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Asymptotic theory for differentiated products demand models with many markets

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  • Freyberger, Joachim

Abstract

This paper develops asymptotic theory for differentiated product demand models with a large number of markets T. It takes into account that the predicted market shares are approximated by Monte Carlo integration with R draws and that the observed market shares are approximated from a sample of N consumers. The estimated parameters are T consistent and asymptotically normal as long as R and N grow fast enough relative to T. Both approximations yield additional bias and variance terms in the asymptotic expansion. I propose a bias corrected estimator and a variance adjustment that takes the leading terms into account. Monte Carlo simulations show that these adjustments should be used in applications to avoid severe undercoverage caused by the approximation errors.

Suggested Citation

  • Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    • Handle: RePEc:eee:econom:v:185:y:2015:i:1:p:162-181
    DOI: 10.1016/j.jeconom.2014.10.009
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    2. Steven T. Berry & Philip A. Haile, 2021. "Foundations of Demand Estimation," Cowles Foundation Discussion Papers 2301, Cowles Foundation for Research in Economics, Yale University.
    3. Stépahne Auray & Nicolas Lepage-Saucier & Purevdorj Tuvaandor, 2018. "Doubly Robust GMM Inference and Differentiated Products Demand Models," Working Papers 2018-13, Center for Research in Economics and Statistics.
    4. Ketz, Philipp, 2019. "On asymptotic size distortions in the random coefficients logit model," Journal of Econometrics, Elsevier, vol. 212(2), pages 413-432.
    5. Kandelhardt, Johannes, 2023. "Flexible estimation of random coefficient logit models of differentiated product demand," DICE Discussion Papers 399, Heinrich Heine University Düsseldorf, Düsseldorf Institute for Competition Economics (DICE).
    6. Alessandro Iaria, & Wang, Ao, 2021. "An Empirical Model of Quantity Discounts with Large Choice Sets," The Warwick Economics Research Paper Series (TWERPS) 1378, University of Warwick, Department of Economics.
    7. Amit Gandhi & Zhentong Lu & Xiaoxia Shi, 2023. "Estimating demand for differentiated products with zeroes in market share data," Quantitative Economics, Econometric Society, vol. 14(2), pages 381-418, May.
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    9. 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.
    10. Tomohiro Ando & Jushan Bai, 2020. "Quantile Co-Movement in Financial Markets: A Panel Quantile Model With Unobserved Heterogeneity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 266-279, January.
    11. Hong, Han & Li, Huiyu & Li, Jessie, 2021. "BLP estimation using Laplace transformation and overlapping simulation draws," Journal of Econometrics, Elsevier, vol. 222(1), pages 56-72.
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    13. Pál, László & Sándor, Zsolt, 2023. "Comparing procedures for estimating random coefficient logit demand models with a special focus on obtaining global optima," International Journal of Industrial Organization, Elsevier, vol. 88(C).
    14. 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.
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    16. Christopher Conlon & Jeff Gortmaker, 2020. "Best practices for differentiated products demand estimation with PyBLP," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 1108-1161, December.

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    More about this item

    Keywords

    Demand estimation; Differentiated products; Many markets; Bias correction; Adjusted standard errors;
    All these keywords.

    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
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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