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The behavior of trust-region methods in FIML estimation

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  • Weihs, Claus
  • Calzolari, Giorgio
  • Panattoni, Lorenzo

Abstract

This paper presents a Monte-Carlo study on the practical reliability of numerical algorithms for FIML-estimation in nonlinear econometric models. The performance of different techniques of Hessian approximation in trust-region algorithms is compared regarding their "robustness" against "bad" starting points and their "global" and "local" convergence speed, i.e. the gain in the objective function, caused by individual iteration steps far off from and near to the optimum. Concerning robustness and global convergence speed the crude GLS-type Hessian approximations performed best, efficiently exploiting the special structure of the likelihood function. But, concerning local speed, general purpose techniques were strongly superior. So, some appropriate mixtures of these two types of approximations turned out to be the only techniques to be recommended.

Suggested Citation

  • Weihs, Claus & Calzolari, Giorgio & Panattoni, Lorenzo, 1986. "The behavior of trust-region methods in FIML estimation," MPRA Paper 24122, University Library of Munich, Germany, revised 1987.
    • Handle: RePEc:pra:mprapa:24122
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    References listed on IDEAS

    as
    1. Besley, David A., 1979. "On the computational competitiveness of full-information maximum-likelihood and three-stage least-squares in the estimation of nonlinear, simultaneous-equations models," Journal of Econometrics, Elsevier, vol. 9(3), pages 315-342, February.
    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 & Weihs, Claus, 1987. "Computational efficiency of FIML estimation," Journal of Econometrics, Elsevier, vol. 36(3), pages 299-310, November.
    4. Calzolari, Giorgio & Panattoni, Lorenzo, 1984. "A Simulation Study on FIML Covariance Matrix," MPRA Paper 28804, University Library of Munich, Germany.
    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.
    6. Parke, William R, 1982. "An Algorithm for FIML and 3SLS Estimation of Large Nonlinear Models," Econometrica, Econometric Society, vol. 50(1), pages 81-95, January.
    7. Dagenais, Marcel G, 1978. "The Computation of FIML Estimates as Iterative Generalized Least Squares Estimates in Linear and Nonlinear Simultaneous Equations Models," Econometrica, Econometric Society, vol. 46(6), pages 1351-1362, November.
    8. 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.
    9. Amemiya, Takeshi, 1977. "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model," Econometrica, Econometric Society, vol. 45(4), pages 955-968, May.
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    More about this item

    Keywords

    Econometrics; Monte Carlo methods; numerical methods; trust-region methods; FIML estimation;
    All these keywords.

    JEL classification:

    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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