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Limit theorems for estimating the parameters of differentiated product demand systems

Author

Listed:
  • Berry, Steve
  • Linton, Oliver
  • Pakes, Ariel

Abstract

We provide an asymptotic distribution theory for a class of Generalized Method of Moments estimators that arise in the study of differentiated product markets when the number of observations is associated with the number of products within a given market. We allow for three sources of error: the sampling error in estimating market shares, the simulation error in approximating the shares predicted by the model, and the underlying model error. The limiting distribution of the parameter estimator is normal provided the size of the consumer sample and the number of simulation draws grow at a large enough rate relative to the number of products. The required rates differ for two frequently used demand models, and a small Monte Carlo study shows that the difference in asymptotic properties of the two models are reflected in the models’ small sample properties. The differences impact directly on the computational burden of the two models.

Suggested Citation

  • Berry, Steve & Linton, Oliver & Pakes, Ariel, 2000. "Limit theorems for estimating the parameters of differentiated product demand systems," LSE Research Online Documents on Economics 2032, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:2032
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    File URL: https://researchonline.lse.ac.uk/id/eprint/2032/
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    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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