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An Empirical Analysis of Competitive Nonlinear Pricing

Author

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  • Gaurab Aryal

Abstract

In this paper I estimate a model of competitive nonlinear pricing with multidimensional adverse selection. I model competition using a Stackelberg duopoly and solve the multidimensional screening problem by aggregating the multidimensional type into a single dimensional type. I study identification and estimation of the utility and cost parameters and the joint density of consumer types. The truncated marginal densities of the aggregated types can be nonparametrically identified but not the joint density. I use the classic Cramér-von Mises and Vuong’s test to select one parametric family of copula to estimate the joint density from the unspecified marginals. Using a unique data for advertisements collected from two Yellow Pages Directories in Central Pennsylvania I find that: (a) Joe copula characterizes the joint density of adverse selection; (b) there is a substantial heterogeneity among advertisers; (c) the estimated density rationalizes why there is more competition at the lower end of the ads than at the upper end; (d) consumers treat the ads as substitutes; and (e) a counterfactual exercise suggests that there is a substantial (3.8% of the sales) loss of welfare due to asymmetric information.

Suggested Citation

  • Gaurab Aryal, 2013. "An Empirical Analysis of Competitive Nonlinear Pricing," ANU Working Papers in Economics and Econometrics 2013-610, Australian National University, College of Business and Economics, School of Economics.
    • Handle: RePEc:acb:cbeeco:2013-610
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    File URL: https://www.cbe.anu.edu.au/researchpapers/econ/wp610.pdf
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    Cited by:

    1. Wang, Li & Zhang, Xin-Hua & Zhang, Yue-Jun, 2023. "Designing the pricing mechanism of residents’ self-selection sales electricity based on household size," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 860-878.
    2. Chen, Liang & Luo, Yao, 2023. "Empirical analysis of network effects in nonlinear pricing data," International Journal of Industrial Organization, Elsevier, vol. 91(C).
    3. Liang Chen & Yao Luo, 2023. "Empirical Analysis of Network Effects in Nonlinear Pricing Data," Working Papers tecipa-758, University of Toronto, Department of Economics.
    4. Alessandro Iaria, & Wang, Ao, 2021. "An Empirical Model of Quantity Discounts with Large Choice Sets," The Warwick Economics Research Paper Series (TWERPS) 1378, University of Warwick, Department of Economics.
    5. Ambarish Chandra, 2020. "Price Discrimination along Multiple Dimensions: New Evidence from a Regional Airline," Working Papers tecipa-676, University of Toronto, Department of Economics.
    6. Gaurab Aryal & Charles Murry & Jonathan W Williams, 2024. "Price Discrimination in International Airline Markets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(2), pages 641-689.
    7. Gaurab Aryal & Federico Zincenko, 2014. "Identification and Estimation of Multidimensional Screening," Papers 1411.6250, arXiv.org, revised Oct 2024.
    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.

    More about this item

    Keywords

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D22 - Microeconomics - - Production and Organizations - - - Firm Behavior: Empirical Analysis
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets

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