IDEAS home Printed from https://ideas.repec.org/p/cpr/ceprdp/14363.html
   My bibliography  Save this paper

Identification and Estimation of Demand for Bundles

Author

Listed:
  • Iaria, Alessandro
  • WANG, Ao

Abstract

We present novel identification and estimation results for a mixed logit model of demand for bundles with endogenous prices given bundle-level market shares. Our approach hinges on an affine relationship between the utilities of single products and of bundles, on an essential real analytic property of the mixed logit model, and on the existence of exogenous cost shifters. We propose a new demand inverse in the presence of complementarity that enables to concentrate out of the likelihood function the (potentially numerous) market-product specific average utilities, substantially alleviating the challenge of dimensionality inherent in estimation. To illustrate the use of our methods, we estimate demand and supply in the US ready-to-eat cereal industry, where the proposed MLE reduces the numerical search from approximately 12000 to 130 parameters. Our estimates suggest that ignoring Hicksian complementarity among different products often purchased in bundles may result in misleading demand estimates and counterfactuals.

Suggested Citation

  • Iaria, Alessandro & WANG, Ao, 2020. "Identification and Estimation of Demand for Bundles," CEPR Discussion Papers 14363, C.E.P.R. Discussion Papers.
  • Handle: RePEc:cpr:ceprdp:14363
    as

    Download full text from publisher

    File URL: http://www.cepr.org/active/publications/discussion_papers/dp.php?dpno=14363
    Download Restriction: CEPR Discussion Papers are free to download for our researchers, subscribers and members. If you fall into one of these categories but have trouble downloading our papers, please contact us at subscribers@cepr.org

