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Estimating demand for differentiated products with error in market shares

Author

Listed:
  • Amit Gandhi Gandhi

    (Institute for Fiscal Studies and University of Wisconsin-Madison)

  • Zhentong Lu

    (Institute for Fiscal Studies)

  • Xiaoxia Shi

    (Institute for Fiscal Studies)

Abstract

In this paper we introduce a new approach to estimating a differentiated product demand system that allows for error in market shares as measures of choice probabilities. In particular, our approach allows for products with zero sales in the data, which is a frequent phenomenon that arises in product differentiated markets but lies outside the scope of existing demand estimation techniques. Although we find that error in market shares generally undermine the standard point identification of discrete choice models of demand, we exploit shape restrictions on demand implied by discrete choice to generate a system of moment inequalities that partially identify demand parameters. These moment inequalities are fully robust to the variability in market shares yet are also adaptive to the information revealed by market shares in a way that allows for informative inferences. In addition, we construct a profiling approach for parameter inference with moment inequalities, making it feasible to study models with a large number of parameters (as typically required in demand applications) by focusing attention on a profile of the parameters, such as the price coefficient. We use our approach to study consumer demand from scanner data using the Dominick's Finer Foods database, and find that even for the baseline logit model, demand elasticities nearly double when the full error in market shares is taken into account.

Suggested Citation

  • Amit Gandhi Gandhi & Zhentong Lu & Xiaoxia Shi, 2013. "Estimating demand for differentiated products with error in market shares," CeMMAP working papers CWP03/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:03/13
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    File URL: http://www.cemmap.ac.uk/wps/cwp031313.pdf
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    References listed on IDEAS

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    Cited by:

    1. Bugni, Federico A. & Canay, Ivan A. & Shi, Xiaoxia, 2015. "Specification tests for partially identified models defined by moment inequalities," Journal of Econometrics, Elsevier, vol. 185(1), pages 259-282.
    2. Thomas W. Quan & Kevin R. Williams, 2016. "Product Variety, Across-Market Demand Heterogeneity, and the Value of Online Retail," Cowles Foundation Discussion Papers 2054, Cowles Foundation for Research in Economics, Yale University.
    3. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    4. 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.
    5. Xavier D’Haultfœuille & Isis Durrmeyer & Philippe Février, 2019. "Automobile Prices in Market Equilibrium with Unobserved Price Discrimination," Review of Economic Studies, Oxford University Press, vol. 86(5), pages 1973-1998.
    6. Joonhwi Joo & Ali Hortacsu, 2016. "Semiparametric estimation of CES demand system with observed and unobserved product characteristics," 2016 Meeting Papers 36, Society for Economic Dynamics.
    7. Khai Xiang Chiong & Matthew Shum, 2019. "Random Projection Estimation of Discrete-Choice Models with Large Choice Sets," Management Science, INFORMS, vol. 65(1), pages 256-271, January.
    8. Arkadiusz Szydlowski, 2017. "Stochastic processes of limited frequency and the effects of oversampling," Discussion Papers in Economics 17/04, Division of Economics, School of Business, University of Leicester.
    9. Arkadiusz Szydlowski, 2015. "Endogenous Censoring in the Mixed Proportional Hazard Model with an Application to Optimal Unemployment Insurance," Discussion Papers in Economics 15/06, Division of Economics, School of Business, University of Leicester.
    10. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    11. Dingel, Jonathan & Tintelnot, Felix, 2020. "Spatial Economics for Granular Settings," CEPR Discussion Papers 14819, C.E.P.R. Discussion Papers.
    12. D’Haultfœuille, Xavier & Durrmeyer, Isis & Février, Philippe, 2016. "Disentangling sources of vehicle emissions reduction in France: 2003–2008," International Journal of Industrial Organization, Elsevier, vol. 47(C), pages 186-229.
    13. Kattih Nour & Mixon Franklin G., 2020. "Employee Choice and the Demand for Health Insurance Coverage: Evidence from Random Coefficients Models," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 20(2), pages 1-13, April.
    14. Szydłowski, Arkadiusz, 2017. "Endogenously censored median regression with an application to benefit elasticity of US unemployment duration," Economics Letters, Elsevier, vol. 159(C), pages 42-45.

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    More about this item

    Keywords

    Demand Estimation; Differentiated Products; Profile; Measurement Error; Moment Inequality.;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General
    • L81 - Industrial Organization - - Industry Studies: Services - - - Retail and Wholesale Trade; e-Commerce

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