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Local and Global Rank Tests for Multivariate Varying-Coefficient Models

Author

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  • Donald, Stephen G.
  • Fortuna, Natércia
  • Pipiras, Vladas

Abstract

In a multivariate varying-coefficient model, the response vectors Y are regressed on known functions u(X) of some explanatory variables X and the coefficients in an unknown regression matrix q(Z) depend on another set of explanatory variables Z. We provide statistical tests, called local and global rank tests, which allow to estimate the rank of an unknown regression coefficient matrix q(Z) locally at a fixed level of the variable Z or globally as the maximum rank over all levels of Z, respectively. In the case of local rank tests, we do so by applying already available rank tests to a kernel-based estimator of the coefficient matrix q(z). Global rank tests are obtained by integrating test statistics used in estimation of local rank tests. We present a simulation study where, focusing on global ranks, we examine small sample properties of the considered statistical tests. We also apply our results to estimate the so-called local and global ranks in a demand system where budget shares are regressed on known functions of total expenditures and the coefficients in a regression matrix depend on prices faced by a consumer.
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Suggested Citation

  • Donald, Stephen G. & Fortuna, Natércia & Pipiras, Vladas, 2011. "Local and Global Rank Tests for Multivariate Varying-Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(2), pages 295-306.
  • Handle: RePEc:bes:jnlbes:v:29:i:2:y:2011:p:295-306
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    File URL: http://pubs.amstat.org/doi/abs/10.1198/jbes.2010.07303
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    References listed on IDEAS

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    1. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    2. repec:cup:etheor:v:10:y:1994:i:2:p:233-53 is not listed on IDEAS
    3. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(02), pages 151-175, April.
    4. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 412-422, July.
    5. James Banks & Richard Blundell & Arthur Lewbel, 1997. "Quadratic Engel Curves And Consumer Demand," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 527-539, November.
    6. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.
    7. Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, vol. 65(1), pages 103-132, January.
    8. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, vol. 9(02), pages 222-240, April.
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    10. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
    11. Christopher J. Nicol, 2001. "The rank and model specification of demand systems: an empirical analysis using United States microdata," Canadian Journal of Economics, Canadian Economics Association, vol. 34(1), pages 259-289, February.
    12. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, vol. 59(3), pages 711-730, May.
    13. Jianqing Fan, 2000. "Simultaneous Confidence Bands and Hypothesis Testing in Varying-coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731.
    14. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, vol. 44(5), pages 979-999, September.
    15. John Muellbauer, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Oxford University Press, vol. 42(4), pages 525-543.
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    1. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, vol. 142(1), pages 162-182, January.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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