Paolo, Foschi (2005): Estimating regressions and seemingly unrelated regressions with error component disturbances.

PDF
MPRA_paper_1424.pdf Download (141kB)  Preview 
Abstract
The estimation of regressions models with twoway error component disurbances, is considered for the case where both the random effects are nonspherically 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.
Item Type:  MPRA Paper 

Institution:  University of Bologna 
Original Title:  Estimating regressions and seemingly unrelated regressions with error component disturbances 
Language:  English 
Keywords:  panel data models; regressions; seemingly unrelated regressions; generalized leastsquares; error components; orthogonal transformation; numerical methods 
Subjects:  C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C32  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes ; State Space Models C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C33  Panel Data Models ; Spatiotemporal Models C  Mathematical and Quantitative Methods > C6  Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C63  Computational Techniques ; Simulation Modeling 
Item ID:  1424 
Depositing User:  Paolo Foschi 
Date Deposited:  11 Jan 2007 
Last Modified:  27 Sep 2019 05:19 
References:  T. Amemiya, The estimation of the variances in a variancecomponents model, International Economic Review 12 (1971), 1–13. T.W. Anderson and C. Hsiao, Formulation and estimation of dynamic models using panel data, Journal of Econometrics 18 (1982), 47–82. R.B. Avery, Error components and seemingly unrelated regressions, Econometrica 45(1977), 199–209. P. Balestra and J.Krishnakumar, Full information estimations of a system of simultaneous equations with error components structure, Econometric Theory 3 (1987), 223–246. P. Balestra and M. Nerlove, Pooling crosssection and timeseries data in the estimation of a dynamic model: The demand for natural gas, Econometrica 34 (1966), 585–612. B.H. Baltagi, On seemingly unrelated regressions with error components, Econometrica 48 (1980), 1547–1551. B.H. Baltagi, Simultaneous equations with error components, Journal of Econometrics 17 (1981), 189–200. B.H. Baltagi, Econometric analysis of panal data, 2nd ed., John Wiley and Sons, 2001. B.H. Baltagi and Q. Li, A transformation that will cirumvent the problem of autocorrelation in an error component model, Journal of Econometrics 48 (1991), 385–393. B.H. Baltagi and Q. Li, Estimating error component models with general ma(q) disturbances, Econometric Theory 10 (1994), 396–408. C.G. Broyden and M.T. Vespucci, Krylov solvers for linear algebraic systems, Studies in Computational Mathematics, vol. 11, Elsevier, 2004. G. Chamberlain, Multivariate regression models for panel data, Journal of Econometrics 18 (1982), 5–46. G. Chamberlain, Panel data, ch. 22, pp. 1247–1318, NorthHolland, Amsterdam, 1984. P. Foschi, D.A. Belsley, and E.J. Kontoghiorghes, A comparative study of algorithms for solving seemingly unrelated regressions models, Computational Statistic & Data Analysis 44 (2003), 3–35. W.A. Fuller and G.E. Battese, Transformations for estimation of linear models with nested error structure, Journal of American Statistical Association 68 (1973), 626–632. W.A. Fuller and G.E. Battese, Estimation of linear models with crosserror structure, Journal of Econometrics 2 (1974), 67–78. J.W. Galbraith and V. ZindeWalsh, Transforming the errorcomponent model for esti mation with general arma disturbances, Journal of Econometrics 66 (1995), 349–355. G.H. Golub and C.F. Van Loan, Matrix computations, 3ed ed., Johns Hopkins University Press, Baltimore, Maryland, 1996. S. Karlsson and J. Skoglund, Maximumlikelihood based inference in the twoway random effects model with serially correlated time effects, Empirical Economics 29 (2004), 79–88. E.J. Kontoghiorghes, Inconsistencies and redundancies in SURE models: computational aspects, Computational Economics 16 (2000), no. 1+2, 63–70. E.J. Kontoghiorghes, Parallel algorithms for linear models: Numerical methods and estimation problems, Advances in Computational Economics, vol. 15, Kluwer Academic Publishers, Boston, MA, 2000. E.J. Kontoghiorghes, Computational methods for modifying seemingly unrelated regressions models, Journal of Computational and Applied Mathematics 162 (2004), no. 1, 247–261. E.J. Kontoghiorghes and M. R. B. Clarke, An alternative approach for the numerical solution of seemingly unrelated regression equations models, Computational Statistics & Data Analysis 19 (1995), no. 4, 369–377. S. Kourouklis and C.C. Paige, A constrained least squares approach to the general Gauss–Markov linear model, Journal of the American Statistical Association 76 (1981), no. 375, 620–625. J. Krishnakumar, Estimating simultaneous equation models with error components structure, SpringerVerlag, Berlin, 1988. L.F. Lee, Estimation of autocorrelated error components model with panel data, working paper, Tech. report, Department of Economics, University of Minnesota, 1979. L.A. Lillard and R.J. Willis, Dynamic aspects of earning mobility, Econometrica 47 (1978), 985–1012. J.R. Magnus and A.D. Wooland, On the maximum likelihood estimation of multivariate regression models containing serially correlated error components, Economic Review 29 (1988), 707–725. P. Mazodier and A. Trognon, Heteroskedasticity and strification in error component models, Annales de l’INSEE 3031 (1978), 451–482. M.A. McCurdy, The use of time series processes to model the error structure of earnings in a longitudinal data analysis, Journal of Econometrics 18 (1982), 83–114. M. Nerlove, A note on error components models, Econometrica 39 (1971), 383–396. C.C. Paige, Numerically stable computations for general univariate linear models, Communications on Statistical and Simulation Computation 7 (1978), no. 5, 437–453. N.S. Revankar, Error component models with serial correlated time effects, Journal of the Indian Statistical Association 17 (1979), 137–160. J. Skoglund and S. Karlsson, Specification and estimation of random effects models with correlation of general form, Tech. Report 433, Stockholm School of Economics, 2001. T.D. Wallace and A. Hussain, The use of error components models in combining crosssection and timeseries data, Econometrica 37 (1969), 55–72. T.J. Wansbeek and A. Kapteyn, A note on the spectral decomposition and maximum likelihood estimation of anova models with balanced data, Statistics and Probability 1 (1982), 213–215. T.J. Wansbeek and A. Kapteyn, A simple way to obtain the spectral decomposition of variance components models for balanced data, Communications in Statistics A11 (1982), 2105–2112. P. Yanev and E.J. Kontoghiorghes, Updating the SUR model, Tech. report, Univ. of Neuchatel, 2005, to be submitted. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/1424 