IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/1424.html

Estimating regressions and seemingly unrelated regressions with error component disturbances

Author

Listed:
  • Paolo, Foschi

Abstract

The estimation of regressions models with two-way error component disurbances, is considered for the case where both the random effects are non-spherically distributed. The usual approach that first transforms the effects into uncorrelated ones and then applies within and between transformations, cannot be conveniently applied. Here, it is proposed to revert this scheme by firstly applying the within and between transformations. This results in simple General Linear Model which can be partitioned into three smaller GLMs. Then, by exploiting the structure of the models and using the Generalized QR decomposition as a tool, a computationally efficient and numerically reliable method for estimating the regression parameters is derived. This estimation method is generalized to the case of a system of seemingly unrelated regressions.

Suggested Citation

  • Paolo, Foschi, 2005. "Estimating regressions and seemingly unrelated regressions with error component disturbances," MPRA Paper 1424, University Library of Munich, Germany, revised 07 Sep 2006.
    • Handle: RePEc:pra:mprapa:1424
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/1424/1/MPRA_paper_1424.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Magnus, Jan R & Woodland, Alan D, 1988. "On the Maximum Likelihood Estimation of Multivariate Regression Models Containing Serially Correlated Error Components," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 707-725, November.
    2. Lillard, Lee A & Willis, Robert J, 1978. "Dynamic Aspects of Earning Mobility," Econometrica, Econometric Society, vol. 46(5), pages 985-1012, September.
    3. Kontoghiorghes, E. J. & Clarke, M. R. B., 1995. "An alternative approach for the numerical solution of seemingly unrelated regression equations models," Computational Statistics & Data Analysis, Elsevier, vol. 19(4), pages 369-377, April.
    4. Badi H. Baltagi, 2021. "Simultaneous Equations with Error Components," Springer Texts in Business and Economics, in: Econometric Analysis of Panel Data, edition 6, chapter 0, pages 157-186, Springer.
    5. Baltagi, Badi H. & Li, Qi, 1991. "A transformation that will circumvent the problem of autocorrelation in an error-component model," Journal of Econometrics, Elsevier, vol. 48(3), pages 385-393, June.
    6. Amemiya, Takeshi, 1971. "The Estimation of the Variances in a Variance-Components Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(1), pages 1-13, February.
    7. Badi H. Baltagi, 2021. "Seemingly Unrelated Regressions with Error Components," Springer Texts in Business and Economics, in: Econometric Analysis of Panel Data, edition 6, chapter 0, pages 149-155, Springer.
    8. Erricos Kontoghiorghes, 1999. "Updating SURE Models," Computing in Economics and Finance 1999 1324, Society for Computational Economics.
    9. Skoglund, Jimmy & Karlsson, Sune, 2001. "Specification and estimation of random effects models with serial correlation of general form," SSE/EFI Working Paper Series in Economics and Finance 0433, Stockholm School of Economics.
    10. MaCurdy, Thomas E., 1982. "The use of time series processes to model the error structure of earnings in a longitudinal data analysis," Journal of Econometrics, Elsevier, vol. 18(1), pages 83-114, January.
    11. Avery, Robert B, 1977. "Error Components and Seemingly Unrelated Regressions," Econometrica, Econometric Society, vol. 45(1), pages 199-209, January.
    12. Erricos J. Kontoghiorghes, 2000. "Inconsistencies in SURE Models: Computational Aspects," Computational Economics, Springer;Society for Computational Economics, vol. 16(1/2), pages 63-70, October.
    13. Galbraith, John W. & Zinde-Walsh, Victoria, 1995. "Transforming the error-components model for estimation with general ARMA disturbances," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 349-355.
    14. Chamberlain, Gary, 1982. "Multivariate regression models for panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 5-46, January.
    15. Foschi, Paolo & Belsley, David A. & Kontoghiorghes, Erricos J., 2003. "A comparative study of algorithms for solving seemingly unrelated regressions models," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 3-35, October.
    16. Sune Karlsson & Jimmy Skoglund, 2004. "Maximum-likelihood based inference in the two-way random effects model with serially correlated time effects," Empirical Economics, Springer, vol. 29(1), pages 79-88, January.
    17. Nerlove, Marc, 1971. "A Note on Error Components Models," Econometrica, Econometric Society, vol. 39(2), pages 383-396, March.
