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Estimating Very Large Demand Systems

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  • Lanier, Joshua
  • Large, Jeremy
  • Quah, John

Abstract

We present a discrete choice, random utility model and a new estimation technique for analyzing consumer demand for large numbers of products. We allow the consumer to purchase multiple units of any product and to purchase multiple products at once (think of a consumer selecting a bundle of goods in a supermarket). In our model each product has an associated unobservable vector of attributes from which the consumer derives utility. Our model allows for heterogeneous utility functions across consumers, complex patterns of substitution and complementarity across products, and nonlinear price effects. The dimension of the attribute space is, by assumption, much smaller than the number of products, which effectively reduces the size of the consumption space and simplifies estimation. Nonetheless, because the number of bundles available is massive, a new estimation technique, which is based on the practice of negative sampling in machine learning, is needed to sidestep an intractable likelihood function. We prove consistency of our estimator, validate the consistency result through simulation exercises, and estimate our model using supermarket scanner data.

Suggested Citation

  • Lanier, Joshua & Large, Jeremy & Quah, John, 2022. "Estimating Very Large Demand Systems," INET Oxford Working Papers 2023-01, Institute for New Economic Thinking at the Oxford Martin School, University of Oxford.
  • Handle: RePEc:amz:wpaper:2023-01
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    File URL: https://www.inet.ox.ac.uk/files/LanierLargeQuah2022.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    discrete choice; demand estimation; negative sampling; machine learning; scanner data;
    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
    • L20 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - General
    • L66 - Industrial Organization - - Industry Studies: Manufacturing - - - Food; Beverages; Cosmetics; Tobacco

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