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Identification and Estimation of Demand for Bundles

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  • Iaria, Alessandro
  • ,
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.

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  • Iaria, Alessandro & ,, 2020. "Identification and Estimation of Demand for Bundles," CEPR Discussion Papers 14363, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:14363
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    as
    1. Arthur Lewbel, 2012. "Using Heteroscedasticity to Identify and Estimate Mismeasured and Endogenous Regressor Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 67-80.
    2. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    3. Paola Manzini & Marco Mariotti & Levent Ülkü, 2019. "Stochastic Complementarity," The Economic Journal, Royal Economic Society, vol. 129(619), pages 1343-1363.
    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," The Review of Economic Studies, Review of Economic Studies Ltd, 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. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    23. Mark Armstrong & John Vickers, 2010. "Competitive Non-linear Pricing and Bundling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(1), pages 30-60.
    24. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    25. 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.
    26. 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.
    27. Jidong Zhou, 2017. "Competitive Bundling," Econometrica, Econometric Society, vol. 85, pages 145-172, January.
    28. 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.
    29. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    30. 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.
    31. 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.
    32. 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.
    33. 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.
    34. Lewbel, Arthur, 1985. "Bundling of substitutes or complements," International Journal of Industrial Organization, Elsevier, vol. 3(1), pages 101-107, March.
    35. 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.
    36. 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.
    37. 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.
    38. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    39. 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.
    40. 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.
    41. Armstrong, Mark, 2013. "A more general theory of commodity bundling," Journal of Economic Theory, Elsevier, vol. 148(2), pages 448-472.
    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. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    45. Freyberger, Joachim, 2015. "Asymptotic theory for differentiated products demand models with many markets," Journal of Econometrics, Elsevier, vol. 185(1), pages 162-181.
    46. Igal Hendel, 1999. "Estimating Multiple-Discrete Choice Models: An Application to Computerization Returns," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(2), pages 423-446.
    47. 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.
    48. R. Preston McAfee & John McMillan & Michael D. Whinston, 1989. "Multiproduct Monopoly, Commodity Bundling, and Correlation of Values," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 104(2), pages 371-383.
    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. Angelique Augereau & Shane Greenstein & Marc Rysman, 2006. "Coordination versus differentiation in a standards war: 56K modems," RAND Journal of Economics, The RAND Corporation, vol. 37(4), pages 887-909, December.
    52. Roy Allen & John Rehbeck, 2019. "Identification With Additively Separable Heterogeneity," Econometrica, Econometric Society, vol. 87(3), pages 1021-1054, May.
    53. William James Adams & Janet L. Yellen, 1976. "Commodity Bundling and the Burden of Monopoly," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(3), pages 475-498.
    54. 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.
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    Cited by:

    1. Mogens Fosgerau & Julien Monardo & André de Palma, 2024. "The Inverse Product Differentiation Logit Model," American Economic Journal: Microeconomics, American Economic Association, vol. 16(4), pages 329-370, November.
    2. Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
    3. Rui Wang, 2023. "Testing and Identifying Substitution and Complementarity Patterns," Papers 2304.00678, arXiv.org.
    4. Allen, Roy & Rehbeck, John, 2022. "Latent complementarity in bundles models," Journal of Econometrics, Elsevier, vol. 228(2), pages 322-341.

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