    18. Balestra, Pietro & Varadharajan-Krishnakumar, Jayalakshmi, 1987. "Full Information Estimations of a System of Simultaneous Equations with Error Component Structure," Econometric Theory, Cambridge University Press, vol. 3(2), pages 223-246, April.
    19. Baltagi, Badi H. & Li, Qi, 1994. "Estimating Error Component Models With General MA(q) Disturbances," Econometric Theory, Cambridge University Press, vol. 10(2), pages 396-408, June.
    20. Anderson, T. W. & Hsiao, Cheng, 1982. "Formulation and estimation of dynamic models using panel data," Journal of Econometrics, Elsevier, vol. 18(1), pages 47-82, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jimmy Skoglund & Sune Karlsson, 2002. "Asymptotics for random effects models with serial correlation," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 A6-1, International Conferences on Panel Data.
    2. Badi H. Baltagi, 2008. "Forecasting with panel data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(2), pages 153-173.
    3. Badi H. Baltagi & Georges Bresson & Jean-Michel Etienne, 2025. "Two-way random effects model with serial correlation," Empirical Economics, Springer, vol. 68(5), pages 2041-2072, May.
    4. Jaya Krishnakumar, 2002. "A SUR-EC-AR System Gravity Model of Trade," 10th International Conference on Panel Data, Berlin, July 5-6, 2002 B4-4, International Conferences on Panel Data.
    5. Qiu, Jin & Ma, Qing & Wu, Lang, 2019. "A moving blocks empirical likelihood method for panel linear fixed effects models with serial correlations and cross-sectional dependences," Economic Modelling, Elsevier, vol. 83(C), pages 394-405.
    6. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    7. Mitze, Timo & Stephan, Andreas, 2013. "Simultaneous-equations Analysis in Regional Science and Economic Geography," Working Paper Series in Economics and Institutions of Innovation 309, Royal Institute of Technology, CESIS - Centre of Excellence for Science and Innovation Studies.
    8. Marius C. O. Amba, 2021. "Simultaneous Equations with Three Way Error Components," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(3), pages 583-596, September.
    9. M. Hashem Pesaran & Liying Yang, 2024. "Heterogeneous autoregressions in short T panel data models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(7), pages 1359-1378, November.
    10. Walter Sosa-Escudero & Mariana Marchionni & Omar Arias, 2011. "Sources of Income Persistence: Evidence from Rural El Salvador," Journal of Income Distribution, Ad libros publications inc., vol. 20(1), pages 3-28, March.
    11. Marcel die Dama & Boniface ngah Epo & Galex syrie Soh, 2013. "Developing a two way error component estimation model with disturbances following a special autoregressive (4) for quarterly data," Economics Bulletin, AccessEcon, vol. 33(1), pages 625-634.
    12. Giorgio Calzolari & Laura Magazzini, 2012. "Autocorrelation and masked heterogeneity in panel data models estimated by maximum likelihood," Empirical Economics, Springer, vol. 43(1), pages 145-152, August.
    13. Santos, Antonio Loureiro & Souza, André Portela, 2007. "Earnings Inequality in Brazil: Is it Permanent or Transitory?," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 27(2), November.
    14. Samuel Freije & Andre Potela Souza, 2002. "Earnings Dynamics and Inequality in Venezuela: 1995-1997," Vanderbilt University Department of Economics Working Papers 0211, Vanderbilt University Department of Economics.
    15. De Blander, Rembert, 2020. "Iterative estimation correcting for error auto-correlation in short panels, applied to lagged dependent variable models," Econometrics and Statistics, Elsevier, vol. 15(C), pages 3-29.
    16. Amacher, Gregory S & Hellerstein, Daniel, 1999. "The Error Structure of Time Series Cross-Section Hedonic Models with Sporadic Event Timing and Serial Correlation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 233-252, May-June.
    17. Hayakawa, Kazuhiko, 2024. "Recent development of covariance structure analysis in economics," Econometrics and Statistics, Elsevier, vol. 29(C), pages 31-48.
    18. Seppo Laaksonen, 1989. "Use of panel data in applications of income dynamics," Finnish Economic Papers, Finnish Economic Association, vol. 2(1), pages 55-64, Spring.
    19. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    20. repec:elg:eechap:14395_7 is not listed on IDEAS
    21. Baltagi, Badi H. & Griffin, James M., 1997. "Pooled estimators vs. their heterogeneous counterparts in the context of dynamic demand for gasoline," Journal of Econometrics, Elsevier, vol. 77(2), pages 303-327, April.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:1424. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.