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Estimation and inference in sur models when the number of equations is large


  • Denzil Fiebig
  • Jae Kim


There is a tendency for the true variability of feasible GLS estimators to be understated by asymptotic standard errors. For estimation of SUR models, this tendency becomes more severe in large equation systems when estimation of the error covariance matrix, C, becomes problematic. We explore a number of potential solutions involving the use of improved estimators for the disturbance covariance matrix and bootstrapping. In particular, Ullah and Racine (1992) have recently introduced a new class of estimators for SUR models that use nonparametric kernel density estimation techniques. The proposed estimators have the same structure as the feasible GLS estimator of Zellner (1962) differing only in the choice of estimator for C. Ullah and Racine (1992) prove that their nonparametric density estimator of C can be expressed as Zellner's original estimator plus a positive definite matrix that depends on the smoothing parameter chosen for the density estimation. It is this structure of the estimator that most interests us as it has the potential to be especially useful in large equation systems. Atkinson and Wilson (1992) investigated the bias in the conventional and bootstrap estimators of coefficient standard errors in SUR models. They demonstrated that under certain conditions the former were superior, but they caution that neither estimator uniformly dominated and hence bootstrapping provides little improvement in the estimation of standard errors for the regression coefficients. Rilstone and Veal1 (1996) argue that an important qualification needs to be made to this somewhat negative conclusion. They demonstrated that bootstrapping can result in improvements in inferences if the procedures are applied to the t-ratios rather than to the standard errors. These issues are explored for the case of large equation systems and when bootstrapping is combined with improved covariance estimation.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:emetrv:v:19:y:2000:i:1:p:105-130
    DOI: 10.1080/07474930008800461

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    Cited by:

    1. 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.
    2. Chotikapanich, D. & Griffiths, W.E. & Skeels, C.L., 2001. "Sample Size Requirements for Estimation in SUR Models," Department of Economics - Working Papers Series 794, The University of Melbourne.
    3. Zeebari, Zangin & Shukur, Ghazi & Kibria, B. M. Golam, 2010. "Modified Ridge Parameters for Seemingly Unrelated Regression Model," HUI Working Papers 43, HUI Research.
    4. Benjamin Verhelst & Dirk Van den Poel, 2014. "Deep habits in consumption: a spatial panel analysis using scanner data," Empirical Economics, Springer, vol. 47(3), pages 959-976, November.
    5. Griffiths, W.E., 2001. "Bayesian Inference in the Seemingly Unrelated Regressions Models," Department of Economics - Working Papers Series 793, The University of Melbourne.
    6. repec:eee:stapro:v:126:y:2017:i:c:p:119-126 is not listed on IDEAS
    7. Yihui Lan, 2003. "The Long-Term Behaviour of Exchange Rates, Part V: The Stationarity of Exchange Rates," Economics Discussion / Working Papers 03-09, The University of Western Australia, Department of Economics.


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