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Simulation error and numerical instability in estimating random coefficient logit demand models

Author

Listed:
  • Brunner, Daniel
  • Heiss, Florian
  • Romahn, André
  • Weiser, Constantin

Abstract

The nonlinear GMM-IV estimator of Berry, Levinsohn and Pakes (1995) can suffer from numerical instability resulting in a wide range of parameter estimates and economic implications. This has been reported to depend on technical details such as the choice of the optimization algorithm, starting values, and convergence criteria. We show that numerical approximation errors in the estimator’s moment function are the main driver of this instability. With accurate approximation, the estimation approach is well-behaved. We provide a simple method to determine the required number of simulation draws.

Suggested Citation

  • Brunner, Daniel & Heiss, Florian & Romahn, André & Weiser, Constantin, 2025. "Simulation error and numerical instability in estimating random coefficient logit demand models," Journal of Econometrics, Elsevier, vol. 247(C).
    • Handle: RePEc:eee:econom:v:247:y:2025:i:c:s0304407625000077
    DOI: 10.1016/j.jeconom.2025.105953
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    References listed on IDEAS

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    Keywords

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • L62 - Industrial Organization - - Industry Studies: Manufacturing - - - Automobiles; Other Transportation Equipment; Related Parts and Equipment

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