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Hessian and approximated Hessian matrices in maximum likelihood estimation: a Monte Carlo study

Author

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  • Calzolari, Giorgio
  • Panattoni, Lorenzo

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.

Suggested Citation

  • Calzolari, Giorgio & Panattoni, Lorenzo, 1983. "Hessian and approximated Hessian matrices in maximum likelihood estimation: a Monte Carlo study," MPRA Paper 28847, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:28847
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    File URL: https://mpra.ub.uni-muenchen.de/28847/1/MPRA_paper_28847.pdf
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    References listed on IDEAS

    as
    1. Hendry, D F, 1971. "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 12(2), pages 257-272, June.
    2. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665 National Bureau of Economic Research, Inc.
    3. Belsley, David A., 1980. "On the efficient computation of the nonlinear full-information maximum-likelihood estimator," Journal of Econometrics, Elsevier, vol. 14(2), pages 203-225, October.
    4. Jerry A. Hausman, 1974. "Full Information Instrumental Variables Estimation of Simultaneous Equations Systems," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 641-652 National Bureau of Economic Research, Inc.
    5. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    6. Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984. "Pseudo Maximum Likelihood Methods: Theory," Econometrica, Econometric Society, vol. 52(3), pages 681-700, May.
    7. Brundy, James M & Jorgenson, Dale W, 1971. "Efficient Estimation of Simultaneous Equations by Instrumental Variables," The Review of Economics and Statistics, MIT Press, vol. 53(3), pages 207-224, August.
    8. James M. Brundy & Dale W. Jorgenson, 1971. "Efficient estimation of simultaneous equations by instrumental variables," Working Papers in Applied Economic Theory 3, Federal Reserve Bank of San Francisco.
    9. Klein, Lawrence R, 1969. "Estimation on Interdependent Systems in Macroeconometrics," Econometrica, Econometric Society, vol. 37(2), pages 171-192, April.
    10. Hatanaka, Michio, 1978. "On the efficient estimation methods for the macro-economic models nonlinear in variables," Journal of Econometrics, Elsevier, vol. 8(3), pages 323-356, December.
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    Citations

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    Cited by:

    1. Calzolari, Giorgio & Panattoni, Lorenzo, 1984. "Evaluating Forecast Uncertainty in Econometric Models: The Effect of Alternative Estimators of Maximum Likelihood Covariance Matrix," MPRA Paper 28806, University Library of Munich, Germany.
    2. Calzolari, Giorgio & Panattoni, Lorenzo, 1985. "Gradient methods in FIML estimation of econometric models," MPRA Paper 24843, University Library of Munich, Germany.
    3. Calzolari, Giorgio & Panattoni, Lorenzo, 1984. "A Simulation Study on FIML Covariance Matrix," MPRA Paper 28804, University Library of Munich, Germany.

    More about this item

    Keywords

    Hessian matrix; full information maximum likelihood; Newton like methods; gradient methods; covariance matrix estimators;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables

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