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Note on the Uniqueness of the Maximum Likelihood Estimator for a Heckman’s Simultaneous Equations Model

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  • Akashi, Kentaro
  • Horie, Tetsushi

Abstract

It is shown that the likelihood function of a Heckman’s simultaneous equations model is identified by complementing the approach of parameter transformation. Therefore, the expectation of the log-likelihood function has a single maximum. Thus, the maximum likelihood estimator becomes asymptotically consistent without an initial consistent estimator. Additionally, the approach can show the uniqueness of the log-likelihood functions for the simultaneous Tobit, sample selection (Type 2 Tobit), and simultaneous generalized selectivity models.

Suggested Citation

  • Akashi, Kentaro & Horie, Tetsushi, 2025. "Note on the Uniqueness of the Maximum Likelihood Estimator for a Heckman’s Simultaneous Equations Model," Econometrics and Statistics, Elsevier, vol. 34(C), pages 69-77.
    • Handle: RePEc:eee:ecosta:v:34:y:2025:i:c:p:69-77
    DOI: 10.1016/j.ecosta.2022.02.004
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    JEL classification:

    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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