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PML versus minimum $${\chi }^{2}$$ χ 2 : the comeback

Author

Listed:
  • Dante Amengual

    (CEMFI)

  • Gabriele Fiorentini

    (Università di Firenze and RCEA)

  • Enrique Sentana

    (CEMFI)

Abstract

Arellano (J Econ 42:247–265, 1989a) showed that valid equality restrictions on covariance matrices could result in efficiency losses for Gaussian PMLEs in simultaneous equations models. We revisit his two-equation example using finite normal mixtures PMLEs instead, which are also consistent for mean and variance parameters regardless of the true distribution of the shocks. Because such mixtures provide good approximations to many distributions, we relate the asymptotic variance of our estimators to the relevant semiparametric efficiency bound. Our Monte Carlo results indicate that they systematically dominate MD and that the version that imposes the valid covariance restriction is more efficient than the unrestricted one.

Suggested Citation

  • Dante Amengual & Gabriele Fiorentini & Enrique Sentana, 2023. "PML versus minimum $${\chi }^{2}$$ χ 2 : the comeback," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 14(3), pages 253-300, December.
    • Handle: RePEc:spr:series:v:14:y:2023:i:3:d:10.1007_s13209-023-00280-4
    DOI: 10.1007/s13209-023-00280-4
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    Keywords

    Covariance restrictions; Distributional misspecification; Efficiency bound; Finite normal mixtures; Partial adaptivity; Sieves;
    All these keywords.

    JEL classification:

    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation

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