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Estimating demand for differentiated products with error in market shares


  • Amit Gandhi Gandhi

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

  • Zhentong Lu

    (Institute for Fiscal Studies)

  • Xiaoxia Shi

    (Institute for Fiscal Studies)


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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    References listed on IDEAS

    1. Hausman, Jerry A & Leonard, Gregory K, 2002. "The Competitive Effects of a New Product Introduction: A Case Study," Journal of Industrial Economics, Wiley Blackwell, vol. 50(3), pages 237-263, September.
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    3. Guillermo Israilevich, 2004. "Assessing Supermarket Product-Line Decisions: The Impact of Slotting Fees," Quantitative Marketing and Economics (QME), Springer, vol. 2(2), pages 141-167, June.
    4. John C. Driscoll & Aart C. Kraay, 1998. "Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 549-560, November.
    5. Steven Berry & Panle Jia, 2010. "Tracing the Woes: An Empirical Analysis of the Airline Industry," American Economic Journal: Microeconomics, American Economic Association, vol. 2(3), pages 1-43, August.
    6. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    7. Austan Goolsbee & Amil Petrin, 2004. "The Consumer Gains from Direct Broadcast Satellites and the Competition with Cable TV," Econometrica, Econometric Society, vol. 72(2), pages 351-381, March.
    8. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, January.
    9. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
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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. D’Haultfoeuille, Xavier & Durrmeyer, Isis & Février, Philippe, 2014. "Automobile Prices in Market Equilibrium with Unobserved Price Discrimination," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 477, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    4. Hyungsik Roger Moon & Matthew Shum & Martin Weidner, 2012. "Estimation of random coefficients logit demand models with interactive fixed effects," CeMMAP working papers CWP08/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. 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.
    6. Arkadiusz Szyd?owski, 2017. "Stochastic processes of limited frequency and the effects of oversampling," Discussion Papers in Economics 17/04, Department of Economics, University of Leicester.
    7. Arkadiusz Szydlowski, 2015. "Endogenous Censoring in the Mixed Proportional Hazard Model with an Application to Optimal Unemployment Insurance," Discussion Papers in Economics 15/06, Department of Economics, University of Leicester.
    8. 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.
    9. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    10. repec:eee:ecolet:v:159:y:2017:i:c:p:42-45 is not listed on IDEAS

    More about this item


    Demand Estimation; Differentiated Products; Profile; Measurement Error; Moment Inequality.;

    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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