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Sparse demand systems: corners and complements

Author

Listed:
  • Arthur Lewbel

    (Boston College)

  • Lars Nesheim

    (CeMMAP)

Abstract
We propose a demand model where consumers simultaneously choose a few different goods from a large menu of available goods, and choose how much to consume of each good. The model nests multinomial discrete choice and continuous demand systems as special cases. Goods can be substitutes or complements. Random coefficients are employed to capture the wide variation in the composition of consumption baskets. Non-negativity constraints produce corners that account for different consumers purchasing different numbers of types of goods. We show semiparametric identification of the model. We apply the model to the demand for fruit in the United Kingdom. We estimate the model’s parameters using UK scanner data for 2008 from the Kantar World Panel. Using our parameter estimates, we estimate a matrix of demand elasticities for 27 categories of fruit and analyze a range of tax and policy change scenarios.

Suggested Citation

  • Arthur Lewbel & Lars Nesheim, 2019. "Sparse demand systems: corners and complements," Boston College Working Papers in Economics 1005, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:1005
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    References listed on IDEAS

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    Cited by:

    1. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    2. Martin O'Connell & Pierre Dubois & Rachel Griffith, 2022. "The Use of Scanner Data for Economics Research," Annual Review of Economics, Annual Reviews, vol. 14(1), pages 723-745, August.
    3. Han Yuan, 2020. "Competing for Time: A Study of Mobile Applications," 2020 Papers pyu309, Job Market Papers.
    4. Fu Ouyang & Thomas T. Yang, 2023. "Semiparametric Discrete Choice Models for Bundles," Papers 2306.04135, arXiv.org, revised Nov 2023.
    5. Fu Ouyang & Thomas Tao Yang, 2020. "Semiparametric Discrete Choice Models for Bundles," Discussion Papers Series 625, School of Economics, University of Queensland, Australia.
    6. Bryan S. Graham, 2020. "Sparse network asymptotics for logistic regression," Papers 2010.04703, arXiv.org.

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    More about this item

    Keywords

    sparse demand; discrete choice; continuous choice; complements; complementarity; substitutes; demand estimation; scanner data; fruit; quadratic utility;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C34 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Truncated and Censored Models; Switching Regression Models
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • L40 - Industrial Organization - - Antitrust Issues and Policies - - - General
    • L66 - Industrial Organization - - Industry Studies: Manufacturing - - - Food; Beverages; Cosmetics; Tobacco

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