Vol. 14, No. 2, 612-652.

[22] Reinsel. G. (1997): Elements of multivariate time series, Springer-Verlag, New York.

[23] Kitamura, Y. and P.C. Phillips (1997), Fully modifi�ed IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments, Journal of Econometrics 80, 85-123.

[24] Stoffer, D.S. and K. Wall, (1991): Bootstrapping state space models: Gaussian maximum likelihood estimation and the Kalman �filter, Journal of the American Statistical Association 86, 1024-1033.

[25] Swofford, J.L. and G.A. Whitney (1987): Non-Parametric tests of utility maximization and weak separability for consumption, leisure, and money, Review of Economic Studies 69, 458-�464.

[26] Swofford, J.L. and G.A. Whitney (1994): A revealed preference test for weakly separable utility maximization with incomplete adjustment, Journal of Econometrics 60, 235-49.

[27] Varian, H. (1982): The Nonparametric Approach to Demand Analysis, Econometrica 50, 945-�973.

[28] Varian, H. (1983): Nonparametric Tests of Consumer Behavior, Review of Economic Studies 50, 99�-110.

[29] Varian, H. (1985): Non-Parametric Analysis of Optimizing Behavior With Measurement Error, Journal of Econometrics 30, 445-�458.