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Who's Afraid of Reduced-Rank Parameterizations of Multivariate Models? Theory and Example

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  • Scott Gilbert
  • Petr Zemcik

Abstract

Reduced-rank restrictions can add useful parsimony to coefficient matrices of multivariate models, but their use is limited by the daunting complexity of the methods and their theory. The present work takes the easy road, focusing on unifying themes and simplified methods. For Gaussian and non-Gaussian (GLM, GAM, etc.) multivariate models, the present work gives a unified, explicit theory for the general asymptotic (normal) distribution of maximum likelihood estimators (MLE). MLE can be complex and computationally difficult, but we show a strong asymptotic equivalence between MLE and a relatively simple minimum (Mahalanobis) distance estimator. The latter method yields particularly simple tests of rank, and we describe its asymptotic behavior in detail. We also examine the method's performance in simulation and via analytical and empirical examples.

Suggested Citation

  • Scott Gilbert & Petr Zemcik, 2004. "Who's Afraid of Reduced-Rank Parameterizations of Multivariate Models? Theory and Example," CERGE-EI Working Papers wp223, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    • Handle: RePEc:cer:papers:wp223
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    References listed on IDEAS

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    1. Scott Gilbert & Petr Zemčík, 2005. "Testing for Latent Factors in Models with Autocorrelation and Heteroskedasticity of Unknown Form," Southern Economic Journal, John Wiley & Sons, vol. 72(1), pages 236-252, July.

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    More about this item

    Keywords

    Conditional median; Conditional standard deviation; Multivariate coefficient matrix; Reduced-rank estimation test; Asymptotic theory;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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