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A discrete choice model for partially ordered alternatives

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  • Eleni Aristodemou

    (Institute for Fiscal Studies and University College London)

Abstract

In this paper we analyze a discrete choice model for partially ordered alternatives. The alternatives are differentiated along two dimensions, the ?rst an unordered “horizontal” dimension, and the second an ordered “vertical” dimension. The model can be used in circumstances in which individuals choose amongst products of different brands, wherein each brand offers an ordered choice menu, for example by offering products of varying quality. The unordered-ordered nature of the discrete choice problem is used to characterize the identi?ed set of model parameters. Following an initial nonparametric analysis that relies on shape restrictions inherent in the ordered dimension of the problem, we then provide a specialized analysis for parametric speci?cations that generalize common ordered choice models. We characterize conditional choice probabilities as a function of model primitives with particular analysis focusing on cases in which unobservable taste for quality of each brand offering is multivariate normally distributed. We provide explicit formulae used for estimation and inference via maximum likelihood, and we consider inference based on Wald and quasi-likelihood ratio statistics, the latter of which can be robust to a possible lack of point identi?cation. An empirical illustration is conducted using consumer purchase data in the UK to study consumers’ choice of razor blades in which each brand has product o?erings vertically di?erentiated by quality.

Suggested Citation

  • Eleni Aristodemou, 2021. "A discrete choice model for partially ordered alternatives," CeMMAP working papers CWP35/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:35/21
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    References listed on IDEAS

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    1. Hausman, Jerry A & Wise, David A, 1978. "A Conditional Probit Model for Qualitative Choice: Discrete Decisions Recognizing Interdependence and Heterogeneous Preferences," Econometrica, Econometric Society, vol. 46(2), pages 403-426, March.
    2. Dubin, Jeffrey A & McFadden, Daniel L, 1984. "An Econometric Analysis of Residential Electric Appliance Holdings and Consumption," Econometrica, Econometric Society, vol. 52(2), pages 345-362, March.
    3. Aradillas-López, Andrés & Rosen, Adam M., 2022. "Inference in ordered response games with complete information," Journal of Econometrics, Elsevier, vol. 226(2), pages 451-476.
    4. Andrew Chesher & Adam M. Rosen, 2017. "Generalized Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 959-989, May.
    5. Andrew Chesher & Adam Rosen & Zahra Siddique, 2019. "Estimating Endogenous Effects on Ordinal Outcomes," CeMMAP working papers CWP66/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    6. Goldberg, Pinelopi Koujianou, 1995. "Product Differentiation and Oligopoly in International Markets: The Case of the U.S. Automobile Industry," Econometrica, Econometric Society, vol. 63(4), pages 891-951, July.
    7. Milgrom, Paul & Shannon, Chris, 1994. "Monotone Comparative Statics," Econometrica, Econometric Society, vol. 62(1), pages 157-180, January.
    8. Andrew Chesher & Adam Rosen, 2020. "Econometric Modeling of Interdependent Discrete Choice with Applications to Market Structure," CeMMAP working papers CWP25/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Xiaohong Chen & Elie Tamer & Alexander Torgovitsky, 2011. "Sensitivity Analysis in Semiparametric Likelihood Models," Cowles Foundation Discussion Papers 1836, Cowles Foundation for Research in Economics, Yale University.
    10. Xiaohong Chen & Timothy M. Christensen & Elie Tamer, 2018. "Monte Carlo Confidence Sets for Identified Sets," Econometrica, Econometric Society, vol. 86(6), pages 1965-2018, November.
    11. Minjae Song, 2015. "A Hybrid Discrete Choice Model Of Differentiated Product Demand With An Application To Personal Computers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56(1), pages 265-301, February.
    12. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    13. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
    14. Minjae Song, 2015. "A Hybrid Discrete Choice Model Of Differentiated Product Demand With An Application To Personal Computers," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 56, pages 265-301, February.
    15. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    16. 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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