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A General Method for Demand Inversion

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  • Lixiong Li

Abstract

This paper describes a numerical method to solve for mean product qualities which equates the real market share to the market share predicted by a discrete choice model. The method covers a general class of discrete choice model, including the pure characteristics model in Berry and Pakes(2007) and the random coefficient logit model in Berry et al.(1995) (hereafter BLP). The method transforms the original market share inversion problem to an unconstrained convex minimization problem, so that any convex programming algorithm can be used to solve the inversion. Moreover, such results also imply that the computational complexity of inverting a demand model should be no more than that of a convex programming problem. In simulation examples, I show the method outperforms the contraction mapping algorithm in BLP. I also find the method remains robust in pure characteristics models with near-zero market shares.

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  • Lixiong Li, 2018. "A General Method for Demand Inversion," Papers 1802.04444, arXiv.org, revised Feb 2018.
    • Handle: RePEc:arx:papers:1802.04444
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    1. 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.
    2. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    3. Steven Berry & Ariel Pakes, 2007. "The Pure Characteristics Demand Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1193-1225, November.
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    2. Stanimirović, Predrag S. & Mourtas, Spyridon D. & Mosić, Dijana & Katsikis, Vasilios N. & Cao, Xinwei & Li, Shuai, 2024. "Zeroing neural network approaches for computing time-varying minimal rank outer inverse," Applied Mathematics and Computation, Elsevier, vol. 465(C).
    3. David Muller & Emerson Melo & Ruben Schlotter, 2023. "A Distributionally Robust Random Utility Model," Papers 2303.05888, arXiv.org.
    4. Ho, Manh-Toan & La, Viet-Phuong & Nguyen, Minh-Hoang & Pham, Thanh-Hang & Vuong, Thu-Trang & Vuong, Ha-My & Pham, Hung-Hiep & Hoang, Anh-Duc & Vuong, Quan-Hoang, 2020. "An analytical view on STEM education and outcomes: Examples of the social gap and gender disparity in Vietnam," Children and Youth Services Review, Elsevier, vol. 119(C).

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