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Structural Analysis of Nonlinear Pricing

Author

Listed:
  • Yao Luo
  • Isabelle Perrigne
  • Quang Vuong

Abstract

This paper proposes a new methodology for analyzing nonlinear pricing data. We establish identification of the model primitives with a known tariff and characterize the model restrictions on observables. We propose a quantile-based nonparametric estimator that achieves consistency at the parametric rate. We introduce unobserved product heterogeneity with an unknown tariff and show how our identification and estimation results extend. A Monte Carlo study analyzes the robustness of our methodology to menus of two-part tariffs. Analysis of cellular service data assesses the performance of various pricing strategies. We discuss extensions to network effects, multiproduct firms, bundling, differentiated products, and oligopolies.

Suggested Citation

  • Yao Luo & Isabelle Perrigne & Quang Vuong, 2018. "Structural Analysis of Nonlinear Pricing," Journal of Political Economy, University of Chicago Press, vol. 126(6), pages 2523-2568.
    • Handle: RePEc:ucp:jpolec:doi:10.1086/699978
    DOI: 10.1086/699978
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    Cited by:

    1. Daiqiang Zhang, 2021. "Testing Passive Versus Symmetric Beliefs In Contracting With Externalities," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 723-767, May.
    2. Hui Liu & Yao Luo, 2025. "Demand Analysis under Price Rigidity and Endogenous Assortment: An Application to China's Tobacco Industry," Papers 2501.17251, arXiv.org.
    3. Felipe Brugués, 2026. "Take the Goods and Run: Contracting Frictions and Market Power in Supply Chains," American Economic Review, American Economic Association, vol. 116(2), pages 582-626, February.
    4. Enache, Andreea & Florens, Jean-Pierre, 2024. "Quantile analysis of “hazard-rate” game models," Journal of Econometrics, Elsevier, vol. 238(2).
    5. Chen, Liang & Luo, Yao, 2023. "Empirical analysis of network effects in nonlinear pricing data," International Journal of Industrial Organization, Elsevier, vol. 91(C).
    6. Aaron L. Bodoh-Creed & Brent R. Hickman & John A. List & Ian Muir & Gregory K. Sun, 2023. "Stress Testing Structural Models of Unobserved Heterogeneity: Robust Inference on Optimal Nonlinear Pricing," NBER Working Papers 31647, National Bureau of Economic Research, Inc.
    7. Skreta, Vasiliki & Doval, Laura, 2021. "Purchase history and product personalization," CEPR Discussion Papers 15969, C.E.P.R. Discussion Papers.
    8. Soheil Ghili & K. Sudhir & Nitish Jain & Ankur Garg, 2025. "Second-degree Price Discrimination: Theoretical Analysis, Experiment Design, and Empirical Estimation," Papers 2507.13426, arXiv.org, revised Oct 2025.
    9. Yao Luo & Peijun Sang, 2022. "Efficient Estimation of Structural Models via Sieves," Papers 2204.13488, arXiv.org, revised Feb 2025.
    10. Aaron L. Bodoh-Creed & Brent R. Hickman & John A. List & Ian Muir & Gregory K. Sun, 2026. "Salience and (Non-)Buyer's Remorse: Optimal Nonlinear Pricing with Cognitively Constrained Consumers," NBER Working Papers 35003, National Bureau of Economic Research, Inc.
    11. Soheil Ghili & Russ Yoon, 2023. "An Empirical Analysis of Optimal Nonlinear Pricing in Business-to-Business Markets," Papers 2302.11643, arXiv.org, revised Aug 2024.
    12. Zheng, Han & Fujii, Daisuke, 2021. "Nonlinear Pricing in the Transport Industry and the Gains from Trade," Discussion paper series HIAS-E-112, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    13. Yao Luo, 2023. "Bundling and nonlinear pricing in telecommunications," RAND Journal of Economics, RAND Corporation, vol. 54(2), pages 268-298, June.
    14. An, Yonghong & Hong, Shengjie & Zhang, Daiqiang, 2023. "A structural analysis of simple contracts," Journal of Econometrics, Elsevier, vol. 236(2).
    15. Luo, Yao, 2018. "Identification of participation constraints in contracts," Economics Letters, Elsevier, vol. 173(C), pages 84-87.
    16. Gaurab Aryal & Isabelle Perrigne & Quang Vuong, 2011. "Identification of Insurance Models with Multidimensional Screening," ANU Working Papers in Economics and Econometrics 2011-538, Australian National University, College of Business and Economics, School of Economics.
    17. Liang Chen & Yao Luo, 2023. "Empirical Analysis of Network Effects in Nonlinear Pricing Data," Working Papers tecipa-758, University of Toronto, Department of Economics.
    18. Matteo Benetton & Alessandro Gavazza & Paolo Surico, 2025. "Mortgage Pricing and Monetary Policy," American Economic Review, American Economic Association, vol. 115(3), pages 823-863, March.
    19. Chen, Chuan & Jia, Yanrong & Martin, Xiumin & Silveira, Bernardo, 2025. "Assessing the objective function of the SEC against financial misconduct: A structural approach," Journal of Accounting and Economics, Elsevier, vol. 80(1).
    20. Nianqing Liu & Yao Luo, 2014. "A Nonparametric Test of Exogenous Participation in First-Price Auctions," Working Papers tecipa-519, University of Toronto, Department of Economics.

    More about this item

    JEL classification:

    • L8 - Industrial Organization - - Industry Studies: Services
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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