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Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation

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  • Lee, Jinhyuk
  • Seo, Kyoungwon

Abstract

This paper examines the numerical properties of the nested fixed-point algorithm (NFP) in the estimation of Berry et al. (1995) random coefficient logit demand model. Dubé et al. (2012) find the bound on the errors of the NFP estimates computed by contraction mappings (NFP/CTR) has the order of the square root of the inner loop tolerance. Under our assumptions, we theoretically derive an upper bound on the numerical bias in the NFP/CTR, which has the same order of the inner loop tolerance. We also discuss that, compared with NFP/CTR, NFP using Newton’s method has a smaller bound on the estimate error.

Suggested Citation

  • Lee, Jinhyuk & Seo, Kyoungwon, 2016. "Revisiting the nested fixed-point algorithm in BLP random coefficients demand estimation," Economics Letters, Elsevier, vol. 149(C), pages 67-70.
    • Handle: RePEc:eee:ecolet:v:149:y:2016:i:c:p:67-70
    DOI: 10.1016/j.econlet.2016.10.019
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    References listed on IDEAS

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    1. Rust, John, 1987. "Optimal Replacement of GMC Bus Engines: An Empirical Model of Harold Zurcher," Econometrica, Econometric Society, vol. 55(5), pages 999-1033, September.
    2. Jean‐Pierre Dubé & Jeremy T. Fox & Che‐Lin Su, 2012. "Improving the Numerical Performance of Static and Dynamic Aggregate Discrete Choice Random Coefficients Demand Estimation," Econometrica, Econometric Society, vol. 80(5), pages 2231-2267, September.
    3. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    4. Daniel Ackerberg & John Geweke & Jinyong Hahn, 2009. "Comments on "Convergence Properties of the Likelihood of Computed Dynamic Models"," Econometrica, Econometric Society, vol. 77(6), pages 2009-2017, November.
    5. Fedor Iskhakov & Jinhyuk Lee & John Rust & Bertel Schjerning & Kyoungwon Seo, 2016. "Comment on “Constrained Optimization Approaches to Estimation of Structural Models”," Econometrica, Econometric Society, vol. 84, pages 365-370, January.
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    Cited by:

    1. Odran Bonnet & Alfred Galichon & Yu-Wei Hsieh & Keith O’Hara & Matt Shum, 2022. "Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    2. Xavier D’Haultfœuille & Isis Durrmeyer & Philippe Février, 2019. "Automobile Prices in Market Equilibrium with Unobserved Price Discrimination," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 1973-1998.
    3. Christopher Conlon & Jeff Gortmaker, 2020. "Best practices for differentiated products demand estimation with PyBLP," RAND Journal of Economics, RAND Corporation, vol. 51(4), pages 1108-1161, December.
    4. Sun, Yutec & Ishihara, Masakazu, 2019. "A computationally efficient fixed point approach to dynamic structural demand estimation," Journal of Econometrics, Elsevier, vol. 208(2), pages 563-584.

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    More about this item

    Keywords

    Random coefficients logit demand; Numerical methods; Nested fixed-point algorithm; Newton’s method;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • L1 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance

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