    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. repec:taf:jnlbes:v:30:y:2012:i:1:p:67-80 is not listed on IDEAS
    2. Paola Manzini & Marco Mariotti & Levent Ülkü, 2019. "Stochastic Complementarity," Economic Journal, Royal Economic Society, vol. 129(619), pages 1343-1363.
    3. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    4. Gregory S. Crawford & Robin S. Lee & Michael D. Whinston & Ali Yurukoglu, 2018. "The Welfare Effects of Vertical Integration in Multichannel Television Markets," Econometrica, Econometric Society, vol. 86(3), pages 891-954, May.
    5. Kyoo il Kim, 2014. "Identification of the Distribution of Random Coefficients in Static and Dynamic Discrete Choice Models," Korean Economic Review, Korean Economic Association, vol. 30, pages 191-216.
    6. Ying Fan, 2013. "Ownership Consolidation and Product Characteristics: A Study of the US Daily Newspaper Market," American Economic Review, American Economic Association, vol. 103(5), pages 1598-1628, August.
    7. Fox, Jeremy T. & Kim, Kyoo il & Ryan, Stephen P. & Bajari, Patrick, 2012. "The random coefficients logit model is identified," Journal of Econometrics, Elsevier, vol. 166(2), pages 204-212.
    8. Minjae Song & Sean Nicholson & Claudio Lucarelli, 2017. "Mergers with interfirm bundling: a case of pharmaceutical cocktails," RAND Journal of Economics, RAND Corporation, vol. 48(3), pages 810-834, August.
    9. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82(5), pages 1749-1797, September.
    10. Aviv Nevo, 2000. "Mergers with Differentiated Products: The Case of the Ready-to-Eat Cereal Industry," RAND Journal of Economics, The RAND Corporation, vol. 31(3), pages 395-421, Autumn.
    11. Chenghuan Sean Chu & Phillip Leslie & Alan Sorensen, 2011. "Bundle-Size Pricing as an Approximation to Mixed Bundling," American Economic Review, American Economic Association, vol. 101(1), pages 263-303, February.
    12. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-1074, November.
    13. Steve Berry & Oliver B. Linton & Ariel Pakes, 2004. "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems," Review of Economic Studies, Oxford University Press, vol. 71(3), pages 613-654.
    14. Nevo, Aviv, 2001. "Measuring Market Power in the Ready-to-Eat Cereal Industry," Econometrica, Econometric Society, vol. 69(2), pages 307-342, March.
    15. Gregory S. Crawford & Ali Yurukoglu, 2012. "The Welfare Effects of Bundling in Multichannel Television Markets," American Economic Review, American Economic Association, vol. 102(2), pages 643-685, April.
    16. Timothy B. Armstrong, 2016. "Large Market Asymptotics for Differentiated Product Demand Estimators With Economic Models of Supply," Econometrica, Econometric Society, vol. 84, pages 1961-1980, September.
    17. Steven Berry & James Levinsohn & Ariel Pakes, 2004. "Differentiated Products Demand Systems from a Combination of Micro and Macro Data: The New Car Market," Journal of Political Economy, University of Chicago Press, vol. 112(1), pages 68-105, February.
    18. Komunjer, Ivana, 2012. "Global Identification In Nonlinear Models With Moment Restrictions," Econometric Theory, Cambridge University Press, vol. 28(4), pages 719-729, August.
    19. Lukasz Grzybowski & Frank Verboven, 2016. "Substitution between fixed-line and mobile access: the role of complementarities," Journal of Regulatory Economics, Springer, vol. 49(2), pages 113-151, April.
    20. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    21. Katherine Ho & Justin Ho & Julie Holland Mortimer, 2012. "The Use of Full-Line Forcing Contracts in the Video Rental Industry," American Economic Review, American Economic Association, vol. 102(2), pages 686-719, April.
    22. Mark Armstrong & John Vickers, 2010. "Competitive Non-linear Pricing and Bundling," Review of Economic Studies, Oxford University Press, vol. 77(1), pages 30-60.
    23. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    24. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, September.
    25. Angelique Augereau & Shane Greenstein & Marc Rysman, 2006. "Coordination versus differentiation in a standards war: 56K modems," RAND Journal of Economics, RAND Corporation, vol. 37(4), pages 887-909, December.
    26. Jidong Zhou, 2017. "Competitive Bundling," Econometrica, Econometric Society, vol. 85, pages 145-172, January.
    27. Tobias Kretschmer & Eugenio J. Miravete & Jose C. Pernias, 2012. "Competitive Pressure and the Adoption of Complementary Innovations," American Economic Review, American Economic Association, vol. 102(4), pages 1540-1570, June.
    28. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    29. Matthew Gentzkow, 2007. "Valuing New Goods in a Model with Complementarity: Online Newspapers," American Economic Review, American Economic Association, vol. 97(3), pages 713-744, June.
    30. Daniel McFadden & Kenneth Train, 2000. "Mixed MNL models for discrete response," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(5), pages 447-470.
    31. Aviv Nevo & Daniel L. Rubinfeld & Mark McCabe, 2005. "Academic Journal Pricing and the Demand of Libraries," American Economic Review, American Economic Association, vol. 95(2), pages 447-452, May.
    32. Steven T. Berry, 1994. "Estimating Discrete-Choice Models of Product Differentiation," RAND Journal of Economics, The RAND Corporation, vol. 25(2), pages 242-262, Summer.
    33. Lewbel, Arthur, 1985. "Bundling of substitutes or complements," International Journal of Industrial Organization, Elsevier, vol. 3(1), pages 101-107, March.
    34. Matthew Gentzkow & Jesse M. Shapiro & Michael Sinkinson, 2014. "Competition and Ideological Diversity: Historical Evidence from US Newspapers," American Economic Review, American Economic Association, vol. 104(10), pages 3073-3114, October.
    35. Sanghak Lee & Jaehwan Kim & Greg M. Allenby, 2013. "A Direct Utility Model for Asymmetric Complements," Marketing Science, INFORMS, vol. 32(3), pages 454-470, May.
    36. Kwak, Kyuseop & Duvvuri, Sri Devi & Russell, Gary J., 2015. "An Analysis of Assortment Choice in Grocery Retailing," Journal of Retailing, Elsevier, vol. 91(1), pages 19-33.
    37. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    38. Steve Berry & Ahmed Khwaja & Vineet Kumar & Andres Musalem & Kenneth Wilbur & Greg Allenby & Bharat Anand & Pradeep Chintagunta & W. Hanemann & Przemek Jeziorski & Angelo Mele, 2014. "Structural models of complementary choices," Marketing Letters, Springer, vol. 25(3), pages 245-256, September.
    39. Andrea Pozzi, 2012. "Shopping Cost and Brand Exploration in Online Grocery," American Economic Journal: Microeconomics, American Economic Association, vol. 4(3), pages 96-120, August.
    40. Armstrong, Mark, 2013. "A more general theory of commodity bundling," Journal of Economic Theory, Elsevier, vol. 148(2), pages 448-472.
    41. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    42. Arthur Lewbel, 2019. "The Identification Zoo: Meanings of Identification in Econometrics," Journal of Economic Literature, American Economic Association, vol. 57(4), pages 835-903, December.
    43. Øyvind Thomassen & Howard Smith & Stephan Seiler & Pasquale Schiraldi, 2017. "Multi-category Competition and Market Power: A Model of Supermarket Pricing," American Economic Review, American Economic Association, vol. 107(8), pages 2308-2351, August.
    44. Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    45. Igal Hendel, 1999. "Estimating Multiple-Discrete Choice Models: An Application to Computerization Returns," Review of Economic Studies, Oxford University Press, vol. 66(2), pages 423-446.
    46. Hongju Liu & Pradeep K. Chintagunta & Ting Zhu, 2010. "Complementarities and the Demand for Home Broadband Internet Services," Marketing Science, INFORMS, vol. 29(4), pages 701-720, 07-08.
    47. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, Oxford University Press, vol. 104(2), pages 371-383.
    48. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    49. Jeremy T. Fox & Natalia Lazzati, 2017. "A note on identification of discrete choice models for bundles and binary games," Quantitative Economics, Econometric Society, vol. 8(3), pages 1021-1036, November.
    50. Sher, Itai & Kim, Kyoo il, 2014. "Identifying combinatorial valuations from aggregate demand," Journal of Economic Theory, Elsevier, vol. 153(C), pages 428-458.
    51. repec:rje:randje:v:37:y:2006:i:4:p:887-909 is not listed on IDEAS
    52. Roy Allen & John Rehbeck, 2019. "Identification With Additively Separable Heterogeneity," Econometrica, Econometric Society, vol. 87(3), pages 1021-1054, May.
    53. Samuelson, Paul A, 1974. "Complementarity-An Essay on the 40th Anniversary of the Hicks-Allen Revolution in Demand Theory," Journal of Economic Literature, American Economic Association, vol. 12(4), pages 1255-1289, December.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:cpr:ceprdp:14363. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (). General contact details of provider: https://www.cepr.org .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.