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Local and global rank tests for multivariate varying-coefficient models

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  • Stephen G. Donald

    ()
    (Dept. of Economics, University of Texas at Austin)

  • Natércia Fortuna

    ()
    (CEMPRE, Faculdade de Economia, Universidade do Porto)

  • Vladas Pipiras

    ()
    (Dept. of Statistics and Operations Research, UNC at Chapel Hill)

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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Bibliographic Info

Paper provided by Universidade do Porto, Faculdade de Economia do Porto in its series FEP Working Papers with number 196.

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Length: 25 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:por:fepwps:196

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Keywords: varying-coefficient model; kernel smoothing; matrix rank estimation; demand systems; local and global ranks;

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References

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  1. 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, Canadian Economics Association, vol. 34(1), pages 259-289, February.
  2. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
  3. Fortuna, Natercia, 2008. "Local rank tests in a multivariate nonparametric relationship," Journal of Econometrics, Elsevier, Elsevier, vol. 142(1), pages 162-182, January.
  4. Muellbauer, John, 1976. "Community Preferences and the Representative Consumer," Econometrica, Econometric Society, Econometric Society, vol. 44(5), pages 979-99, September.
  5. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 16(02), pages 151-175, April.
  6. 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, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 715-731.
  7. Muellbauer, John, 1975. "Aggregation, Income Distribution and Consumer Demand," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 42(4), pages 525-43, October.
  8. 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.
  9. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(02), pages 1-21, June.
  10. Cragg, John G. & Donald, Stephen G., 1993. "Testing Identifiability and Specification in Instrumental Variable Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 9(02), pages 222-240, April.
  11. Stephen G. Donald, 1997. "Inference Concerning the Number of Factors in a Multivariate Nonparametric Relationship," Econometrica, Econometric Society, Econometric Society, vol. 65(1), pages 103-132, January.
  12. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, Elsevier, vol. 76(1-2), pages 223-250.
  13. Li, Qi, et al, 2002. "Semiparametric Smooth Coefficient Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 412-22, July.
  14. Lewbel, Arthur, 1991. "The Rank of Demand Systems: Theory and Nonparametric Estimation," Econometrica, Econometric Society, Econometric Society, vol. 59(3), pages 711-30, May.
  15. repec:cup:etheor:v:10:y:1994:i:2:p:233-53 is not listed on IDEAS
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Cited by:
  1. Natércia Fortuna, 2004. "Local rank tests in a multivariate nonparametric relationship," FEP Working Papers, Universidade do Porto, Faculdade de Economia do Porto 137, Universidade do Porto, Faculdade de Economia do Porto.

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