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Estimation of random coefficients logit demand models with interactive fixed effects

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  • Moon, Hyungsik Roger
  • Shum, Matthew
  • Weidner, Martin

Abstract

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete-choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodate endogeneity and, at the same time, capture strong persistence in market shares across products and markets. We propose a two-step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical illustration to US automobile demand.

Suggested Citation

  • Moon, Hyungsik Roger & Shum, Matthew & Weidner, Martin, 2018. "Estimation of random coefficients logit demand models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 613-644.
  • Handle: RePEc:eee:econom:v:206:y:2018:i:2:p:613-644
    DOI: 10.1016/j.jeconom.2018.06.016
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    3. Ando, Tomohiro & Bai, Jushan & Li, Kunpeng, 2022. "Bayesian and maximum likelihood analysis of large-scale panel choice models with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 230(1), pages 20-38.
    4. Daniel Czarnowske & Amrei Stammann, 2020. "Inference in Unbalanced Panel Data Models with Interactive Fixed Effects," Papers 2004.03414, arXiv.org.
    5. Vira Semenova & Matt Goldman & Victor Chernozhukov & Matt Taddy, 2023. "Inference on heterogeneous treatment effects in high‐dimensional dynamic panels under weak dependence," Quantitative Economics, Econometric Society, vol. 14(2), pages 471-510, May.
    6. Fabian Dunker & Stefan Hoderlein & Hiroaki Kaido, 2023. "Nonparametric identification of random coefficients in aggregate demand models for differentiated products," The Econometrics Journal, Royal Economic Society, vol. 26(2), pages 279-306.
    7. Ando, Tomohiro & Bai, Jushan, 2021. "Large-scale generalized linear longitudinal data models with grouped patterns of unobserved heterogeneity," MPRA Paper 111431, University Library of Munich, Germany.
    8. Hugo Freeman & Martin Weidner, 2021. "Linear Panel Regressions with Two-Way Unobserved Heterogeneity," Papers 2109.11911, arXiv.org, revised Aug 2022.
    9. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    10. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
    11. Ye, Xiaoqing & Xu, Juan & Wu, Xiangjun, 2018. "Estimation of an unbalanced panel data Tobit model with interactive effects," Journal of choice modelling, Elsevier, vol. 28(C), pages 108-123.
    12. Robert Donnelly & Francisco J.R. Ruiz & David Blei & Susan Athey, 2021. "Counterfactual inference for consumer choice across many product categories," Quantitative Marketing and Economics (QME), Springer, vol. 19(3), pages 369-407, December.
    13. Lu, Xun & Su, Liangjun, 2016. "Shrinkage estimation of dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 190(1), pages 148-175.
    14. Walter Beckert & Elaine Kelly, 2021. "Divided by choice? For‐profit providers, patient choice and mechanisms of patient sorting in the English National Health Service," Health Economics, John Wiley & Sons, Ltd., vol. 30(4), pages 820-839, April.
    15. Freeman, Hugo & Weidner, Martin, 2023. "Linear panel regressions with two-way unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 237(1).
    16. Bokhari, Farasat A.S. & Mariuzzo, Franco, 2018. "Demand estimation and merger simulations for drugs: Logits v. AIDS," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 653-685.
    17. Lu, Zhentong & Shi, Xiaoxia & Tao, Jing, 2023. "Semi-nonparametric estimation of random coefficients logit model for aggregate demand," Journal of Econometrics, Elsevier, vol. 235(2), pages 2245-2265.
    18. Hugo Freeman & Martin Weidner, 2021. "Linear panel regressions with two-way unobserved heterogeneity," CeMMAP working papers CWP39/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Galvao, Antonio F. & Wang, Liang, 2015. "Efficient minimum distance estimator for quantile regression fixed effects panel data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 1-26.
    20. Chen, Mingli, 2016. "Estimation of Nonlinear Panel Models with Multiple Unobserved Effects," Economic Research Papers 269326, University of Warwick - Department of Economics.
    21. Miao, Ke & Li, Kunpeng & Su, Liangjun, 2020. "Panel threshold models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 219(1), pages 137-170.
    22. Hong, Shengjie & Su, Liangjun & Jiang, Tao, 2023. "Profile GMM estimation of panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 235(2), pages 927-948.

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    More about this item

    Keywords

    Discrete-choice demand model; Interactive fixed effects; Factor analysis; Panel data; Random utility model;
    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

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