Advertisement

Empirical Economics

, Volume 47, Issue 2, pp 451–468 | Cite as

Estimating SUR system with random coefficients: the unbalanced panel data case

  • Erik BiørnEmail author
Article

Abstract

A system of regression equations for analyzing panel data with random heterogeneity in intercepts and coefficients, and unbalanced panel data is considered. A maximum likelihood (ML) procedure for joint estimation of all parameters is described. Since its implementation for numerical computation is complicated, simplified procedures are presented. The simplifications essentially concern the estimation of the covariance matrices of the random coefficients. The application and ‘anatomy’ of the proposed algorithm for modified ML estimation are illustrated by using panel data for output, inputs and costs for 111 manufacturing firms observed up to 22 years.

Keywords

Panel data Unbalanced data Random coefficients  Heterogeneity Regression systems Iterated maximum likelihood 

JEL Classification

C33 C51 C63 D24 

Notes

Acknowledgments

An earlier version of the paper was presented at the Sixteenth International Conference on Panel Data, Amsterdam, July 2010. I am grateful to Xuehui Han for excellent programming assistance and Terje Skjerpen and a referee for comments.

References

  1. Avery RB (1977) Error components and seemingly unrelated regressions. Econometrica 45:199–209CrossRefGoogle Scholar
  2. Baltagi BH (1980) On seemingly unrelated regressions with error components. Econometrica 48:1547–1551CrossRefGoogle Scholar
  3. Baltagi BH (1985) Pooling cross-sections with unequal time-series lengths. Econ Lett 18:133–136CrossRefGoogle Scholar
  4. Baltagi BH (2008) Econometric analysis of panel data, 4th edn. Wiley, ChichesterGoogle Scholar
  5. Baltagi BH, Song SH (2006) Unbalanced panel data: a survey. Stat Pap 47:493–523Google Scholar
  6. Biørn E (1981) Estimating economic relations from incomplete cross-section/time-series data. J Econ 16:221–236CrossRefGoogle Scholar
  7. Biørn E (2004) Regression systems for unbalanced panel data: a stepwise maximum likelihood procedure. J Econ 122:281–291CrossRefGoogle Scholar
  8. Biørn E, Lindquist K-G, Skjerpen T (2002) Heterogeneity in returns to scale: a random coefficient analysis with unbalanced panel data. J Prod Anal 18:39–57CrossRefGoogle Scholar
  9. Hsiao C (1975) Some Estimation Methods for a Random Coefficient Model. Econometrica 43:305–325CrossRefGoogle Scholar
  10. Hsiao C (2003) Analysis of panel data. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  11. Hsiao C, Pesaran MH (2008) Random coefficients models, chap 6. In: Mátyás L, Sevestre P (eds) The econometrics of panel data: Fundamentals and recent developments in theory and practice. Springer, BerlinGoogle Scholar
  12. Longford NT (1995) Random coefficient models, chap 10. In: Arminger G, Clogg CC, Sobel ME (eds) Handbook of statistical modeling for the social and behavioral sciences. Plenum Press, New YorkGoogle Scholar
  13. Platoni S, Sckokai P, Moro D (2012) A note on two-way ECM estimation of SUR systems on unbalanced panel data. Econ Rev 31:119–141CrossRefGoogle Scholar
  14. Swamy PAVB (1970) Efficient estimation in a random coefficient regression model. Econometrica 38:311–323CrossRefGoogle Scholar
  15. Swamy PAVB, Mehta JS (1977) Estimation of linear models with time and cross-sectionally varying coefficients. J Am Stat Assoc 72:890–898Google Scholar
  16. Verbeek M, Nijman TE (1996) Incomplete panels and selection bias, chap 18. In: Mátyás L, Sevestre P (eds) The econometrics of panel data. A handbook of the theory with applications. Kluwer, DordrechtGoogle Scholar
  17. Wansbeek T, Kapteyn A (1982) A class of decompositions of the variance-covariance matrix of a generalized error components model. Econometrica 50:713–724CrossRefGoogle Scholar
  18. Wansbeek T, Kapteyn A (1989) Estimation of the error components model with incomplete panels. J Econ 41:341–361CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of EconomicsUniversity of OsloOsloNorway

Personalised recommendations