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

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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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    References listed on IDEAS

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    5. 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.
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    11. 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.
    12. Hendry, David F, 1974. "Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process: A Correction," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 260-260, February.
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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, 1984. "A Simulation Study on FIML Covariance Matrix," MPRA Paper 28804, University Library of Munich, Germany.
    3. Calzolari, Giorgio & Panattoni, Lorenzo, 1985. "Gradient methods in FIML estimation of econometric models," MPRA Paper 24843, University Library of Munich, Germany.
    4. Jansson, Leif & Mellander, Erik, 1984. "CONRAD – A Maximum Likelihood Program for Estimation of Simultaneous Equations Models that are Non-Linear in the Parameters," Working Paper Series 131, Research Institute of Industrial Economics.

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    More about this item

    Keywords

    Hessian matrix; full information maximum likelihood; Newton like methods; gradient methods; covariance matrix estimators;
    All these keywords.

    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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