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<p>This paper develops novel shrinkage estimation methodologies for the seemingly unrelated regression (SUR) model in the presence of multicollinearity and elliptical error distributions, a context frequently encountered in empirical economic analysis. Recognizing the limitations of traditional estimators under multicollinearity, we introduce a unified class of Liu-type shrinkage learners that systematically regularize parameter estimates, thereby improving estimation precision and predictive performance. Our approach extends the SUR framework by accommodating both partially linear structures and linear restrictions, offering enhanced flexibility for complex econometric modeling. We derive the asymptotic properties of the proposed estimators and provide comprehensive risk analyses to evaluate their theoretical advantages. Extensive Monte Carlo simulations demonstrate the superior performance of the proposed shrinkage learners compared to conventional methods. The results underscore the practical value of advanced shrinkage techniques for high-dimensional and ill-conditioned econometric systems, contributing to the robust and computationally efficient estimation strategies central to modern computational economics.</p>

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Development of Shrinkage Learners in the Elliptical SUR Model with Multicollinearity

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • M. Arashi,
  • M. Roozbeh,
  • M. Amini

摘要

This paper develops novel shrinkage estimation methodologies for the seemingly unrelated regression (SUR) model in the presence of multicollinearity and elliptical error distributions, a context frequently encountered in empirical economic analysis. Recognizing the limitations of traditional estimators under multicollinearity, we introduce a unified class of Liu-type shrinkage learners that systematically regularize parameter estimates, thereby improving estimation precision and predictive performance. Our approach extends the SUR framework by accommodating both partially linear structures and linear restrictions, offering enhanced flexibility for complex econometric modeling. We derive the asymptotic properties of the proposed estimators and provide comprehensive risk analyses to evaluate their theoretical advantages. Extensive Monte Carlo simulations demonstrate the superior performance of the proposed shrinkage learners compared to conventional methods. The results underscore the practical value of advanced shrinkage techniques for high-dimensional and ill-conditioned econometric systems, contributing to the robust and computationally efficient estimation strategies central to modern computational economics.