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Injectivity and the law of demand

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  • Allen, Roy

Abstract

A variety of methodologies require demand to be injective to invert quantities to prices or utility indices. When a version of the law of demand holds, global injectivity and local injectivity are equivalent. Moreover, both can be checked by seeing whether the demand mapping is constant over any line segments.

Suggested Citation

  • Allen, Roy, 2022. "Injectivity and the law of demand," Economics Letters, Elsevier, vol. 215(C).
  • Handle: RePEc:eee:ecolet:v:215:y:2022:i:c:s0165176522001252
    DOI: 10.1016/j.econlet.2022.110496
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    References listed on IDEAS

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    1. Steven Berry & Amit Gandhi & Philip Haile, 2013. "Connected Substitutes and Invertibility of Demand," Econometrica, Econometric Society, vol. 81(5), pages 2087-2111, September.
    2. Walter Beckert & Richard Blundell, 2008. "Heterogeneity and the Non-Parametric Analysis of Consumer Choice: Conditions for Invertibility," Review of Economic Studies, Oxford University Press, vol. 75(4), pages 1069-1080.
    3. Steven T. Berry & Philip A. Haile, 2018. "Identification of Nonparametric Simultaneous Equations Models With a Residual Index Structure," Econometrica, Econometric Society, vol. 86(1), pages 289-315, January.
    4. Richard Blundell & Dennis Kristensen & Rosa Matzkin, 2017. "Individual counterfactuals with multidimensional unobserved heterogeneity," CeMMAP working papers 60/17, Institute for Fiscal Studies.
    5. 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.
    6. Rodrigo Adao & Arnaud Costinot & Dave Donaldson, 2017. "Nonparametric Counterfactual Predictions in Neoclassical Models of International Trade," American Economic Review, American Economic Association, vol. 107(3), pages 633-689, March.
    7. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    8. Donald J. Brown & Rosa L. Matzkin, 1998. "Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand," Cowles Foundation Discussion Papers 1175, Cowles Foundation for Research in Economics, Yale University.
    9. Odran Bonnet & Alfred Galichon & Yu-Wei Hsieh & Keith O’Hara & Matt Shum, 2022. "Yogurts Choose Consumers? Estimation of Random-Utility Models via Two-Sided Matching [Unobserved Product Differentiation in Discrete-Choice Models: Estimating Price Elasticities and Welfare Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(6), pages 3085-3114.
    10. Rosa L. Matzkin, 2008. "Identification in Nonparametric Simultaneous Equations Models," Econometrica, Econometric Society, vol. 76(5), pages 945-978, September.
    11. Mogens Fosgerau & Julien Monardo & André de Palma, 2019. "The Inverse Product Differentiation Logit Model," Working Papers hal-02183411, HAL.
    12. 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.
    13. 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.
    14. Iaria, Alessandro & ,, 2020. "Identification and Estimation of Demand for Bundles," CEPR Discussion Papers 14363, C.E.P.R. Discussion Papers.
    15. Allen, Roy & Rehbeck, John, 2022. "Latent complementarity in bundles models," Journal of Econometrics, Elsevier, vol. 228(2), pages 322-341.
    16. Steven T. Berry & Philip A. Haile, 2009. "Nonparametric Identification of Multinomial Choice Demand Models with Heterogeneous Consumers," Cowles Foundation Discussion Papers 1718, Cowles Foundation for Research in Economics, Yale University, revised Mar 2010.
    17. Xiaoxia Shi & Matthew Shum & Wei Song, 2018. "Estimating Semi‐Parametric Panel Multinomial Choice Models Using Cyclic Monotonicity," Econometrica, Econometric Society, vol. 86(2), pages 737-761, March.
    18. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    19. Donald Brown & Caterina Calsamiglia, 2007. "The Nonparametric Approach to Applied Welfare Analysis," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 31(1), pages 183-188, April.
    20. Hyungtaik Ahn & Hidehiko Ichimura & James L. Powell & Paul A. Ruud, 2018. "Simple Estimators for Invertible Index Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 1-10, January.
    21. Hyungtaik Ahn & Hidehiko Ichimura & James L. Powell & Paul A. Ruud, 2018. "Rejoinder for “Simple Estimators for Invertible Index Models”," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 22-23, January.
    22. Wang, Ao, 2021. "A BLP Demand Model of Product-Level Market Shares with Complementarity," The Warwick Economics Research Paper Series (TWERPS) 1351, University of Warwick, Department of Economics.
    23. Rosa L. Matzkin, 2015. "Estimation of Nonparametric Models With Simultaneity," Econometrica, Econometric Society, vol. 83, pages 1-66, January.
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