Calzolari, Giorgio and Panattoni, Lorenzo (1983): Hessian and approximated Hessian matrices in maximum likelihood estimation: a Monte Carlo study.

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Abstract
Full information maximum likelihood estimation of econometric models, linear and nonlinear in variables, is performed by means of two gradient algorithms, using either the Hessian matrix or a computationally simpler approximation. In the first part of the paper, the behavior of the two methods in getting the optimum is investigated with Monte Carlo experimentation on some models of small and medium size. In the second part of the paper, the behavior of the two matrices in producing estimates of the asymptotic covariance matrix of coefficients is analyzed and, again. experimented with Monte Carlo on the same models. Some systematic differences are evidenced.
Item Type:  MPRA Paper 

Original Title:  Hessian and approximated Hessian matrices in maximum likelihood estimation: a Monte Carlo study 
Language:  English 
Keywords:  Hessian matrix, full information maximum likelihood, Newton like methods, gradient methods, covariance matrix estimators 
Subjects:  C  Mathematical and Quantitative Methods > C6  Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63  Computational Techniques; Simulation Modeling C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models; Multiple Variables 
Item ID:  28847 
Depositing User:  Giorgio Calzolari 
Date Deposited:  28. Feb 2011 15:31 
Last Modified:  13. Feb 2013 14:10 
References:  Amemiya, T. (1977), "The Maximum Likelihood and the Nonlinear ThreeStage Least Squares in the General Nonlinear Simultaneous Equation Model", Econometrica 45, 955968. Artus, P., G. Laroque, and G.Michel (1982), "Estimation of a Quarterly Model with Quantity Rationing". Paris: INSEE, discussion paper presented at the European Meeting of the Econometric Society, Dublin. Belsley, D. A. (1980): "On the Efficient Computation of the Nonlinear FullInformation MaximumLikelihood Estimator", Journal of Econometrics 14, 203225. Berndt, E. K., B. H. Hall, R. E. Hall, and J. A. Hausman (1974): "Estimation and Inference in Nonlinear Structural Models", Annals of Economic and Social Measurement 3, 653665. Brundy, J. M., and D. W. Jorgenson (1971): "Efficient Estimation of Simultaneous Equations by Instrumental Variables", The Review of Economics and Statistics 53, 207224. Dhrymes, P. J. (1970): Econometrics: Statistical Foundations and Applications. New York: Harper & Row. Eisenpress, H. and J. Greenstadt (1966), "The Estimation of Nonlinear Econometric Systems". Econometrica 34, 85186l. Gourieroux, C., A. Monfort, and A. Trognon (1984), "Pseudo Maximum Likelihood Methods: Theory". Econometrica 52, 681700. Hatanaka, M. (1978), "On the Efficient Estimation Methods for the MacroEconomic Models Nonlinear in Variables", Journal of Econometrics 8, 323356. Hausman, J. A. (1974), "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems", Annals of Economic and Social Measurement 3, 641652. Hendry, D. F. (1971), "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process", International Economic Review 12, 257272. Klein, L. R. (1969), "Estimation of lnterdependent Systems in Macroeconometrics", Econometrica 37, 171192. Parke, W. R. (1982), "An algorithm for FIML and 3SLS estimation of large nonlinear models", Econometrica 50, 8195 Pierre, D.A. (1969), Optimization Theory with Applications. New York: John Wiley & Sons. Rothenberg,T.J. and C.T.Leenders (1964), "Efficient Estimation of Simultaneous Equation Systems", Econometrica 32, 5716. Rothenberg.T.J. (1973). Efficient Estimation with A Priori Information, Cowles Foundation Monograph 23. New Haven: Yale Unlversity Press. Sitzia, B., and M. Tivegna (1975), "Un Modello Aggregato dell'Economia Italiana 19521971", in Contributi alla Ricerca Economica No.4. Roma: Banca d'ltalia, 195223. White, H. (1982), "Maximum Likelihood Estimation of Misspecified Models", Econometrica 50, 125. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/28847 