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Developing Ridge Parameters for SUR Models

Author

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  • Alkhamisi, M.A.

    (Department of Mathematics, Salahaddin University, Kurdistan-Region, Iraq)

  • Shukur, Ghazi

    () (Departments of Economics and Statistics, Jönköping International Business School (JIBS), Sweden)

Abstract

In this paper, a number of procedures have been proposed for developing new biased estimators of seemingly unrelated regression (SUR) parameters, when the explanatory variables are affected by multicollinearity. Several ridge parameters are proposed and then compared in terms of the trace mean squared error (TMSE) and(PR) criterion. The PR is the proportion of replication (out of 1,000) for which the SUR version of the generalised least squares, (SGLS) estimator has a smaller TMSE than the others. The study has been made using Monte Carlo simulations where the number of equations in the system, number of observations, correlation among equations and correlation between explanatory variables have been varied. For each model we performed 1,000 replications. Our results show that under certain conditions the performance of the multivariate regression estimators based on SUR ridge parameters RSarith, RSqarith and RSmax are superior to other estimators in terms of TMSE and PR criterion. In large samples and when the collinearity between the explanatory variables is not high the unbiased SUR, estimator produces a smaller TMSEs.

Suggested Citation

  • Alkhamisi, M.A. & Shukur, Ghazi, 2007. "Developing Ridge Parameters for SUR Models," Working Paper Series in Economics and Institutions of Innovation 80, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
  • Handle: RePEc:hhs:cesisp:0080
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    References listed on IDEAS

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    1. Vinod, Hrishikesh D, 1978. "A Survey of Ridge Regression and Related Techniques for Improvements over Ordinary Least Squares," The Review of Economics and Statistics, MIT Press, vol. 60(1), pages 121-131, February.
    2. Chib, Siddhartha & Greenberg, Edward, 1995. "Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models," Journal of Econometrics, Elsevier, vol. 68(2), pages 339-360, August.
    3. Denzil Fiebig & Jae Kim, 2000. "Estimation and inference in sur models when the number of equations is large," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 105-130.
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    Citations

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    Cited by:

    1. Månsson, Kristofer & Shukur, Ghazi, 2011. "A Poisson ridge regression estimator," Economic Modelling, Elsevier, vol. 28(4), pages 1475-1481, July.
    2. B. Kibria & Kristofer Månsson & Ghazi Shukur, 2012. "Performance of Some Logistic Ridge Regression Estimators," Computational Economics, Springer;Society for Computational Economics, vol. 40(4), pages 401-414, December.
    3. M. Alkhamisi, 2010. "Simulation study of new estimators combining the SUR ridge regression and the restricted least squares methodologies," Statistical Papers, Springer, vol. 51(3), pages 651-672, September.
    4. Månsson, Kristofer & Shukur, Ghazi & Sjölander, Pär, 2012. "A New Asymmetric Interaction Ridge (AIR) Regression Method," HUI Working Papers 54, HUI Research.
    5. Muniz, Gisela & Kibria, B. M.Golam & Shukur, Ghazi, 2009. "On Developing Ridge Regression Parameters: A Graphical investigation," HUI Working Papers 29, HUI Research.

    More about this item

    Keywords

    Multicollinearity; SUR ridge regression; Monte Carlo simulations; biased estimators; Generalized least squares;

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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