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Identification of Average Marginal Effects in Fixed Effects Dynamic Discrete Choice Models

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  • Aguirregabiria, Victor
  • Carro, Jesus
Abstract
In nonlinear panel data models, fixed effects methods are often criticized because they cannot identify average marginal effects (AMEs) in short panels. The common argument is that the identification of AMEs requires knowledge of the distribution of unobserved heterogeneity, but this distribution is not identified in a fixed effects model with a short panel. In this paper, we derive identification results that contradict this argument. In a panel data dynamic logic model, and for T as small as four, we prove the point identification of different AMEs, including causal effects of changes in the lagged dependent variable or in the duration in last choice. Our proofs are constructive and provide simple closed-form expressions for the AMEs in terms of probabilities of choice histories. We illustrate our results using Monte Carlo experiments and with an empirical application of a dynamic structural model of consumer brand choice with state dependence.

Suggested Citation

  • Aguirregabiria, Victor & Carro, Jesus, 2021. "Identification of Average Marginal Effects in Fixed Effects Dynamic Discrete Choice Models," CEPR Discussion Papers 16354, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:16354
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    Citations

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    Cited by:

    1. Christopher Dobronyi & Jiaying Gu & Kyoo il Kim, 2021. "Identification of Dynamic Panel Logit Models with Fixed Effects," Papers 2104.04590, arXiv.org, revised Apr 2021.
    2. Kevin Dano, 2023. "Transition Probabilities and Moment Restrictions in Dynamic Fixed Effects Logit Models," Papers 2303.00083, arXiv.org, revised Dec 2023.
    3. Laurent Davezies & Xavier D'Haultfoeuille & Louise Laage, 2021. "Identification and Estimation of Average Marginal Effects in Fixed Effects Logit Models," Papers 2105.00879, arXiv.org, revised Oct 2022.
    4. Cavit Pakel & Martin Weidner, 2023. "Bounds on Average Effects in Discrete Choice Panel Data Models," Papers 2309.09299, arXiv.org, revised May 2024.
    5. Bo E. Honor'e & Chris Muris & Martin Weidner, 2021. "Dynamic Ordered Panel Logit Models," Papers 2107.03253, arXiv.org, revised Apr 2024.
    6. Victor Aguirregabiria, 2023. "Dynamic demand for differentiated products with fixed-effects unobserved heterogeneity," The Econometrics Journal, Royal Economic Society, vol. 26(1), pages 1-25.
    7. Irene Botosaru & Chris Muris & Senay Sokullu, 2022. "Time-Varying Linear Transformation Models with Fixed Effects and Endogeneity for Short Panels," Department of Economics Working Papers 2022-01, McMaster University.
    8. St'ephane Bonhomme & Kevin Dano, 2023. "Functional Differencing in Networks," Papers 2307.11484, arXiv.org.
    9. Laura Liu & Alexandre Poirier & Ji-Liang Shiu, 2021. "Identification and Estimation of Partial Effects in Nonlinear Semiparametric Panel Models," Papers 2105.12891, arXiv.org, revised Jul 2024.
    10. Geert Dhaene & Martin Weidner, 2023. "Approximate Functional Differencing," Papers 2301.13736, arXiv.org, revised May 2023.
    11. Irene Botosaru & Chris Muris, 2022. "Identification of time-varying counterfactual parameters in nonlinear panel models," Papers 2212.09193, arXiv.org, revised Nov 2023.

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    More about this item

    Keywords

    Identification; Average marginal effects; Fixed effects models; Panel data; Dynamic discrete choice; State dependence; Dynamic demand of differentiated products;
    All these keywords.

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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