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On asymptotic size distortions in the random coefficients logit model

Author

Listed:
  • Philipp Ketz

    (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique)

Abstract

We show that, in the random coefficients logit model, standard inference procedures can suffer from asymptotic size distortions. The problem arises due to boundary issues and is aggravated by the standard parameterization of the model, in terms of standard deviations. For example, in case of a single random coefficient, the asymptotic size of the nominal 95% confidence interval obtained by inverting the two-sided t-test for the standard deviation equals 83.65%. In seeming contradiction, we also show that standard error estimates for the estimator of the standard deviation can be unreasonably large. This problem is alleviated if the model is reparameterized in terms of variances. Furthermore, a numerical evaluation of a conjectured lower bound suggests that the asymptotic size of the nominal 95% confidence interval obtained by inverting the two-sided t-test for variances (means) is within 0.5 percentage points of the nominal level as long as there are no more than five (four) random coefficients and as long as an optimal weighting matrix is employed.

Suggested Citation

  • Philipp Ketz, 2019. "On asymptotic size distortions in the random coefficients logit model," PSE-Ecole d'économie de Paris (Postprint) halshs-02302067, HAL.
    • Handle: RePEc:hal:pseptp:halshs-02302067
    DOI: 10.1016/j.jeconom.2019.02.008
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    Citations

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    Cited by:

    1. Gregory Fletcher Cox, 2024. "A Simple and Adaptive Confidence Interval when Nuisance Parameters Satisfy an Inequality," Papers 2409.09962, arXiv.org.
    2. Salanié, Bernard & Wolak, Frank, 2018. "Fast, “Robust†, and Approximately Correct: Estimating Mixed Demand Systems," CEPR Discussion Papers 13236, C.E.P.R. Discussion Papers.
    3. Dimri, Aditi & Gille, Véronique & Ketz, Philipp, 2024. "Measuring sex-selective abortion: How many women abort?," Journal of Development Economics, Elsevier, vol. 171(C).
    4. Pesendorfer, Martin & Schiraldi, Pasquale & Silva-Junior, Daniel, 2023. "Omitted budget constraint bias in discrete-choice demand models," International Journal of Industrial Organization, Elsevier, vol. 86(C).
    5. Mathias Reynaert, 2021. "Abatement Strategies and the Cost of Environmental Regulation: Emission Standards on the European Car Market," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 88(1), pages 454-488.
    6. Wang, Ao, 2021. "A BLP Demand Model of Product-Level Market Shares with Complementarity," The Warwick Economics Research Paper Series (TWERPS) 1351, University of Warwick, Department of Economics.
    7. Bernard Salanie & Frank A. Wolak, 2018. "Fast, "robust", and approximately correct: estimating mixed demand systems," CeMMAP working papers CWP64/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Aditi Dimri & Véronique Gille & Philipp Ketz, 2024. "Measuring sex-selective abortion: How many women abort?," Post-Print hal-04671748, HAL.
    9. Aditi Dimri & Véronique Gille & Philipp Ketz, 2024. "Measuring sex-selective abortion: How many women abort?," PSE-Ecole d'économie de Paris (Postprint) hal-04671748, HAL.
    10. Pesendorfer, Martin & Schiraldi, Pasquale & Silva-Junior, Daniel, 2023. "Omitted budget constraint bias in discrete-choice demand models," LSE Research Online Documents on Economics 117353, London School of Economics and Political Science, LSE Library.
    11. Ketz, Philipp, 2019. "Testing overidentifying restrictions with a restricted parameter space," Economics Letters, Elsevier, vol. 185(C).

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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