IDEAS home Printed from https://ideas.repec.org/a/eee/ecolet/v149y2016icp67-70.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165176516304141
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.econlet.2016.10.019?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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 [Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticities and Welfare Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kristensen, Dennis & Salanié, Bernard, 2017. "Higher-order properties of approximate estimators," Journal of Econometrics, Elsevier, vol. 198(2), pages 189-208.
    2. Navid Mojir & K. Sudhir, 2021. "A Structural Model of Organizational Buying for B2B Markets: Innovation Adoption with Share of Wallet Contracts," Cowles Foundation Discussion Papers 2315, Cowles Foundation for Research in Economics, Yale University.
    3. Gautam Gowrisankaran & Marc Rysman, 2012. "Dynamics of Consumer Demand for New Durable Goods," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1173-1219.
    4. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    5. Liu, Yan & Cirillo, Cinzia, 2018. "A generalized dynamic discrete choice model for green vehicle adoption," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PB), pages 288-302.
    6. Abbring, Jaap & Campbell, J.R. & Tilly, J. & Yang, N., 2018. "Very Simple Markov-Perfect Industry Dynamics (revision of 2017-021) : Empirics," Discussion Paper 2018-040, Tilburg University, Center for Economic Research.
    7. Junpei Komiyama & Hajime Shimao, 2018. "Cross Validation Based Model Selection via Generalized Method of Moments," Papers 1807.06993, arXiv.org.
    8. 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.
    9. Jaap H. Abbring & Jeffrey R. Campbell & Jan Tilly & Nan Yang, 2018. "Very Simple Markov-Perfect Industry Dynamics: Empirics," Working Paper Series WP-2018-17, Federal Reserve Bank of Chicago.
    10. Takeshi Fukasawa, 2022. "The Biases in Applying Static Demand Models under Dynamic Demand," Discussion Paper Series DP2022-18, Research Institute for Economics & Business Administration, Kobe University, revised Jul 2022.
    11. Michael Cohen & Rui Huang, 2012. "Corporate Social Responsibility for Kids’ Sake: A Dynamic Model of Firm Participation," Working Papers 12, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
    12. Jeremy T. Fox, 2010. "Estimating the Employer Switching Costs and Wage Responses of Forward-Looking Engineers," Journal of Labor Economics, University of Chicago Press, vol. 28(2), pages 357-412, April.
    13. Xiong, Siqin & Yuan, Yi & Yao, Jia & Bai, Bo & Ma, Xiaoming, 2023. "Exploring consumer preferences for electric vehicles based on the random coefficient logit model," Energy, Elsevier, vol. 263(PA).
    14. Castilho, Rafael, 2018. "Can Switching Costs Reduce Prices?," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 38(1), May.
    15. Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    16. Aamir Rafique Hashmi & Johannes Van Biesebroeck, 2016. "The Relationship between Market Structure and Innovation in Industry Equilibrium: A Case Study of the Global Automobile Industry," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 192-208, March.
    17. Paul Ellickson & Sanjog Misra, 2012. "Enriching interactions: Incorporating outcome data into static discrete games," Quantitative Marketing and Economics (QME), Springer, vol. 10(1), pages 1-26, March.
    18. Greg Lewis & Bora Ozaltun & Georgios Zervas, 2021. "Maximum Likelihood Estimation of Differentiated Products Demand Systems," Papers 2111.12397, arXiv.org.
    19. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    20. Dunker, Fabian & Hoderlein, Stefan & Kaido, Hiroaki, 2014. "Nonparametric Identification of Endogenous and Heterogeneous Aggregate Demand Models: Complements, Bundles and the Market Level," Economics Series 307, Institute for Advanced Studies.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecolet:v:149:y:2016:i:c:p:67-70. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/ecolet .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.